%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL731^5 : 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 : n018.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 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 88 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 332 ( 126 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 817 ( 248 ~; 116 |; 0 &; 408 @)
% ( 3 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 317 ( 317 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 284 ( 0 ^; 248 !; 36 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK10_Eigen,type,
sK10_Eigen: ( a > $o ) > a ).
thf(tp_sK1_SX0,type,
sK1_SX0: ( a > $o ) > $o ).
thf(tp_sK2_SX0,type,
sK2_SX0: ( a > $o ) > a ).
thf(tp_sK3_SY15,type,
sK3_SY15: ( ( a > $o ) > a ) > a > $o ).
thf(tp_sK4_SY14,type,
sK4_SY14: ( a > $o ) > a ).
thf(tp_sK5_SY21,type,
sK5_SY21: ( ( a > $o ) > a ) > a > $o ).
thf(tp_sK6_SY17,type,
sK6_SY17: ( ( a > $o ) > $o ) > a > $o ).
thf(tp_sK7_SY23,type,
sK7_SY23: ( ( a > $o ) > a ) > a ).
thf(tp_sK8_SY19,type,
sK8_SY19: ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(tp_sK9_SY19,type,
sK9_SY19: a > ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(1,conjecture,
( ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
<=> ! [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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM541) ).
thf(2,negated_conjecture,
( ( ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
<=> ! [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 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
<=> ! [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 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ! [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 ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,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 ) ) ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ! [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(polarity_switch,[status(thm)],[4]) ).
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 ) ) ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ~ ( ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ! [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)],[6]) ).
thf(9,plain,
( ( ~ ( ~ ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) )
| ! [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)],[8]) ).
thf(10,plain,
( ( ~ ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) )
| ! [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 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(12,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 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SY8: a > $o] :
( ~ ( sK1_SX0 @ SY8 )
| ~ ! [SX2: a] :
~ ( SY8 @ SX2 ) )
| ~ ! [SY10: ( a > $o ) > a] :
~ ! [SY11: a > $o] :
( ~ ( sK1_SX0 @ SY11 )
| ( SY11 @ ( SY10 @ SY11 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(15,plain,
( ( ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY8: a > $o] :
( ~ ( sK1_SX0 @ SY8 )
| ~ ! [SX2: a] :
~ ( SY8 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SY10: ( a > $o ) > a] :
~ ! [SY11: a > $o] :
( ~ ( sK1_SX0 @ SY11 )
| ( SY11 @ ( SY10 @ SY11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ! [SY12: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SY12 @ SX2 )
| ( SY12 @ ( sK2_SX0 @ SY12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(19,plain,
( ( ! [SY8: a > $o] :
( ~ ( sK1_SX0 @ SY8 )
| ~ ! [SX2: a] :
~ ( SY8 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SY10: ( a > $o ) > a] :
~ ! [SY11: a > $o] :
( ~ ( sK1_SX0 @ SY11 )
| ( SY11 @ ( SY10 @ SY11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ! [SY12: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SY12 @ SX2 )
| ( SY12 @ ( sK2_SX0 @ SY12 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: a > $o] :
( ( ~ ( sK1_SX0 @ SV1 )
| ~ ! [SY14: a] :
~ ( SV1 @ SY14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: ( a > $o ) > a] :
( ( ~ ! [SY15: a > $o] :
( ~ ( sK1_SX0 @ SY15 )
| ( SY15 @ ( SV2 @ SY15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV3: a > $o] :
( ( ~ ~ ! [SY16: a] :
~ ( SV3 @ SY16 )
| ( SV3 @ ( sK2_SX0 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: a > $o] :
( ( ( ~ ( sK1_SX0 @ SV1 ) )
= $true )
| ( ( ~ ! [SY14: a] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: ( a > $o ) > a] :
( ( ! [SY15: a > $o] :
( ~ ( sK1_SX0 @ SY15 )
| ( SY15 @ ( SV2 @ SY15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV3: a > $o] :
( ( ( ~ ~ ! [SY16: a] :
~ ( SV3 @ SY16 ) )
= $true )
| ( ( SV3 @ ( sK2_SX0 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: a > $o] :
( ( ( sK1_SX0 @ SV1 )
= $false )
| ( ( ~ ! [SY14: a] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: ( a > $o ) > a] :
( ( ~ ( sK1_SX0 @ ( sK3_SY15 @ SV2 ) )
| ( sK3_SY15 @ SV2 @ ( SV2 @ ( sK3_SY15 @ SV2 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(30,plain,
! [SV3: a > $o] :
( ( ( ~ ! [SY16: a] :
~ ( SV3 @ SY16 ) )
= $false )
| ( ( SV3 @ ( sK2_SX0 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: a > $o] :
( ( ( ! [SY14: a] :
~ ( SV1 @ SY14 ) )
= $false )
| ( ( sK1_SX0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: ( a > $o ) > a] :
( ( ~ ( sK1_SX0 @ ( sK3_SY15 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: ( a > $o ) > a] :
( ( sK3_SY15 @ SV2 @ ( SV2 @ ( sK3_SY15 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: a > $o] :
( ( ( ! [SY16: a] :
~ ( SV3 @ SY16 ) )
= $true )
| ( ( SV3 @ ( sK2_SX0 @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK4_SY14 @ SV1 ) ) )
= $false )
| ( ( sK1_SX0 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(36,plain,
! [SV2: ( a > $o ) > a] :
( ( sK1_SX0 @ ( sK3_SY15 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: a,SV3: a > $o] :
( ( ( ~ ( SV3 @ SV4 ) )
= $true )
| ( ( SV3 @ ( sK2_SX0 @ SV3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV1: a > $o] :
( ( ( SV1 @ ( sK4_SY14 @ SV1 ) )
= $true )
| ( ( sK1_SX0 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV4: a,SV3: a > $o] :
( ( ( SV3 @ SV4 )
= $false )
| ( ( SV3 @ ( sK2_SX0 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,39,38,36]) ).
