## TSTP Solution File: SEV091^5 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV091^5 : TPTP v6.4.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n096.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.75MB
% OS       : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Wed Jan 18 14:55:11 EST 2017

% Result   : Theorem 0.03s
% Output   : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   55 (  37 unt;   6 typ;   0 def)
%            Number of atoms       :  268 (  64 equ;   0 cnn)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  422 (  55   ~;  57   |;  19   &; 276   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :  134 (   0   ^ 134   !;   0   ?; 134   :)

%------------------------------------------------------------------------------
thf(tp_cP,type,
cP: \$i > \$i > \$o ).

thf(tp_cQ,type,
cQ: \$i > \$i > \$o ).

thf(tp_sK1_Xx,type,
sK1_Xx: \$i ).

thf(tp_sK2_SY14,type,
sK2_SY14: \$i ).

thf(tp_sK3_Xx,type,
sK3_Xx: \$i ).

thf(tp_sK4_SY15,type,
sK4_SY15: \$i ).

thf(1,conjecture,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cP @ Xx @ Xy )
& ( cP @ Xy @ Xz ) )
=> ( cP @ Xx @ Xz ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cQ @ Xx @ Xy )
& ( cQ @ Xy @ Xz ) )
=> ( cQ @ Xx @ Xz ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cQ @ Xx @ Xy )
=> ( cQ @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cP @ Xx @ Xy )
| ( cQ @ Xx @ Xy ) ) )
=> ( ! [Xx: \$i,Xy: \$i] : ( cP @ Xx @ Xy )
| ! [Xx: \$i,Xy: \$i] : ( cQ @ Xx @ Xy ) ) ),

thf(2,negated_conjecture,
( ( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cP @ Xx @ Xy )
& ( cP @ Xy @ Xz ) )
=> ( cP @ Xx @ Xz ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cQ @ Xx @ Xy )
& ( cQ @ Xy @ Xz ) )
=> ( cQ @ Xx @ Xz ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cQ @ Xx @ Xy )
=> ( cQ @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cP @ Xx @ Xy )
| ( cQ @ Xx @ Xy ) ) )
=> ( ! [Xx: \$i,Xy: \$i] : ( cP @ Xx @ Xy )
| ! [Xx: \$i,Xy: \$i] : ( cQ @ Xx @ Xy ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
( ( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cP @ Xx @ Xy )
& ( cP @ Xy @ Xz ) )
=> ( cP @ Xx @ Xz ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cQ @ Xx @ Xy )
& ( cQ @ Xy @ Xz ) )
=> ( cQ @ Xx @ Xz ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cQ @ Xx @ Xy )
=> ( cQ @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i] :
( ( cP @ Xx @ Xy )
| ( cQ @ Xx @ Xy ) ) )
=> ( ! [Xx: \$i,Xy: \$i] : ( cP @ Xx @ Xy )
| ! [Xx: \$i,Xy: \$i] : ( cQ @ Xx @ Xy ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cP @ Xx @ Xy )
& ( cP @ Xy @ Xz ) )
=> ( cP @ Xx @ Xz ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( cQ @ Xx @ Xy )
& ( cQ @ Xy @ Xz ) )
=> ( cQ @ Xx @ Xz ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
( ( ! [Xx: \$i,Xy: \$i] :
( ( cQ @ Xx @ Xy )
=> ( cQ @ Xy @ Xx ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
( ( ! [Xx: \$i,Xy: \$i] :
( ( cP @ Xx @ Xy )
| ( cQ @ Xx @ Xy ) ) )
= \$true ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
( ( ! [Xx: \$i,Xy: \$i] : ( cP @ Xx @ Xy )
| ! [Xx: \$i,Xy: \$i] : ( cQ @ Xx @ Xy ) )
= \$false ),
inference(standard_cnf,[status(thm)],[3]) ).

thf(9,plain,
( ( ~ ( ! [Xx: \$i,Xy: \$i] : ( cP @ Xx @ Xy )
| ! [Xx: \$i,Xy: \$i] : ( cQ @ Xx @ Xy ) ) )
= \$true ),
inference(polarity_switch,[status(thm)],[8]) ).

thf(10,plain,
( ( ~ ( cP @ sK3_Xx @ sK4_SY15 )
& ~ ( cQ @ sK1_Xx @ sK2_SY14 ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[9]) ).

thf(11,plain,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ~ ( cP @ Xx @ Xy )
| ~ ( cP @ Xy @ Xz )
| ( cP @ Xx @ Xz ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[4]) ).

