%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU654^2 : 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 : n003.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 10:45:59 AM UTC 2026
% Result : Theorem 0.08s 0.19s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 25 unt; 0 typ; 2 def)
% Number of atoms : 108 ( 77 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 520 ( 16 ~; 13 |; 0 &; 478 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 2 ^; 82 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_SY22,type,
sK3_SY22: $i ).
thf(tp_sK4_SY25,type,
sK4_SY25: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setukpairinjR2,type,
setukpairinjR2: $o ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [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 ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(1,conjecture,
( setukpairinjR2
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(2,negated_conjecture,
( ( setukpairinjR2
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,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 ) ) )
=> ( Xy = Xu ) )
=> ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY1 = SY3 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,kpair,setukpairinjR2]) ).
thf(4,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 ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY1 = SY3 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY1 = SY3 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
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 ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i,SY3: $i] :
( ( ( setadjoin @ ( setadjoin @ SY0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY0 @ ( setadjoin @ SY1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2 @ ( setadjoin @ SY3 @ emptyset ) ) @ emptyset ) ) )
=> ( SY1 = SY3 ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,kpair,setukpairinjR2]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,kpair,setukpairinjR2]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i,SY16: $i] :
( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY14 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY15 @ ( setadjoin @ SY16 @ emptyset ) ) @ emptyset ) ) )
| ( SY14 = SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY17: $i,SY18: $i,SY19: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY17 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY18 @ ( setadjoin @ SY19 @ emptyset ) ) @ emptyset ) ) )
| ( SY17 = SY19 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY20 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY20 @ ( setadjoin @ SY21 @ emptyset ) ) @ emptyset ) ) )
| ( SV2 = SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SY22: $i,SY23: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY17 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY22 @ ( setadjoin @ SY23 @ emptyset ) ) @ emptyset ) ) )
| ( sK2_SY17 = SY23 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY24: $i] :
( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SY24 @ emptyset ) ) @ emptyset ) ) )
| ( SV2 = SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SY25: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY17 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY22 @ ( setadjoin @ SY25 @ emptyset ) ) @ emptyset ) ) )
| ( sK2_SY17 = SY25 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(18,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY17 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY22 @ ( setadjoin @ sK4_SY25 @ emptyset ) ) @ emptyset ) ) )
| ( sK2_SY17 = sK4_SY25 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(20,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY17 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY22 @ ( setadjoin @ sK4_SY25 @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( sK2_SY17 = sK4_SY25 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV4 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY17 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY22 @ ( setadjoin @ sK4_SY25 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,24,23]) ).
thf(26,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU654^2 : 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
% 0.08/0.16 % Computer : n003.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 15:32:09 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19
% 0.08/0.19 No.of.Axioms: 0
% 0.08/0.19
% 0.08/0.19 Length.of.Defs: 608
% 0.08/0.19
% 0.08/0.19 Contains.Choice.Funs: false
% 0.08/0.19 .
% 0.08/0.19
% 0.08/0.19 ********************************
% 0.08/0.19 * All subproblems solved! *
% 0.08/0.19 ********************************
% 0.08/0.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.19
% 0.08/0.19 %**** Beginning of derivation protocol ****
% 0.08/0.19 % SZS output start CNFRefutation
% See solution above
% 0.08/0.19
% 0.08/0.19 %**** End of derivation protocol ****
% 0.08/0.19 %**** no. of clauses in derivation: 26 ****
% 0.08/0.19 %**** clause counter: 25 ****
% 0.08/0.19
% 0.08/0.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:1,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:25,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------