TSTP Solution File: SEU651^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU651^2 : 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 : n029.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 12:13:40 EDT 2022
% Result : Theorem 0.63s 0.84s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 37 unt; 10 typ; 3 def)
% Number of atoms : 178 ( 111 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 509 ( 43 ~; 19 |; 4 &; 418 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 0 ^ 68 !; 0 ?; 68 :)
% 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_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY19,type,
sK4_SY19: $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setukpairinjR12,type,
setukpairinjR12: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(1,conjecture,
( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [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 ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(2,negated_conjecture,
( ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [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 ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) )
=> ! [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 ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,secondinupair,setukpairinjR12,uniqinunit]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
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 ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
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 ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
& ( sK3_SY17 = sK4_SY19 )
& ( sK2_SY14 != sK4_SY19 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(12,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
& ( sK3_SY17 = sK4_SY19 )
& ( sK2_SY14 != sK4_SY19 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(16,plain,
( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
| ~ ~ ( ( sK3_SY17 != sK4_SY19 )
| ~ ( ( sK2_SY14 != sK4_SY19 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,secondinupair,setukpairinjR12,uniqinunit]) ).
thf(17,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
( ( SV1 != SY20 )
| ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY20 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(18,plain,
! [SV2: $i] :
( ( ! [SY21: $i] : ( in @ SY21 @ ( setadjoin @ SV2 @ ( setadjoin @ SY21 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(19,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( in @ SV3 @ ( setadjoin @ SY22 @ emptyset ) )
| ( SV3 = SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(20,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY14 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY17 @ ( setadjoin @ sK4_SY19 @ emptyset ) ) @ emptyset ) ) )
| ~ ~ ( ( sK3_SY17 != sK4_SY19 )
| ~ ( ( sK2_SY14 != sK4_SY19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV4: $i,SV1: $i] :
( ( ( SV1 != SV4 )
| ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV2: $i,SV5: $i] :
( ( in @ SV5 @ ( setadjoin @ SV2 @ ( setadjoin @ SV5 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( setadjoin @ SV6 @ emptyset ) )
| ( SV3 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( 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)],[20]) ).
thf(25,plain,
( ( ~ ~ ( ( sK3_SY17 != sK4_SY19 )
| ~ ( ( sK2_SY14 != sK4_SY19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
! [SV4: $i,SV1: $i] :
( ( ( ( SV1 != SV4 ) )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $true )
| ( ( SV3 = SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( 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)],[24]) ).
thf(29,plain,
( ( ~ ( ( sK3_SY17 != sK4_SY19 )
| ~ ( ( sK2_SY14 != sK4_SY19 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV4: $i,SV1: $i] :
( ( ( SV1 = SV4 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ SV3 @ ( setadjoin @ SV6 @ emptyset ) )
= $false )
| ( ( SV3 = SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ( sK3_SY17 != sK4_SY19 )
| ~ ( ( sK2_SY14 != sK4_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( sK3_SY17 != sK4_SY19 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(34,plain,
( ( ~ ( ( sK2_SY14 != sK4_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
( ( sK3_SY17 = sK4_SY19 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ( sK2_SY14 != sK4_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( sK2_SY14 = sK4_SY19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,37,35,31,30,28]) ).
thf(39,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU651^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n029.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 01:07:00 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 695
% 0.14/0.35
% 0.14/0.35 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)..
% 0.63/0.84
% 0.63/0.84 ********************************
% 0.63/0.84 * All subproblems solved! *
% 0.63/0.84 ********************************
% 0.63/0.84 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:38,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.63/0.84
% 0.63/0.84 %**** Beginning of derivation protocol ****
% 0.63/0.84 % SZS output start CNFRefutation
% See solution above
% 0.63/0.84
% 0.63/0.84 %**** End of derivation protocol ****
% 0.63/0.84 %**** no. of clauses in derivation: 39 ****
% 0.63/0.84 %**** clause counter: 38 ****
% 0.63/0.84
% 0.63/0.84 % 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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:38,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------