thf(41,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 ) ) ) )
=> ? [Xf: ( a > $o ) > a] :
! [X: a > $o] :
( ? [Xt: a] : ( X @ Xt )
=> ( X @ ( Xf @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(42,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 ) ) ) )
| ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(43,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 ) ) ) )
| ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,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 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(45,plain,
( ( ~ ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(46,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(extcnf_not_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ! [SX0: ( a > $o ) > a] :
~ ! [SX1: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SX1 @ SX2 )
| ( SX1 @ ( SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,plain,
! [SV5: ( a > $o ) > $o] :
( ( ~ ! [SY17: a > $o] :
( ~ ( SV5 @ SY17 )
| ~ ! [SX2: a] :
~ ( SY17 @ SX2 ) )
| ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(49,plain,
! [SV6: ( a > $o ) > a] :
( ( ~ ! [SY21: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SY21 @ SX2 )
| ( SY21 @ ( SV6 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY17: a > $o] :
( ~ ( SV5 @ SY17 )
| ~ ! [SX2: a] :
~ ( SY17 @ SX2 ) ) )
= $true )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV6: ( a > $o ) > a] :
( ( ! [SY21: a > $o] :
( ~ ~ ! [SX2: a] :
~ ( SY21 @ SX2 )
| ( SY21 @ ( SV6 @ SY21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY17: a > $o] :
( ~ ( SV5 @ SY17 )
| ~ ! [SX2: a] :
~ ( SY17 @ SX2 ) ) )
= $false )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV6: ( a > $o ) > a] :
( ( ~ ~ ! [SY23: a] :
~ ( sK5_SY21 @ SV6 @ SY23 )
| ( sK5_SY21 @ SV6 @ ( SV6 @ ( sK5_SY21 @ SV6 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(54,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK6_SY17 @ SV5 ) )
| ~ ! [SY24: a] :
~ ( sK6_SY17 @ SV5 @ SY24 ) )
= $false )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[52]) ).
thf(55,plain,
! [SV6: ( a > $o ) > a] :
( ( ~ ~ ! [SY23: a] :
~ ( sK5_SY21 @ SV6 @ SY23 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV6: ( a > $o ) > a] :
( ( sK5_SY21 @ SV6 @ ( SV6 @ ( sK5_SY21 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK6_SY17 @ SV5 ) ) )
= $false )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY24: a] :
~ ( sK6_SY17 @ SV5 @ SY24 ) )
= $false )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV6: ( a > $o ) > a] :
( ( ~ ! [SY23: a] :
~ ( sK5_SY21 @ SV6 @ SY23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(61,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY24: a] :
~ ( sK6_SY17 @ SV5 @ SY24 ) )
= $true )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV6: ( a > $o ) > a] :
( ( ! [SY23: a] :
~ ( sK5_SY21 @ SV6 @ SY23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $false )
| ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV7: a,SV5: ( a > $o ) > $o] :
( ( ( ~ ( sK6_SY17 @ SV5 @ SV7 ) )
= $true )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV6: ( a > $o ) > a] :
( ( ~ ( sK5_SY21 @ SV6 @ ( sK7_SY23 @ SV6 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(66,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY25: a > $o] :
( ~ ( SV5 @ SY25 )
| ( SY25 @ ( sK8_SY19 @ SV5 @ SY25 ) ) ) )
= $false )
| ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(67,plain,
! [SV7: a,SV5: ( a > $o ) > $o] :
( ( ( sK6_SY17 @ SV5 @ SV7 )
= $false )
| ( ( ~ ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV6: ( a > $o ) > a] :
( ( sK5_SY21 @ SV6 @ ( sK7_SY23 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV5: ( a > $o ) > $o] :
( ( ( ! [SY25: a > $o] :
( ~ ( SV5 @ SY25 )
| ( SY25 @ ( sK8_SY19 @ SV5 @ SY25 ) ) ) )
= $true )
| ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(70,plain,
! [SV7: a,SV5: ( a > $o ) > $o] :
( ( ( ! [SY19: ( a > $o ) > a] :
~ ! [SY20: a > $o] :
( ~ ( SV5 @ SY20 )
| ( SY20 @ ( SY19 @ SY20 ) ) ) )
= $false )
| ( ( sK6_SY17 @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV8: a > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ SV8 )
