## TSTP Solution File: SYN367+1 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n006.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 : Thu Jul 21 08:25:39 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   50 (  36 unt;   5 typ;   0 def)
%            Number of atoms       :  234 (  51 equ;   0 cnn)
%            Maximal formula atoms :    6 (   5 avg)
%            Number of connectives :  248 (  84   ~;  68   |;  16   &;  77   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

%------------------------------------------------------------------------------
thf(tp_big_q,type,
big_q: \$i > \$o ).

thf(tp_big_r,type,
big_r: \$i > \$o ).

thf(tp_p,type,
p: \$o ).

thf(tp_sK1_X,type,
sK1_X: \$i ).

thf(tp_sK2_X,type,
sK2_X: \$i ).

thf(1,conjecture,
( ! [X: \$i] :
( ( p
& ( big_q @ X ) )
| ( ~ p
& ( big_r @ X ) ) )
=> ( ! [X: \$i] : ( big_q @ X )
| ! [X: \$i] : ( big_r @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2118) ).

thf(2,negated_conjecture,
( ( ! [X: \$i] :
( ( p
& ( big_q @ X ) )
| ( ~ p
& ( big_r @ X ) ) )
=> ( ! [X: \$i] : ( big_q @ X )
| ! [X: \$i] : ( big_r @ X ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
( ( ! [X: \$i] :
( ( p
& ( big_q @ X ) )
| ( ~ p
& ( big_r @ X ) ) )
=> ( ! [X: \$i] : ( big_q @ X )
| ! [X: \$i] : ( big_r @ X ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
( ( ! [X: \$i] :
( ( p
& ( big_q @ X ) )
| ( ~ p
& ( big_r @ X ) ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
( ( ! [X: \$i] : ( big_q @ X )
| ! [X: \$i] : ( big_r @ X ) )
= \$false ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
( ( ~ ( ! [X: \$i] : ( big_q @ X )
| ! [X: \$i] : ( big_r @ X ) ) )
= \$true ),
inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
( ( ~ ( big_q @ sK2_X )
& ~ ( big_r @ sK1_X ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
( ( ( ! [X: \$i] : ( big_q @ X )
| ~ p )
& ! [X: \$i] :
( ( big_q @ X )
| ( big_r @ X ) )
& ( p
| ~ p )
& ( p
| ! [X: \$i] : ( big_r @ X ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
( ( ( ! [X: \$i] : ( big_q @ X )
| ~ p )
& ! [X: \$i] :
( ( big_q @ X )
| ( big_r @ X ) )
& ( p
| ~ p )
& ( p
| ! [X: \$i] : ( big_r @ X ) ) )
= \$true ),
inference(copy,[status(thm)],[8]) ).

thf(10,plain,
( ( ~ ( big_q @ sK2_X )
& ~ ( big_r @ sK1_X ) )
= \$true ),
inference(copy,[status(thm)],[7]) ).

thf(11,plain,
( ( ~ ( ~ ~ ( ~ ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p )
| ~ ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) )
| ~ ~ ( ~ ( p
| ~ p )
| ~ ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[9]) ).

thf(12,plain,
( ( ~ ( ~ ~ ( big_q @ sK2_X )
| ~ ~ ( big_r @ sK1_X ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[10]) ).

thf(13,plain,
( ( ~ ~ ( ~ ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p )
| ~ ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) )
| ~ ~ ( ~ ( p
| ~ p )
| ~ ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) ) ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(14,plain,
( ( ~ ~ ( big_q @ sK2_X )
| ~ ~ ( big_r @ sK1_X ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
( ( ~ ~ ( ~ ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p )
| ~ ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(16,plain,
( ( ~ ~ ( ~ ( p
| ~ p )
| ~ ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).

thf(17,plain,
( ( ~ ~ ( big_q @ sK2_X ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
( ( ~ ~ ( big_r @ sK1_X ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(19,plain,
( ( ~ ( ~ ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p )
| ~ ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(20,plain,
( ( ~ ( ~ ( p
| ~ p )
| ~ ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(21,plain,
( ( ~ ( big_q @ sK2_X ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(22,plain,
( ( ~ ( big_r @ sK1_X ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
( ( ~ ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p )
| ~ ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(24,plain,
( ( ~ ( p
| ~ p )
| ~ ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(25,plain,
( ( big_q @ sK2_X )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(26,plain,
( ( big_r @ sK1_X )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(27,plain,
( ( ~ ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(28,plain,
( ( ~ ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).

thf(29,plain,
( ( ~ ( p
| ~ p ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(30,plain,
( ( ~ ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(31,plain,
( ( ! [SX0: \$i] : ( big_q @ SX0 )
| ~ p )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(32,plain,
( ( ! [SX0: \$i] :
( ( big_q @ SX0 )
| ( big_r @ SX0 ) ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(33,plain,
( ( p
| ~ p )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
( ( p
| ! [SX0: \$i] : ( big_r @ SX0 ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(35,plain,
( ( ( ! [SX0: \$i] : ( big_q @ SX0 ) )
= \$true )
| ( ( ~ p )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(36,plain,
! [SV1: \$i] :
( ( ( big_q @ SV1 )
| ( big_r @ SV1 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(37,plain,
( ( p = \$true )
| ( ( ~ p )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(38,plain,
( ( p = \$true )
| ( ( ! [SX0: \$i] : ( big_r @ SX0 ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(39,plain,
! [SV2: \$i] :
( ( ( big_q @ SV2 )
= \$true )
| ( ( ~ p )
= \$true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(40,plain,
! [SV1: \$i] :
( ( ( big_q @ SV1 )
= \$true )
| ( ( big_r @ SV1 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(41,plain,
( ( p = \$false )
| ( p = \$true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(42,plain,
! [SV3: \$i] :
( ( ( big_r @ SV3 )
= \$true )
| ( p = \$true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(43,plain,
! [SV2: \$i] :
( ( p = \$false )
| ( ( big_q @ SV2 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(44,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[25,43,42,41,40,26]) ).

thf(45,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 14:50:05 EDT 2022
% 0.13/0.35  % CPUTime  :
% 0.13/0.35
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.38
% 0.13/0.38  ********************************
% 0.13/0.38  *   All subproblems solved!    *
% 0.13/0.38  ********************************
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:44,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38  %**** Beginning of derivation protocol ****
% 0.13/0.38  % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38  %**** End of derivation protocol ****
% 0.13/0.38  %**** no. of clauses in derivation: 45 ****
% 0.13/0.38  %**** clause counter: 44 ****
% 0.13/0.38
% 0.13/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:44,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```