## TSTP Solution File: LAT270-2 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 05:45:23 EDT 2022

% Result   : Unsatisfiable 0.12s 0.38s
% Output   : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   44 (  25 unt;  10 typ;   0 def)
%            Number of atoms       :  157 (  42 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  363 (  32   ~;  39   |;   0   &; 292   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-4 aty)
%            Number of variables   :   39 (   0   ^  39   !;   0   ?;  39   :)

%------------------------------------------------------------------------------
thf(tp_c_Tarski_Ointerval,type,
c_Tarski_Ointerval: \$i > \$i > \$i > \$i > \$i ).

thf(tp_c_in,type,
c_in: \$i > \$i > \$i > \$o ).

thf(tp_c_lessequals,type,
c_lessequals: \$i > \$i > \$i > \$o ).

thf(tp_t_a,type,
t_a: \$i ).

thf(tp_tc_set,type,
tc_set: \$i > \$i ).

thf(tp_v_A,type,
v_A: \$i ).

thf(tp_v_S,type,
v_S: \$i ).

thf(tp_v_a,type,
v_a: \$i ).

thf(tp_v_b,type,
v_b: \$i ).

thf(tp_v_r,type,
v_r: \$i ).

thf(1,axiom,
! [V_b: \$i,V_a: \$i,V_S: \$i] :
( ~ ( c_in @ V_b @ v_A @ t_a )
| ~ ( c_in @ V_a @ v_A @ t_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ v_r @ V_a @ V_b @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0) ).

thf(2,conjecture,
\$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(3,negated_conjecture,
\$false = \$false,
inference(negate_conjecture,[status(cth)],[2]) ).

thf(4,negated_conjecture,
~ ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(5,negated_conjecture,
c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(6,negated_conjecture,
c_in @ v_b @ v_A @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(7,negated_conjecture,
c_in @ v_a @ v_A @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(8,plain,
\$false = \$false,
inference(unfold_def,[status(thm)],[3]) ).

thf(9,plain,
( ( ! [V_b: \$i,V_a: \$i,V_S: \$i] :
( ~ ( c_in @ V_b @ v_A @ t_a )
| ~ ( c_in @ V_a @ v_A @ t_a )
| ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ v_r @ V_a @ V_b @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
( ( ~ ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[4]) ).

thf(11,plain,
( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
= \$true ),
inference(unfold_def,[status(thm)],[5]) ).

thf(12,plain,
( ( c_in @ v_b @ v_A @ t_a )
= \$true ),
inference(unfold_def,[status(thm)],[6]) ).

thf(13,plain,
( ( c_in @ v_a @ v_A @ t_a )
= \$true ),
inference(unfold_def,[status(thm)],[7]) ).

thf(14,plain,
( ( ~ \$false )
= \$true ),
inference(polarity_switch,[status(thm)],[8]) ).

thf(15,plain,
( ( ! [V_b: \$i] :
( ~ ( c_in @ V_b @ v_A @ t_a )
| ! [V_a: \$i] :
( ~ ( c_in @ V_a @ v_A @ t_a )
| ! [V_S: \$i] :
( ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ v_r @ V_a @ V_b @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) ) ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[9]) ).

thf(16,plain,
( ( c_in @ v_a @ v_A @ t_a )
= \$true ),
inference(copy,[status(thm)],[13]) ).

thf(17,plain,
( ( c_in @ v_b @ v_A @ t_a )
= \$true ),
inference(copy,[status(thm)],[12]) ).

thf(18,plain,
( ( c_lessequals @ v_S @ ( c_Tarski_Ointerval @ v_r @ v_a @ v_b @ t_a ) @ ( tc_set @ t_a ) )
= \$true ),
inference(copy,[status(thm)],[11]) ).

thf(19,plain,
( ( ~ ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) ) )
= \$true ),
inference(copy,[status(thm)],[10]) ).

thf(20,plain,
( ( ! [V_b: \$i] :
( ~ ( c_in @ V_b @ v_A @ t_a )
| ! [V_a: \$i] :
( ~ ( c_in @ V_a @ v_A @ t_a )
| ! [V_S: \$i] :
( ~ ( c_lessequals @ V_S @ ( c_Tarski_Ointerval @ v_r @ V_a @ V_b @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) ) ) ) ) )
= \$true ),
inference(copy,[status(thm)],[15]) ).

thf(21,plain,
( ( ~ \$false )
= \$true ),
inference(copy,[status(thm)],[14]) ).

