%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL726^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:30:06 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 54 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 82 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 486 ( 114 ~; 61 |; 0 &; 287 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 231 ( 231 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 166 ( 0 ^; 144 !; 22 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_SX0,type,
sK1_SX0: ( ( a > $o ) > a ) > a > $o ).
thf(tp_sK2_SY9,type,
sK2_SY9: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK3_SY17,type,
sK3_SY17: ( ( a > $o ) > a ) > a ).
thf(tp_sK4_SY11,type,
sK4_SY11: ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(tp_sK5_SY11,type,
sK5_SY11: a > ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(tp_sK6_Eigen,type,
sK6_Eigen: ( a > $o ) > a ).
thf(1,conjecture,
( ! [Xs: ( a > $o ) > $o] :
( ! [X: a > $o] :
( ( Xs @ X )
=> ? [Xt: a] : ( X @ Xt ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) )
=> ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM534) ).
thf(2,negated_conjecture,
( ( ! [Xs: ( a > $o ) > $o] :
( ! [X: a > $o] :
( ( Xs @ X )
=> ? [Xt: a] : ( X @ Xt ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) )
=> ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xs: ( a > $o ) > $o] :
( ! [X: a > $o] :
( ( Xs @ X )
=> ? [Xt: a] : ( X @ Xt ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) )
=> ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xs: ( a > $o ) > $o] :
( ! [X: a > $o] :
( ( Xs @ X )
=> ? [Xt: a] : ( X @ Xt ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [Xs: ( a > $o ) > $o] :
( ! [X: a > $o] :
( ( Xs @ X )
=> ? [Xt: a] : ( X @ Xt ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [Xg: ( ( a > $o ) > a ) > a > $o] :
( ! [Xh: ( a > $o ) > a] :
? [Xu: a] : ( Xg @ Xh @ Xu )
=> ? [Xf: ( a > $o ) > a] : ( Xg @ Xf @ ( Xf @ ( Xg @ Xf ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: ( ( a > $o ) > a ) > a > $o] :
( ~ ! [SX1: ( a > $o ) > a] :
~ ! [SX2: a] :
~ ( SX0 @ SX1 @ SX2 )
| ~ ! [SX1: ( a > $o ) > a] :
~ ( SX0 @ SX1 @ ( SX1 @ ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SX0: ( a > $o ) > $o] :
( ~ ! [SX1: a > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: a] :
~ ( SX1 @ SX2 ) )
| ~ ! [SX1: ( a > $o ) > a] :
~ ! [SX2: a > $o] :
( ~ ( SX0 @ SX2 )
| ( SX2 @ ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: ( ( a > $o ) > a ) > a > $o] :
( ~ ! [SX1: ( a > $o ) > a] :
~ ! [SX2: a] :
~ ( SX0 @ SX1 @ SX2 )
| ~ ! [SX1: ( a > $o ) > a] :
~ ( SX0 @ SX1 @ ( SX1 @ ( SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: ( a > $o ) > $o] :
( ( ~ ! [SY9: a > $o] :
( ~ ( SV1 @ SY9 )
| ~ ! [SX2: a] :
~ ( SY9 @ SX2 ) )
| ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SY13: ( a > $o ) > a] :
~ ! [SY14: a] :
~ ( sK1_SX0 @ SY13 @ SY14 )
| ~ ! [SY15: ( a > $o ) > a] :
~ ( sK1_SX0 @ SY15 @ ( SY15 @ ( sK1_SX0 @ SY15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ! [SY9: a > $o] :
( ~ ( SV1 @ SY9 )
| ~ ! [SX2: a] :
~ ( SY9 @ SX2 ) ) )
= $true )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ! [SY13: ( a > $o ) > a] :
~ ! [SY14: a] :
~ ( sK1_SX0 @ SY13 @ SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY15: ( a > $o ) > a] :
~ ( sK1_SX0 @ SY15 @ ( SY15 @ ( sK1_SX0 @ SY15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ! [SY9: a > $o] :
( ~ ( SV1 @ SY9 )
| ~ ! [SX2: a] :
~ ( SY9 @ SX2 ) ) )
= $false )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SY13: ( a > $o ) > a] :
~ ! [SY14: a] :
~ ( sK1_SX0 @ SY13 @ SY14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY15: ( a > $o ) > a] :
~ ( sK1_SX0 @ SY15 @ ( SY15 @ ( sK1_SX0 @ SY15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY9 @ SV1 ) )
