%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU650^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:45:56 AM UTC 2026
% Result : Theorem 0.11s 0.23s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 21 unt; 0 typ; 1 def)
% Number of atoms : 93 ( 65 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 262 ( 19 ~; 8 |; 2 &; 222 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_SY6,type,
sK2_SY6: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(1,conjecture,
( setukpairinjR11
=> ! [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(2,negated_conjecture,
( ( setukpairinjR11
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setukpairinjR11]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $false ),
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(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( sK1_Xx = sK2_SY6 )
& ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( sK1_Xx = sK2_SY6 )
& ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ( sK1_Xx != sK2_SY6 )
| ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,setukpairinjR11]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY7: $i] :
( ( SV1 != SY7 )
| ( ( setadjoin @ SV1 @ ( setadjoin @ SY7 @ emptyset ) )
= ( setadjoin @ SV1 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ( sK1_Xx != sK2_SY6 )
| ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1 != SV2 )
| ( ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) )
= ( setadjoin @ SV1 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( sK1_Xx != sK2_SY6 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1 != SV2 )
= $true )
| ( ( ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) )
= ( setadjoin @ SV1 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( sK1_Xx = sK2_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: $i,SV1: $i] :
( ( ( SV1 = SV2 )
= $false )
| ( ( ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) )
= ( setadjoin @ SV1 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ emptyset ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,21,20]) ).
thf(23,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU650^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.19 % Computer : n007.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 15:28:00 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.23
% 0.11/0.23 No.of.Axioms: 0
% 0.11/0.23
% 0.11/0.23 Length.of.Defs: 234
% 0.11/0.23
% 0.11/0.23 Contains.Choice.Funs: false
% 0.11/0.23
% 0.11/0.23 ********************************
% 0.11/0.23 * All subproblems solved! *
% 0.11/0.23 ********************************
% 0.11/0.23 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.11/0.23
% 0.11/0.23 %**** Beginning of derivation protocol ****
% 0.11/0.23 % SZS output start CNFRefutation
% See solution above
% 0.11/0.23
% 0.11/0.23 %**** End of derivation protocol ****
% 0.11/0.23 %**** no. of clauses in derivation: 23 ****
% 0.11/0.23 %**** clause counter: 22 ****
% 0.11/0.23
% 0.11/0.23 % 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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------