## TSTP Solution File: SYN969+1 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n007.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 08:30:53 EDT 2022

% Result   : Theorem 0.19s 0.37s
% Output   : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   28 (  19 unt;   4 typ;   0 def)
%            Number of atoms       :  108 (  26 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   96 (  10   ~;  10   |;   4   &;  54   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   23 (   0   ^  23   !;   0   ?;  23   :)

%------------------------------------------------------------------------------
thf(tp_p,type,
p: \$i > \$o ).

thf(tp_q,type,
q: \$i > \$o ).

thf(tp_r,type,
r: \$i > \$o ).

thf(tp_sK1_B,type,
sK1_B: \$i ).

thf(1,conjecture,
! [B: \$i] :
( ( ! [X: \$i] :
( ( p @ X )
=> ( q @ X ) )
& ( r @ B ) )
=> ( ! [Y: \$i] :
( ( r @ Y )
=> ( p @ Y ) )
=> ( q @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(2,negated_conjecture,
( ( ! [B: \$i] :
( ( ! [X: \$i] :
( ( p @ X )
=> ( q @ X ) )
& ( r @ B ) )
=> ( ! [Y: \$i] :
( ( r @ Y )
=> ( p @ Y ) )
=> ( q @ B ) ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
( ( ! [B: \$i] :
( ( ! [X: \$i] :
( ( p @ X )
=> ( q @ X ) )
& ( r @ B ) )
=> ( ! [Y: \$i] :
( ( r @ Y )
=> ( p @ Y ) )
=> ( q @ B ) ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
( ( ( ! [X: \$i] :
( ( p @ X )
=> ( q @ X ) )
& ( r @ sK1_B ) )
=> ( ! [Y: \$i] :
( ( r @ Y )
=> ( p @ Y ) )
=> ( q @ sK1_B ) ) )
= \$false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
( ( ! [X: \$i] :
( ( p @ X )
=> ( q @ X ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
( ( r @ sK1_B )
= \$true ),
inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
( ( ! [Y: \$i] :
( ( r @ Y )
=> ( p @ Y ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[4]) ).

thf(8,plain,
( ( q @ sK1_B )
= \$false ),
inference(standard_cnf,[status(thm)],[4]) ).

thf(9,plain,
( ( ~ ( q @ sK1_B ) )
= \$true ),
inference(polarity_switch,[status(thm)],[8]) ).

thf(10,plain,
( ( ! [X: \$i] :
( ~ ( p @ X )
| ( q @ X ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[5]) ).

thf(11,plain,
( ( ! [Y: \$i] :
( ~ ( r @ Y )
| ( p @ Y ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[7]) ).

thf(12,plain,
( ( ! [Y: \$i] :
( ~ ( r @ Y )
| ( p @ Y ) ) )
= \$true ),
inference(copy,[status(thm)],[11]) ).

thf(13,plain,
( ( r @ sK1_B )
= \$true ),
inference(copy,[status(thm)],[6]) ).

thf(14,plain,
( ( ! [X: \$i] :
( ~ ( p @ X )
| ( q @ X ) ) )
= \$true ),
inference(copy,[status(thm)],[10]) ).

thf(15,plain,
( ( ~ ( q @ sK1_B ) )
= \$true ),
inference(copy,[status(thm)],[9]) ).

thf(16,plain,
! [SV1: \$i] :
( ( ~ ( r @ SV1 )
| ( p @ SV1 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
! [SV2: \$i] :
( ( ~ ( p @ SV2 )
| ( q @ SV2 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(18,plain,
( ( q @ sK1_B )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(19,plain,
! [SV1: \$i] :
( ( ( ~ ( r @ SV1 ) )
= \$true )
| ( ( p @ SV1 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(20,plain,
! [SV2: \$i] :
( ( ( ~ ( p @ SV2 ) )
= \$true )
| ( ( q @ SV2 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).

thf(21,plain,
! [SV1: \$i] :
( ( ( r @ SV1 )
= \$false )
| ( ( p @ SV1 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(22,plain,
! [SV2: \$i] :
( ( ( p @ SV2 )
= \$false )
| ( ( q @ SV2 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(23,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[13,22,21,18]) ).

thf(24,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n007.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 12:34:02 EDT 2022
% 0.19/0.34  % CPUTime  :
% 0.19/0.35
% 0.19/0.35   No.of.Axioms: 0
% 0.19/0.35
% 0.19/0.35   Length.of.Defs: 0
% 0.19/0.35
% 0.19/0.35   Contains.Choice.Funs: false
% 0.19/0.35  (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)
% 0.19/0.37  ********************************
% 0.19/0.37  *   All subproblems solved!    *
% 0.19/0.37  ********************************
% 0.19/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.37
% 0.19/0.37  %**** Beginning of derivation protocol ****
% 0.19/0.37  % SZS output start CNFRefutation
% See solution above
% 0.19/0.37
% 0.19/0.37  %**** End of derivation protocol ****
% 0.19/0.37  %**** no. of clauses in derivation: 24 ****
% 0.19/0.37  %**** clause counter: 23 ****
% 0.19/0.37
% 0.19/0.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```