| ~ ! [SY16: a] :
~ ( sK2_SY9 @ SV1 @ SY16 ) )
= $false )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(21,plain,
! [SV2: ( a > $o ) > a] :
( ( ~ ! [SY17: a] :
~ ( sK1_SX0 @ SV2 @ SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: ( a > $o ) > a] :
( ( ~ ( sK1_SX0 @ SV3 @ ( SV3 @ ( sK1_SX0 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK2_SY9 @ SV1 ) ) )
= $false )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ! [SY16: a] :
~ ( sK2_SY9 @ SV1 @ SY16 ) )
= $false )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(25,plain,
! [SV2: ( a > $o ) > a] :
( ( ! [SY17: a] :
~ ( sK1_SX0 @ SV2 @ SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: ( a > $o ) > a] :
( ( sK1_SX0 @ SV3 @ ( SV3 @ ( sK1_SX0 @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ! [SY16: a] :
~ ( sK2_SY9 @ SV1 @ SY16 ) )
= $true )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV2: ( a > $o ) > a] :
( ( ~ ( sK1_SX0 @ SV2 @ ( sK3_SY17 @ SV2 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(30,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: a,SV1: ( a > $o ) > $o] :
( ( ( ~ ( sK2_SY9 @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: ( a > $o ) > a] :
( ( sK1_SX0 @ SV2 @ ( sK3_SY17 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ~ ! [SY18: a > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( sK4_SY11 @ SV1 @ SY18 ) ) ) )
= $false )
| ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(34,plain,
! [SV4: a,SV1: ( a > $o ) > $o] :
( ( ( sK2_SY9 @ SV1 @ SV4 )
= $false )
| ( ( ~ ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: ( a > $o ) > $o] :
( ( ( ! [SY18: a > $o] :
( ~ ( SV1 @ SY18 )
| ( SY18 @ ( sK4_SY11 @ SV1 @ SY18 ) ) ) )
= $true )
| ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV4: a,SV1: ( a > $o ) > $o] :
( ( ( ! [SY11: ( a > $o ) > a] :
~ ! [SY12: a > $o] :
( ~ ( SV1 @ SY12 )
| ( SY12 @ ( SY11 @ SY12 ) ) ) )
= $false )
| ( ( sK2_SY9 @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: a > $o,SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ SV5 )
| ( SV5 @ ( sK4_SY11 @ SV1 @ SV5 ) ) )
= $true )
| ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV4: a,SV1: ( a > $o ) > $o] :
( ( ( ~ ! [SY19: a > $o] :
( ~ ( SV1 @ SY19 )
| ( SY19 @ ( sK5_SY11 @ SV4 @ SV1 @ SY19 ) ) ) )
= $false )
| ( ( sK2_SY9 @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(39,plain,
! [SV5: a > $o,SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ SV5 ) )
= $true )
| ( ( SV5 @ ( sK4_SY11 @ SV1 @ SV5 ) )
= $true )
| ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV4: a,SV1: ( a > $o ) > $o] :
( ( ( ! [SY19: a > $o] :
( ~ ( SV1 @ SY19 )
| ( SY19 @ ( sK5_SY11 @ SV4 @ SV1 @ SY19 ) ) ) )
= $true )
| ( ( sK2_SY9 @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV5: a > $o,SV1: ( a > $o ) > $o] :
( ( ( SV1 @ SV5 )
= $false )
| ( ( SV5 @ ( sK4_SY11 @ SV1 @ SV5 ) )
= $true )
| ( ( SV1 @ ( sK2_SY9 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV4: a,SV6: a > $o,SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ SV6 )
| ( SV6 @ ( sK5_SY11 @ SV4 @ SV1 @ SV6 ) ) )
= $true )
| ( ( sK2_SY9 @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV4: a,SV6: a > $o,SV1: ( a > $o ) > $o] :
( ( ( ~ ( SV1 @ SV6 ) )
= $true )
| ( ( SV6 @ ( sK5_SY11 @ SV4 @ SV1 @ SV6 ) )
= $true )
| ( ( sK2_SY9 @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV4: a,SV6: a > $o,SV1: ( a > $o ) > $o] :
( ( ( SV1 @ SV6 )
= $false )
| ( ( SV6 @ ( sK5_SY11 @ SV4 @ SV1 @ SV6 ) )
= $true )
| ( ( sK2_SY9 @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
( ( sK1_SX0 @ sK6_Eigen @ ( sK6_Eigen @ ( sK1_SX0 @ sK6_Eigen ) ) )
= $false ),
inference(instantiate,[status(thm)],[26:[bind(SV3,$thf( sK6_Eigen ))]]) ).
