TSTP Solution File: SEU648^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU648^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 12:13:38 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 23 unt; 8 typ; 2 def)
% Number of atoms : 104 ( 73 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 462 ( 21 ~; 10 |; 2 &; 418 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 66 ( 2 ^ 64 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY19,type,
sK4_SY19: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(1,conjecture,
( setukpairinjL2
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(2,negated_conjecture,
( ( setukpairinjL2
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY0 = SY2 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,kpair,setukpairinjL2]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY0 = SY2 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY0 = SY2 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_SY0 != sK3_SY17 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_SY0 != sK3_SY17 ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_SY0 != sK3_SY17 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,kpair,setukpairinjL2]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ! [SY22: $i] :
( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY20 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY21 @ ( setadjoin @ SY22 @ emptyset ) ) @ emptyset ) ) )
| ( SV1 = SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_SY0 != sK3_SY17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY23: $i] :
( ! [SY24: $i] :
( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY23 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY23 @ ( setadjoin @ SY24 @ emptyset ) ) @ emptyset ) ) )
| ( SV1 = SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ( sK1_SY0 != sK3_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY25: $i] :
( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
| ( SV1 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SY0 @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ( sK1_SY0 != sK3_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( ! [SY25: $i] :
( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( sK1_SY0 = sK3_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV1 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(24,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,23,21]) ).
thf(25,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU648^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 23:04:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 608
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (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)..
% 0.13/0.38
% 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/sandbox/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:24,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
% 0.13/0.39
% 0.13/0.39 %**** End of derivation protocol ****
% 0.13/0.39 %**** no. of clauses in derivation: 25 ****
% 0.13/0.39 %**** clause counter: 24 ****
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for /export/starexec/sandbox/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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:24,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------