TSTP Solution File: SEV091^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV091^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 : Tue Jul 19 17:35:04 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : CNFRefutation 0.20s
% 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 ( 5 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 :)
% Comments :
%------------------------------------------------------------------------------
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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCADE13_pme) ).
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
% 0.03/0.12 % Problem : SEV091^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 14:40:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34
% 0.14/0.34 No.of.Axioms: 0
% 0.14/0.34
% 0.14/0.34 Length.of.Defs: 0
% 0.14/0.34
% 0.14/0.34 Contains.Choice.Funs: false
% 0.14/0.35 (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: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)..
% 0.20/0.38
% 0.20/0.38 ********************************
% 0.20/0.38 * All subproblems solved! *
% 0.20/0.38 ********************************
% 0.20/0.38 % 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)
% 0.20/0.38
% 0.20/0.38 %**** Beginning of derivation protocol ****
% 0.20/0.38 % SZS output start CNFRefutation
% See solution above
% 0.20/0.39
% 0.20/0.39 %**** End of derivation protocol ****
% 0.20/0.39 %**** no. of clauses in derivation: 49 ****
% 0.20/0.39 %**** clause counter: 48 ****
% 0.20/0.39
% 0.20/0.39 % 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)
%------------------------------------------------------------------------------