%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV166^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 10:49:40 AM UTC 2026
% Result : Theorem 3.58s 1.02s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 52 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 211 ( 154 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 244 ( 53 ~; 19 |; 17 &; 144 @)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 50 ^; 28 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY6,type,
sK2_SY6: a ).
thf(tp_sK3_SY11,type,
sK3_SY11: a ).
thf(tp_sK4_SY15,type,
sK4_SY15: a ).
thf(tp_sK5_SV113,type,
sK5_SV113: a > a > a ).
thf(1,conjecture,
! [Xx: a,Xy: a,Xu: a,Xv: a] :
( ( ( ^ [Xg: a > a > a] : ( Xg @ Xx @ Xy ) )
= ( ^ [Xg: a > a > a] : ( Xg @ Xu @ Xv ) ) )
<=> ( ( Xx = Xu )
& ( Xy = Xv ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM182_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a,Xy: a,Xu: a,Xv: a] :
( ( ( ^ [Xg: a > a > a] : ( Xg @ Xx @ Xy ) )
= ( ^ [Xg: a > a > a] : ( Xg @ Xu @ Xv ) ) )
<=> ( ( Xx = Xu )
& ( Xy = Xv ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: a,Xy: a,Xu: a,Xv: a] :
( ( ( ^ [Xg: a > a > a] : ( Xg @ Xx @ Xy ) )
= ( ^ [Xg: a > a > a] : ( Xg @ Xu @ Xv ) ) )
<=> ( ( Xx = Xu )
& ( Xy = Xv ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY6: a,SY7: a,SY8: a] :
( ( ( ^ [SY9: a > a > a] : ( SY9 @ sK1_Xx @ SY6 ) )
= ( ^ [Xg: a > a > a] : ( Xg @ SY7 @ SY8 ) ) )
<=> ( ( sK1_Xx = SY7 )
& ( SY6 = SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY11: a,SY12: a] :
( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [Xg: a > a > a] : ( Xg @ SY11 @ SY12 ) ) )
<=> ( ( sK1_Xx = SY11 )
& ( sK2_SY6 = SY12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY15: a] :
( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY17: a > a > a] : ( SY17 @ sK3_SY11 @ SY15 ) ) )
<=> ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = SY15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) )
<=> ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(8,plain,
( ( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) )
=> ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(9,plain,
( ( ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 ) )
=> ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[7]) ).
thf(10,plain,
( ( ~ ( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) )
=> ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 ) )
=> ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(12,plain,
( ( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) )
& ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(13,plain,
( ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 )
& ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(14,plain,
( ( ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) )
& ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
| ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
| ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(18,plain,
( ( ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ! [SV1: a > a > a] :
( ( SV1 @ sK1_Xx @ sK2_SY6 )
= ( SV1 @ sK3_SY11 @ sK4_SY15 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ( sK1_Xx != sK3_SY11 )
= $true )
| ( ( sK2_SY6 != sK4_SY15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: a > a > a] :
( ( ( SV2 @ sK1_Xx @ sK2_SY6 )
= ( SV2 @ sK3_SY11 @ sK4_SY15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ( sK1_Xx = sK3_SY11 )
= $false )
| ( ( sK2_SY6 != sK4_SY15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
( ( ( sK2_SY6 = sK4_SY15 )
= $false )
| ( ( sK1_Xx = sK3_SY11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(39,plain,
! [SV4: a > a > a] :
( ( ( SV4 @ sK1_Xx @ sK2_SY6 )
= ( SV4 @ sK3_SY11 @ sK4_SY15 ) )
= $true ),
inference(rename,[status(thm)],[24]) ).
thf(58,plain,
! [SV7: a > a > a] :
( ( ( SV7 @ sK1_Xx @ sK2_SY6 )
= ( SV7 @ sK3_SY11 @ sK4_SY15 ) )
= $true ),
inference(rename,[status(thm)],[39]) ).
thf(80,plain,
! [SV10: a > a > a] :
( ( ( SV10 @ sK1_Xx @ sK2_SY6 )
= ( SV10 @ sK3_SY11 @ sK4_SY15 ) )
= $true ),
inference(rename,[status(thm)],[58]) ).