thf(22,plain,
( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(23,plain,
! [SV1: \$i] :
( ( ~ ( c_in @ SV1 @ v_A @ t_a )
| ! [SY3: \$i] :
( ~ ( c_in @ SY3 @ v_A @ t_a )
| ! [SY4: \$i] :
( ~ ( c_lessequals @ SY4 @ ( c_Tarski_Ointerval @ v_r @ SY3 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SY4 @ v_A @ ( tc_set @ t_a ) ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
\$false = \$false,
inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
! [SV1: \$i] :
( ( ( ~ ( c_in @ SV1 @ v_A @ t_a ) )
= \$true )
| ( ( ! [SY3: \$i] :
( ~ ( c_in @ SY3 @ v_A @ t_a )
| ! [SY4: \$i] :
( ~ ( c_lessequals @ SY4 @ ( c_Tarski_Ointerval @ v_r @ SY3 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SY4 @ v_A @ ( tc_set @ t_a ) ) ) ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(26,plain,
! [SV1: \$i] :
( ( ( c_in @ SV1 @ v_A @ t_a )
= \$false )
| ( ( ! [SY3: \$i] :
( ~ ( c_in @ SY3 @ v_A @ t_a )
| ! [SY4: \$i] :
( ~ ( c_lessequals @ SY4 @ ( c_Tarski_Ointerval @ v_r @ SY3 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SY4 @ v_A @ ( tc_set @ t_a ) ) ) ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(27,plain,
! [SV1: \$i,SV2: \$i] :
( ( ( ~ ( c_in @ SV2 @ v_A @ t_a )
| ! [SY5: \$i] :
( ~ ( c_lessequals @ SY5 @ ( c_Tarski_Ointerval @ v_r @ SV2 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SY5 @ v_A @ ( tc_set @ t_a ) ) ) )
= \$true )
| ( ( c_in @ SV1 @ v_A @ t_a )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(28,plain,
! [SV1: \$i,SV2: \$i] :
( ( ( ~ ( c_in @ SV2 @ v_A @ t_a ) )
= \$true )
| ( ( ! [SY5: \$i] :
( ~ ( c_lessequals @ SY5 @ ( c_Tarski_Ointerval @ v_r @ SV2 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SY5 @ v_A @ ( tc_set @ t_a ) ) ) )
= \$true )
| ( ( c_in @ SV1 @ v_A @ t_a )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(29,plain,
! [SV1: \$i,SV2: \$i] :
( ( ( c_in @ SV2 @ v_A @ t_a )
= \$false )
| ( ( ! [SY5: \$i] :
( ~ ( c_lessequals @ SY5 @ ( c_Tarski_Ointerval @ v_r @ SV2 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SY5 @ v_A @ ( tc_set @ t_a ) ) ) )
= \$true )
| ( ( c_in @ SV1 @ v_A @ t_a )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(30,plain,
! [SV1: \$i,SV2: \$i,SV3: \$i] :
( ( ( ~ ( c_lessequals @ SV3 @ ( c_Tarski_Ointerval @ v_r @ SV2 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
| ( c_lessequals @ SV3 @ v_A @ ( tc_set @ t_a ) ) )
= \$true )
| ( ( c_in @ SV2 @ v_A @ t_a )
= \$false )
| ( ( c_in @ SV1 @ v_A @ t_a )
= \$false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(31,plain,
! [SV1: \$i,SV2: \$i,SV3: \$i] :
( ( ( ~ ( c_lessequals @ SV3 @ ( c_Tarski_Ointerval @ v_r @ SV2 @ SV1 @ t_a ) @ ( tc_set @ t_a ) ) )
= \$true )
| ( ( c_lessequals @ SV3 @ v_A @ ( tc_set @ t_a ) )
= \$true )
| ( ( c_in @ SV2 @ v_A @ t_a )
= \$false )
| ( ( c_in @ SV1 @ v_A @ t_a )
= \$false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(32,plain,
! [SV1: \$i,SV2: \$i,SV3: \$i] :
( ( ( c_lessequals @ SV3 @ ( c_Tarski_Ointerval @ v_r @ SV2 @ SV1 @ t_a ) @ ( tc_set @ t_a ) )
= \$false )
| ( ( c_lessequals @ SV3 @ v_A @ ( tc_set @ t_a ) )
= \$true )
| ( ( c_in @ SV2 @ v_A @ t_a )
= \$false )
| ( ( c_in @ SV1 @ v_A @ t_a )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(33,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[16,32,24,22,18,17]) ).

thf(34,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LAT270-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun 28 22:30:56 EDT 2022
% 0.12/0.34  % CPUTime  :
% 0.12/0.34
% 0.12/0.34   No.of.Axioms: 5
% 0.12/0.34
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.12/0.38
% 0.12/0.38  ********************************
% 0.12/0.38  *   All subproblems solved!    *
% 0.12/0.38  ********************************
% 0.12/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38
% 0.12/0.38  %**** Beginning of derivation protocol ****
% 0.12/0.38  % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38  %**** End of derivation protocol ****
% 0.12/0.38  %**** no. of clauses in derivation: 34 ****
% 0.12/0.38  %**** clause counter: 33 ****
% 0.12/0.38
% 0.12/0.38  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```