| ( SV8 @ ( sK8_SY19 @ SV5 @ SV8 ) ) )
= $true )
| ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV7: a,SV5: ( a > $o ) > $o] :
( ( ( ~ ! [SY26: a > $o] :
( ~ ( SV5 @ SY26 )
| ( SY26 @ ( sK9_SY19 @ SV7 @ SV5 @ SY26 ) ) ) )
= $false )
| ( ( sK6_SY17 @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(73,plain,
! [SV8: a > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ SV8 ) )
= $true )
| ( ( SV8 @ ( sK8_SY19 @ SV5 @ SV8 ) )
= $true )
| ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV7: a,SV5: ( a > $o ) > $o] :
( ( ( ! [SY26: a > $o] :
( ~ ( SV5 @ SY26 )
| ( SY26 @ ( sK9_SY19 @ SV7 @ SV5 @ SY26 ) ) ) )
= $true )
| ( ( sK6_SY17 @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(75,plain,
! [SV8: a > $o,SV5: ( a > $o ) > $o] :
( ( ( SV5 @ SV8 )
= $false )
| ( ( SV8 @ ( sK8_SY19 @ SV5 @ SV8 ) )
= $true )
| ( ( SV5 @ ( sK6_SY17 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV7: a,SV9: a > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ SV9 )
| ( SV9 @ ( sK9_SY19 @ SV7 @ SV5 @ SV9 ) ) )
= $true )
| ( ( sK6_SY17 @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(77,plain,
! [SV7: a,SV9: a > $o,SV5: ( a > $o ) > $o] :
( ( ( ~ ( SV5 @ SV9 ) )
= $true )
| ( ( SV9 @ ( sK9_SY19 @ SV7 @ SV5 @ SV9 ) )
= $true )
| ( ( sK6_SY17 @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(78,plain,
! [SV7: a,SV9: a > $o,SV5: ( a > $o ) > $o] :
( ( ( SV5 @ SV9 )
= $false )
| ( ( SV9 @ ( sK9_SY19 @ SV7 @ SV5 @ SV9 ) )
= $true )
| ( ( sK6_SY17 @ SV5 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(79,plain,
( ( sK5_SY21 @ sK10_Eigen @ ( sK10_Eigen @ ( sK5_SY21 @ sK10_Eigen ) ) )
= $false ),
inference(instantiate,[status(thm)],[56:[bind(SV6,$thf( sK10_Eigen ))]]) ).
thf(80,plain,
! [SV6: ( a > $o ) > a] :
( ( ~ ~ ! [SV10: a] :
~ ( sK5_SY21 @ SV6 @ SV10 )
| ( sK5_SY21 @ SV6 @ ( sK10_Eigen @ ( sK5_SY21 @ SV6 ) ) ) )
= $true ),
inference(choice,[status(thm)],[56]) ).
thf(81,plain,
! [SV11: ( a > $o ) > a] :
( ( ~ ~ ! [SX0: a] :
~ ( sK5_SY21 @ SV11 @ SX0 )
| ( sK5_SY21 @ SV11 @ ( sK10_Eigen @ ( sK5_SY21 @ SV11 ) ) ) )
= $true ),
inference(rename,[status(thm)],[80]) ).
thf(82,plain,
! [SV11: ( a > $o ) > a] :
( ( ( ~ ~ ! [SX0: a] :
~ ( sK5_SY21 @ SV11 @ SX0 ) )
= $true )
| ( ( sK5_SY21 @ SV11 @ ( sK10_Eigen @ ( sK5_SY21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(83,plain,
! [SV11: ( a > $o ) > a] :
( ( ( ~ ! [SX0: a] :
~ ( sK5_SY21 @ SV11 @ SX0 ) )
= $false )
| ( ( sK5_SY21 @ SV11 @ ( sK10_Eigen @ ( sK5_SY21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(84,plain,
! [SV11: ( a > $o ) > a] :
( ( ( ! [SX0: a] :
~ ( sK5_SY21 @ SV11 @ SX0 ) )
= $true )
| ( ( sK5_SY21 @ SV11 @ ( sK10_Eigen @ ( sK5_SY21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(85,plain,
! [SV12: a,SV11: ( a > $o ) > a] :
( ( ( ~ ( sK5_SY21 @ SV11 @ SV12 ) )
= $true )
| ( ( sK5_SY21 @ SV11 @ ( sK10_Eigen @ ( sK5_SY21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(86,plain,
! [SV12: a,SV11: ( a > $o ) > a] :
( ( ( sK5_SY21 @ SV11 @ SV12 )
= $false )
| ( ( sK5_SY21 @ SV11 @ ( sK10_Eigen @ ( sK5_SY21 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(87,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,86,79,78,75,68]) ).
thf(88,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[87,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL731^5 : 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
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 12:35:21 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 0
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 0
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23 ..
% 0.07/0.23
% 0.07/0.23 *** Modified list of choice operators: sK10_Eigen ***
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:87,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 88 ****
% 0.07/0.23 %**** clause counter: 87 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:0,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:87,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------