thf(82,plain,
! [SV10: a > a > a] :
( ( ( ( ( SV10 @ sK1_Xx @ sK2_SY6 )
= ( SV10 @ sK3_SY11 @ sK4_SY15 ) )
= ( sK2_SY6 = sK4_SY15 ) )
= $false )
| ( ( sK1_Xx = sK3_SY11 )
= $false ) ),
inference(res,[status(thm)],[80,26]) ).
thf(86,plain,
( ( sK1_Xx = sK3_SY11 )
= $false ),
inference(extuni,[status(esa)],[82:[bind(SV10,$thf( ^ [SX0: a] : ^ [SX1: a] : SX1 ))]]) ).
thf(187,plain,
! [SV49: a > a > a] :
( ( ( SV49 @ sK1_Xx @ sK2_SY6 )
= ( SV49 @ sK3_SY11 @ sK4_SY15 ) )
= $true ),
inference(rename,[status(thm)],[80]) ).
thf(551,plain,
! [SV104: a > a > a] :
( ( ( SV104 @ sK1_Xx @ sK2_SY6 )
= ( SV104 @ sK3_SY11 @ sK4_SY15 ) )
= $true ),
inference(rename,[status(thm)],[187]) ).
thf(558,plain,
! [SV104: a > a > a] :
( ( ( ( SV104 @ sK1_Xx @ sK2_SY6 )
= ( SV104 @ sK3_SY11 @ sK4_SY15 ) )
= ( sK1_Xx = sK3_SY11 ) )
= $false ),
inference(res,[status(thm)],[551,86]) ).
thf(563,plain,
$false = $true,
inference(extuni,[status(esa)],[558:[bind(SV104,$thf( ^ [SX0: a] : ^ [SX1: a] : SX0 ))]]) ).
thf(564,plain,
( ( ( sK1_Xx = sK3_SY11 )
& ( sK2_SY6 = sK4_SY15 )
& ( ( ^ [SY13: a > a > a] : ( SY13 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SY19: a > a > a] : ( SY19 @ sK3_SY11 @ sK4_SY15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(565,plain,
( ( ~ ( ~ ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) )
| ~ ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(566,plain,
( ( ~ ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) )
| ~ ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(567,plain,
( ( ~ ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(568,plain,
( ( ~ ( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(569,plain,
( ( ~ ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(570,plain,
( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
!= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(571,plain,
( ( ( sK1_Xx != sK3_SY11 )
| ( sK2_SY6 != sK4_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(572,plain,
( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(573,plain,
( ( sK1_Xx != sK3_SY11 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(574,plain,
( ( sK2_SY6 != sK4_SY15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(575,plain,
( ( ! [SV113: a > a > a] :
( ( SV113 @ sK1_Xx @ sK2_SY6 )
= ( SV113 @ sK3_SY11 @ sK4_SY15 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[572]) ).
thf(576,plain,
( ( ( ^ [SX0: a > a > a] : ( SX0 @ sK1_Xx @ sK2_SY6 ) )
= ( ^ [SX0: a > a > a] : ( SX0 @ sK3_SY11 @ sK4_SY15 ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[572]) ).
thf(577,plain,
( ( sK1_Xx = sK3_SY11 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(578,plain,
( ( sK2_SY6 = sK4_SY15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(579,plain,
( ( ( sK5_SV113 @ sK1_Xx @ sK2_SY6 )
= ( sK5_SV113 @ sK3_SY11 @ sK4_SY15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[575]) ).
thf(580,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[576,579,578,577]) ).
thf(581,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[580,563]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV166^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:45:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/1.02
% 3.58/1.02 No.of.Axioms: 0
% 3.58/1.02
% 3.58/1.02 Length.of.Defs: 0
% 3.58/1.02
% 3.58/1.02 Contains.Choice.Funs: false
% 3.58/1.02 .............................................................
% 3.58/1.02
% 3.58/1.02 ********************************
% 3.58/1.02 * All subproblems solved! *
% 3.58/1.02 ********************************
% 3.58/1.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:580,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.58/1.02
% 3.58/1.02 %**** Beginning of derivation protocol ****
% 3.58/1.02 % SZS output start CNFRefutation
% See solution above
% 3.58/1.02
% 3.58/1.02 %**** End of derivation protocol ****
% 3.58/1.02 %**** no. of clauses in derivation: 52 ****
% 3.58/1.02 %**** clause counter: 580 ****
% 3.58/1.02
% 3.58/1.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:580,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------