TSTP Solution File: SEU647^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU647^2 : 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 : n013.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 27 unt; 9 typ; 2 def)
% Number of atoms : 115 ( 63 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 429 ( 20 ~; 9 |; 2 &; 384 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 0 ^ 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i ).
thf(tp_sK4_SY18,type,
sK4_SY18: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(1,conjecture,
( setadjoinIL
=> ( setukpairinjL1
=> ! [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/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(2,negated_conjecture,
( ( setadjoinIL
=> ( setukpairinjL1
=> ! [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 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ! [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 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setadjoinIL,setukpairinjL1]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,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 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,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(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY13 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY16 @ ( setadjoin @ sK4_SY18 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_Xx != sK3_SY16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY13 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY16 @ ( setadjoin @ sK4_SY18 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_Xx != sK3_SY16 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY13 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY16 @ ( setadjoin @ sK4_SY18 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_Xx != sK3_SY16 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,setadjoinIL,setukpairinjL1]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ( in @ ( setadjoin @ SY20 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY19 @ emptyset ) ) @ emptyset ) ) )
| ( SV1 = SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY21: $i] : ( in @ SV2 @ ( setadjoin @ SV2 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY13 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY16 @ ( setadjoin @ sK4_SY18 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_Xx != sK3_SY16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY22: $i] :
( ~ ( in @ ( setadjoin @ SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) )
| ( SV1 = SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY13 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY16 @ ( setadjoin @ sK4_SY18 @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ( sK1_Xx != sK3_SY16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ~ ( in @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) )
| ( SV1 = SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY13 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY16 @ ( setadjoin @ sK4_SY18 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ( sK1_Xx != sK3_SY16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( sK1_Xx = sK3_SY16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( in @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV3 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,26,25,22]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU647^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 13:54:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 469
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (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).
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38
% 0.12/0.38 %**** Beginning of derivation protocol ****
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38 %**** End of derivation protocol ****
% 0.12/0.38 %**** no. of clauses in derivation: 28 ****
% 0.12/0.38 %**** clause counter: 27 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------