thf(12,plain,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ~ ( cQ @ Xx @ Xy )
| ~ ( cQ @ Xy @ Xz )
| ( cQ @ Xx @ Xz ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[5]) ).

thf(13,plain,
( ( ! [Xx: \$i,Xy: \$i] :
( ~ ( cQ @ Xx @ Xy )
| ( cQ @ Xy @ Xx ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[6]) ).

thf(14,plain,
( ( ! [Xx: \$i,Xy: \$i] :
( ( cP @ Xx @ Xy )
| ( cQ @ Xx @ Xy ) ) )
= \$true ),
inference(copy,[status(thm)],[7]) ).

thf(15,plain,
( ( ! [Xx: \$i,Xy: \$i] :
( ~ ( cQ @ Xx @ Xy )
| ( cQ @ Xy @ Xx ) ) )
= \$true ),
inference(copy,[status(thm)],[13]) ).

thf(16,plain,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ~ ( cQ @ Xx @ Xy )
| ~ ( cQ @ Xy @ Xz )
| ( cQ @ Xx @ Xz ) ) )
= \$true ),
inference(copy,[status(thm)],[12]) ).

thf(17,plain,
( ( ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ~ ( cP @ Xx @ Xy )
| ~ ( cP @ Xy @ Xz )
| ( cP @ Xx @ Xz ) ) )
= \$true ),
inference(copy,[status(thm)],[11]) ).

thf(18,plain,
( ( ~ ( cP @ sK3_Xx @ sK4_SY15 )
& ~ ( cQ @ sK1_Xx @ sK2_SY14 ) )
= \$true ),
inference(copy,[status(thm)],[10]) ).

thf(19,plain,
( ( ~ ( ~ ~ ( cP @ sK3_Xx @ sK4_SY15 )
| ~ ~ ( cQ @ sK1_Xx @ sK2_SY14 ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[18]) ).

