%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO030^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 11:07:24 AM UTC 2026
% Result : Theorem 0.11s 0.19s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 101 ( 39 unt; 0 typ; 1 def)
% Number of atoms : 538 ( 161 equ; 0 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 408 ( 135 ~; 94 |; 0 &; 176 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 78 ^; 43 !; 4 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_leibeq,type,
leibeq: $o > $o > $o ).
thf(tp_sK1_SY1,type,
sK1_SY1: ( $o > $o ) > $o ).
thf(leibeq,definition,
( leibeq
= ( ^ [X: $o,Y: $o] :
! [P: $o > $o] :
( ( P @ X )
=> ( P @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq) ).
thf(1,conjecture,
~ ! [F: $o > $o] :
? [X: $o] : ( leibeq @ ( F @ X ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ~ ! [F: $o > $o] :
? [X: $o] : ( leibeq @ ( F @ X ) @ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ! [SY0: $o > $o] :
? [SY1: $o] :
! [SY4: $o > $o] :
( ( SY4 @ ( SY0 @ SY1 ) )
=> ( SY4 @ SY1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,leibeq]) ).
thf(4,plain,
( ( ! [SY0: $o > $o] :
? [SY1: $o] :
! [SY4: $o > $o] :
( ( SY4 @ ( SY0 @ SY1 ) )
=> ( SY4 @ SY1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $o > $o,SY8: $o > $o] :
( ~ ( SY8 @ ( SY0 @ ( sK1_SY1 @ SY0 ) ) )
| ( SY8 @ ( sK1_SY1 @ SY0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY0: $o > $o,SY8: $o > $o] :
( ~ ( SY8 @ ( SY0 @ ( sK1_SY1 @ SY0 ) ) )
| ( SY8 @ ( sK1_SY1 @ SY0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
! [SV1: $o > $o] :
( ( ! [SY9: $o > $o] :
( ~ ( SY9 @ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
| ( SY9 @ ( sK1_SY1 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $o > $o] :
( ~ ( SX0 @ $true )
| ( SX0
@ ( sK1_SY1
@ ^ [SX1: $o] : $true ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SX0: $o > $o] :
( ~ ( SX0 @ $false )
| ( SX0
@ ( sK1_SY1
@ ^ [SX1: $o] : $false ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(10,plain,
( ( ! [SX0: $o > $o] :
( ~ ( SX0
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) )
| ( SX0
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(11,plain,
( ( ! [SX0: $o > $o] :
( ~ ( SX0
@ ~ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) )
| ( SX0
@ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(12,plain,
! [SV1: $o > $o,SV3: $o > $o] :
( ( ~ ( SV3 @ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
| ( SV3 @ ( sK1_SY1 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(13,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(15,plain,
! [SV1: $o > $o] :
( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) )
| ( sK1_SY1 @ SV1 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(16,plain,
! [SV1: $o > $o] :
( ( ~ ~ ( SV1 @ ( sK1_SY1 @ SV1 ) )
| ~ ( sK1_SY1 @ SV1 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[7]) ).
thf(17,plain,
! [SV5: $o > $o] :
( ( ~ ( SV5 @ $true )
| ( SV5
@ ( sK1_SY1
@ ^ [SX1: $o] : $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[8]) ).
thf(18,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[8]) ).
thf(19,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[8]) ).
thf(20,plain,
( ( ~ $true
| ( sK1_SY1
@ ^ [SX0: $o] : $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[8]) ).
thf(21,plain,
( ( ~ ~ $true
| ~ ( sK1_SY1
@ ^ [SX0: $o] : $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[8]) ).
thf(22,plain,
! [SV7: $o > $o] :
( ( ~ ( SV7 @ $false )
| ( SV7
@ ( sK1_SY1
@ ^ [SX1: $o] : $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(23,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(24,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(25,plain,
( ( ~ $false
| ( sK1_SY1
@ ^ [SX0: $o] : $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(26,plain,
( ( ~ ~ $false
| ~ ( sK1_SY1
@ ^ [SX0: $o] : $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(27,plain,
! [SV9: $o > $o] :
( ( ~ ( SV9
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) )
| ( SV9
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[10]) ).
thf(28,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[10]) ).
thf(29,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[10]) ).
thf(30,plain,
( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
| ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[10]) ).
thf(31,plain,
( ( ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[10]) ).
