%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU642^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:45:50 AM UTC 2026
% Result : Theorem 0.14s 0.26s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 39 unt; 0 typ; 4 def)
% Number of atoms : 214 ( 114 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 407 ( 30 ~; 33 |; 2 &; 316 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 96 ( 0 ^; 96 !; 0 ?; 96 :)
% 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_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(1,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ( upairset2E
=> ( singletonsuniq
=> ! [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(2,negated_conjecture,
( ( setadjoinIL
=> ( uniqinunit
=> ( upairset2E
=> ( singletonsuniq
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ 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] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( 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 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setadjoinIL,singletonsuniq,uniqinunit,upairset2E]) ).
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] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
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(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY15 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_Xx != sK3_SY17 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(14,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(18,plain,
( ( ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY15 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_Xx != sK3_SY17 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ~ ( ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY15 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_Xx != sK3_SY17 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,setadjoinIL,singletonsuniq,uniqinunit,upairset2E]) ).
thf(20,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ( ( setadjoin @ SV1 @ emptyset )
!= ( setadjoin @ SY18 @ emptyset ) )
| ( SV1 = SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ( in @ SY20 @ ( setadjoin @ SV2 @ ( setadjoin @ SY19 @ emptyset ) ) )
| ( SY20 = SV2 )
| ( SY20 = SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY21: $i] :
( ~ ( in @ SV3 @ ( setadjoin @ SY21 @ emptyset ) )
| ( SV3 = SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV4: $i] :
( ( ! [SY22: $i] : ( in @ SV4 @ ( setadjoin @ SV4 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY15 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_Xx != sK3_SY17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( setadjoin @ SV1 @ emptyset )
!= ( setadjoin @ SV5 @ emptyset ) )
| ( SV1 = SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
| ( SY23 = SV2 )
| ( SY23 = SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( setadjoin @ SV7 @ emptyset ) )
| ( SV3 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV8: $i,SV4: $i] :
( ( in @ SV4 @ ( setadjoin @ SV4 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY15 @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( ( sK1_Xx != sK3_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(31,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( setadjoin @ SV1 @ emptyset )
!= ( setadjoin @ SV5 @ emptyset ) )
= $true )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
| ( SV9 = SV2 )
| ( SV9 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( setadjoin @ SV7 @ emptyset ) ) )
= $true )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
( ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY15 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( sK1_Xx != sK3_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV5: $i,SV1: $i] :
( ( ( ( setadjoin @ SV1 @ emptyset )
= ( setadjoin @ SV5 @ emptyset ) )
= $false )
| ( ( SV1 = SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) ) )
= $true )
| ( ( ( SV9 = SV2 )
| ( SV9 = SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV7: $i,SV3: $i] :
( ( ( in @ SV3 @ ( setadjoin @ SV7 @ emptyset ) )
= $false )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( sK1_Xx = sK3_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ( in @ SV9 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $false )
| ( ( ( SV9 = SV2 )
| ( SV9 = SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV6: $i,SV2: $i,SV9: $i] :
( ( ( SV9 = SV2 )
= $true )
| ( ( SV9 = SV6 )
= $true )
| ( ( in @ SV9 @ ( setadjoin @ SV2 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,41,39,38,36,34]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU642^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.20 % Computer : n026.cluster.edu
% 0.14/0.20 % Model : x86_64 x86_64
% 0.14/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.20 % Memory : 8046.5625MB
% 0.14/0.20 % OS : Linux 6.8.0-71-generic
% 0.14/0.20 % CPULimit : 300
% 0.14/0.20 % WCLimit : 300
% 0.14/0.20 % DateTime : Tue Oct 6 15:32:32 UTC 2026
% 0.14/0.20 % CPUTime :
% 0.14/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.26
% 0.14/0.26 No.of.Axioms: 0
% 0.14/0.26
% 0.14/0.26 Length.of.Defs: 783
% 0.14/0.26
% 0.14/0.26 Contains.Choice.Funs: false
% 0.14/0.26 .
% 0.14/0.26
% 0.14/0.26 ********************************
% 0.14/0.26 * All subproblems solved! *
% 0.14/0.26 ********************************
% 0.14/0.26 % SZS status Theorem for /export/starexec/sandbox2/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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.14/0.26
% 0.14/0.26 %**** Beginning of derivation protocol ****
% 0.14/0.26 % SZS output start CNFRefutation
% See solution above
% 0.14/0.26
% 0.14/0.26 %**** End of derivation protocol ****
% 0.14/0.26 %**** no. of clauses in derivation: 43 ****
% 0.14/0.26 %**** clause counter: 42 ****
% 0.14/0.26
% 0.14/0.26 % SZS status Theorem for /export/starexec/sandbox2/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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------