thf(20,plain,
! [SV1: \$i] :
( ( ! [SY16: \$i] :
( ( cP @ SV1 @ SY16 )
| ( cQ @ SV1 @ SY16 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(21,plain,
! [SV2: \$i] :
( ( ! [SY17: \$i] :
( ~ ( cQ @ SV2 @ SY17 )
| ( cQ @ SY17 @ SV2 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(22,plain,
! [SV3: \$i] :
( ( ! [SY18: \$i,SY19: \$i] :
( ~ ( cQ @ SV3 @ SY18 )
| ~ ( cQ @ SY18 @ SY19 )
| ( cQ @ SV3 @ SY19 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(23,plain,
! [SV4: \$i] :
( ( ! [SY20: \$i,SY21: \$i] :
( ~ ( cP @ SV4 @ SY20 )
| ~ ( cP @ SY20 @ SY21 )
| ( cP @ SV4 @ SY21 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(24,plain,
( ( ~ ~ ( cP @ sK3_Xx @ sK4_SY15 )
| ~ ~ ( cQ @ sK1_Xx @ sK2_SY14 ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(25,plain,
! [SV5: \$i,SV1: \$i] :
( ( ( cP @ SV1 @ SV5 )
| ( cQ @ SV1 @ SV5 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(26,plain,
! [SV6: \$i,SV2: \$i] :
( ( ~ ( cQ @ SV2 @ SV6 )
| ( cQ @ SV6 @ SV2 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(27,plain,
! [SV7: \$i,SV3: \$i] :
( ( ! [SY22: \$i] :
( ~ ( cQ @ SV3 @ SV7 )
| ~ ( cQ @ SV7 @ SY22 )
| ( cQ @ SV3 @ SY22 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(28,plain,
! [SV8: \$i,SV4: \$i] :
( ( ! [SY23: \$i] :
( ~ ( cP @ SV4 @ SV8 )
| ~ ( cP @ SV8 @ SY23 )
| ( cP @ SV4 @ SY23 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(29,plain,
( ( ~ ~ ( cP @ sK3_Xx @ sK4_SY15 ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(30,plain,
( ( ~ ~ ( cQ @ sK1_Xx @ sK2_SY14 ) )
= \$false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(31,plain,
! [SV5: \$i,SV1: \$i] :
( ( ( cP @ SV1 @ SV5 )
= \$true )
| ( ( cQ @ SV1 @ SV5 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(32,plain,
! [SV6: \$i,SV2: \$i] :
( ( ( ~ ( cQ @ SV2 @ SV6 ) )
= \$true )
| ( ( cQ @ SV6 @ SV2 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(33,plain,
! [SV9: \$i,SV7: \$i,SV3: \$i] :
( ( ~ ( cQ @ SV3 @ SV7 )
| ~ ( cQ @ SV7 @ SV9 )
| ( cQ @ SV3 @ SV9 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(34,plain,
! [SV10: \$i,SV8: \$i,SV4: \$i] :
( ( ~ ( cP @ SV4 @ SV8 )
| ~ ( cP @ SV8 @ SV10 )
| ( cP @ SV4 @ SV10 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
( ( ~ ( cP @ sK3_Xx @ sK4_SY15 ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(36,plain,
( ( ~ ( cQ @ sK1_Xx @ sK2_SY14 ) )
= \$true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(37,plain,
! [SV6: \$i,SV2: \$i] :
( ( ( cQ @ SV2 @ SV6 )
= \$false )
| ( ( cQ @ SV6 @ SV2 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(38,plain,
! [SV9: \$i,SV7: \$i,SV3: \$i] :
( ( ( ~ ( cQ @ SV3 @ SV7 )
| ~ ( cQ @ SV7 @ SV9 ) )
= \$true )
| ( ( cQ @ SV3 @ SV9 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(39,plain,
! [SV10: \$i,SV8: \$i,SV4: \$i] :
( ( ( ~ ( cP @ SV4 @ SV8 )
| ~ ( cP @ SV8 @ SV10 ) )
= \$true )
| ( ( cP @ SV4 @ SV10 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(40,plain,
( ( cP @ sK3_Xx @ sK4_SY15 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(41,plain,
( ( cQ @ sK1_Xx @ sK2_SY14 )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(42,plain,
! [SV9: \$i,SV7: \$i,SV3: \$i] :
( ( ( ~ ( cQ @ SV3 @ SV7 ) )
= \$true )
| ( ( ~ ( cQ @ SV7 @ SV9 ) )
= \$true )
| ( ( cQ @ SV3 @ SV9 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(43,plain,
! [SV10: \$i,SV8: \$i,SV4: \$i] :
( ( ( ~ ( cP @ SV4 @ SV8 ) )
= \$true )
| ( ( ~ ( cP @ SV8 @ SV10 ) )
= \$true )
| ( ( cP @ SV4 @ SV10 )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(44,plain,
! [SV9: \$i,SV7: \$i,SV3: \$i] :
( ( ( cQ @ SV3 @ SV7 )
= \$false )
| ( ( ~ ( cQ @ SV7 @ SV9 ) )
= \$true )
| ( ( cQ @ SV3 @ SV9 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(45,plain,
! [SV10: \$i,SV8: \$i,SV4: \$i] :
( ( ( cP @ SV4 @ SV8 )
= \$false )
| ( ( ~ ( cP @ SV8 @ SV10 ) )
= \$true )
| ( ( cP @ SV4 @ SV10 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(46,plain,
! [SV3: \$i,SV9: \$i,SV7: \$i] :
( ( ( cQ @ SV7 @ SV9 )
= \$false )
| ( ( cQ @ SV3 @ SV7 )
= \$false )
| ( ( cQ @ SV3 @ SV9 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(47,plain,
! [SV4: \$i,SV10: \$i,SV8: \$i] :
( ( ( cP @ SV8 @ SV10 )
= \$false )
| ( ( cP @ SV4 @ SV8 )
= \$false )
| ( ( cP @ SV4 @ SV10 )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(48,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[31,47,46,41,40,37]) ).

thf(49,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEV091^5 : TPTP v6.4.0. Released v4.0.0.
% 0.00/0.04  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.03/0.23  % Computer : n096.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.75MB
% 0.03/0.23  % OS       : Linux 3.10.0-327.36.3.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Sun Jan 15 23:54:03 CST 2017
% 0.03/0.23  % CPUTime  :
% 0.03/0.24
% 0.03/0.24   No.of.Axioms: 0
% 0.03/0.24
% 0.03/0.24   Length.of.Defs: 0
% 0.03/0.24
% 0.03/0.24   Contains.Choice.Funs: false
% 0.03/0.24  (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.03/0.26
% 0.03/0.26  ********************************
% 0.03/0.26  *   All subproblems solved!    *
% 0.03/0.26  ********************************
% 0.03/0.26  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.03/0.26
% 0.03/0.26  %**** Beginning of derivation protocol ****
% 0.03/0.26  % SZS output start CNFRefutation
% See solution above
% 0.03/0.26  % SZS output end CNFRefutation
% 0.03/0.26
% 0.03/0.26  %**** End of derivation protocol ****
% 0.03/0.26  %**** no. of clauses in derivation: 49 ****
% 0.03/0.26  %**** clause counter: 48 ****
% 0.03/0.26
% 0.03/0.26  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```