%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU652^2 : 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 : n019.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 10:45:58 AM UTC 2026
% Result : Theorem 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 31 unt; 0 typ; 3 def)
% Number of atoms : 131 ( 68 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 216 ( 13 ~; 10 |; 0 &; 174 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 69 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinIL,type,
setadjoinIL: $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/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(1,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).
thf(2,negated_conjecture,
( ( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ) )
= $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] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,secondinupair,setadjoinIL,uniqinunit]) ).
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] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,secondinupair,setadjoinIL,uniqinunit]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,secondinupair,setadjoinIL,uniqinunit]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY12: $i] : ( in @ SY12 @ ( setadjoin @ SV1 @ ( setadjoin @ SY12 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY13: $i] : ( in @ SV2 @ ( setadjoin @ SV2 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
( ~ ( in @ SV3 @ ( setadjoin @ SY14 @ emptyset ) )
| ( SV3 = SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV1: $i,SV4: $i] :
( ( in @ SV4 @ ( setadjoin @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV5: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ! [SY15: $i,SY16: $i] :
( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY15 @ emptyset ) )
!= ( setadjoin @ SY16 @ emptyset ) )
| ( sK1_SX0 = SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(22,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( setadjoin @ SV6 @ emptyset ) )
| ( SV3 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SY17: $i] :
( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ emptyset ) )
!= ( setadjoin @ SY17 @ emptyset ) )
| ( sK1_SX0 = sK2_SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(24,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $true )
| ( ( SV3 = SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ emptyset ) )
!= ( setadjoin @ sK3_SY17 @ emptyset ) )
| ( sK1_SX0 = sK2_SY15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(26,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ SV3 @ ( setadjoin @ SV6 @ emptyset ) )
= $false )
| ( ( SV3 = SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ emptyset ) )
!= ( setadjoin @ sK3_SY17 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( sK1_SX0 = sK2_SY15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY15 @ emptyset ) )
= ( setadjoin @ sK3_SY17 @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,29,28,26,20]) ).
thf(31,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU652^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 15:30:16 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 0
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 542
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 31 ****
% 0.10/0.22 %**** clause counter: 30 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------