thf(46,plain,
! [SV3: ( a > $o ) > a] :
( ( ~ ~ ! [SV7: a] :
~ ( sK1_SX0 @ SV3 @ SV7 )
| ( sK1_SX0 @ SV3 @ ( sK6_Eigen @ ( sK1_SX0 @ SV3 ) ) ) )
= $true ),
inference(choice,[status(thm)],[26]) ).
thf(47,plain,
! [SV8: ( a > $o ) > a] :
( ( ~ ~ ! [SX0: a] :
~ ( sK1_SX0 @ SV8 @ SX0 )
| ( sK1_SX0 @ SV8 @ ( sK6_Eigen @ ( sK1_SX0 @ SV8 ) ) ) )
= $true ),
inference(rename,[status(thm)],[46]) ).
thf(48,plain,
! [SV8: ( a > $o ) > a] :
( ( ( ~ ~ ! [SX0: a] :
~ ( sK1_SX0 @ SV8 @ SX0 ) )
= $true )
| ( ( sK1_SX0 @ SV8 @ ( sK6_Eigen @ ( sK1_SX0 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(49,plain,
! [SV8: ( a > $o ) > a] :
( ( ( ~ ! [SX0: a] :
~ ( sK1_SX0 @ SV8 @ SX0 ) )
= $false )
| ( ( sK1_SX0 @ SV8 @ ( sK6_Eigen @ ( sK1_SX0 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
! [SV8: ( a > $o ) > a] :
( ( ( ! [SX0: a] :
~ ( sK1_SX0 @ SV8 @ SX0 ) )
= $true )
| ( ( sK1_SX0 @ SV8 @ ( sK6_Eigen @ ( sK1_SX0 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(51,plain,
! [SV9: a,SV8: ( a > $o ) > a] :
( ( ( ~ ( sK1_SX0 @ SV8 @ SV9 ) )
= $true )
| ( ( sK1_SX0 @ SV8 @ ( sK6_Eigen @ ( sK1_SX0 @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(52,plain,
! [SV9: a,SV8: ( a > $o ) > a] :
( ( ( sK1_SX0 @ SV8 @ SV9 )
= $false )
| ( ( sK1_SX0 @ SV8 @ ( sK6_Eigen @ ( sK1_SX0 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,52,45,44,41,32]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21 % Computer : n013.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 12:32:21 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
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% 0.08/0.27 No.of.Axioms: 0
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% 0.08/0.27 Length.of.Defs: 0
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% 0.08/0.27 Contains.Choice.Funs: false
% 0.08/0.27 .
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% 0.08/0.27 *** Modified list of choice operators: sK6_Eigen ***
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% 0.08/0.27 ********************************
% 0.08/0.27 * All subproblems solved! *
% 0.08/0.27 ********************************
% 0.08/0.27 % 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:53,loop_count:0,foatp_calls:2,translation:fof_full)
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% 0.08/0.27 %**** Beginning of derivation protocol ****
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
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% 0.08/0.27 %**** End of derivation protocol ****
% 0.08/0.27 %**** no. of clauses in derivation: 54 ****
% 0.08/0.27 %**** clause counter: 53 ****
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% 0.08/0.27 % 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:53,loop_count:0,foatp_calls:2,translation:fof_full)
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