thf(32,plain,
! [SV11: $o > $o] :
( ( ~ ( SV11
@ ~ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) )
| ( SV11
@ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(33,plain,
( ( ~ $true
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(34,plain,
( ( ~ $false
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(35,plain,
( ( ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
| ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(36,plain,
( ( ~ ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[11]) ).
thf(37,plain,
! [SV1: $o > $o,SV3: $o > $o] :
( ( ( ~ ( SV3 @ ( SV1 @ ( sK1_SY1 @ SV1 ) ) ) )
= $true )
| ( ( SV3 @ ( sK1_SY1 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(38,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(39,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(40,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
= $true )
| ( ( sK1_SY1 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(41,plain,
! [SV1: $o > $o] :
( ( ( ~ ~ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
= $true )
| ( ( ~ ( sK1_SY1 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(42,plain,
! [SV5: $o > $o] :
( ( ( ~ ( SV5 @ $true ) )
= $true )
| ( ( SV5
@ ( sK1_SY1
@ ^ [SX1: $o] : $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(43,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(44,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(45,plain,
( ( ( ~ $true ) = $true )
| ( ( sK1_SY1
@ ^ [SX0: $o] : $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(46,plain,
( ( ( ~ ~ $true )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(47,plain,
! [SV7: $o > $o] :
( ( ( ~ ( SV7 @ $false ) )
= $true )
| ( ( SV7
@ ( sK1_SY1
@ ^ [SX1: $o] : $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(48,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(49,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(50,plain,
( ( ( ~ $false ) = $true )
| ( ( sK1_SY1
@ ^ [SX0: $o] : $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(51,plain,
( ( ( ~ ~ $false )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(52,plain,
! [SV9: $o > $o] :
( ( ( ~ ( SV9
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) ) )
= $true )
| ( ( SV9
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(53,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(54,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(55,plain,
( ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(56,plain,
( ( ( ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(57,plain,
! [SV11: $o > $o] :
( ( ( ~ ( SV11
@ ~ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) ) )
= $true )
| ( ( SV11
@ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(58,plain,
( ( ( ~ $true ) = $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(59,plain,
( ( ( ~ $false ) = $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(60,plain,
( ( ( ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(61,plain,
( ( ( ~ ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(62,plain,
! [SV1: $o > $o,SV3: $o > $o] :
( ( ( SV3 @ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
= $false )
| ( ( SV3 @ ( sK1_SY1 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(63,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(64,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(65,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_SY1 @ SV1 ) )
= $false )
| ( ( sK1_SY1 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(66,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1 @ ( sK1_SY1 @ SV1 ) ) )
= $false )
| ( ( ~ ( sK1_SY1 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(67,plain,
! [SV5: $o > $o] :
( ( ( SV5 @ $true )
= $false )
| ( ( SV5
@ ( sK1_SY1
@ ^ [SX1: $o] : $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(68,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(69,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(70,plain,
( ( $true = $false )
| ( ( sK1_SY1
@ ^ [SX0: $o] : $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(71,plain,
( ( ( ~ $true ) = $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(72,plain,
! [SV7: $o > $o] :
( ( ( SV7 @ $false )
= $false )
| ( ( SV7
@ ( sK1_SY1
@ ^ [SX1: $o] : $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(73,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(74,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(75,plain,
( ( $false = $false )
| ( ( sK1_SY1
@ ^ [SX0: $o] : $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(76,plain,
( ( ( ~ $false ) = $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(77,plain,
! [SV9: $o > $o] :
( ( ( SV9
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) )
= $false )
| ( ( SV9
@ ( sK1_SY1
@ ^ [SX1: $o] : SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(78,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(79,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(80,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(81,plain,
( ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(82,plain,
! [SV11: $o > $o] :
( ( ( SV11
@ ~ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) )
= $false )
| ( ( SV11
@ ( sK1_SY1
@ ^ [SX1: $o] : ~ SX1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(83,plain,
( ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(84,plain,
( ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(85,plain,
( ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(86,plain,
( ( ( ~ ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(87,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_SY1 @ SV1 ) )
= $true )
| ( ( ~ ( sK1_SY1 @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(88,plain,
( ( $true = $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(89,plain,
( ( $false = $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : $false ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(90,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(91,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $true )
| ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(92,plain,
( ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(93,plain,
! [SV1: $o > $o] :
( ( ( sK1_SY1 @ SV1 )
= $false )
| ( ( SV1 @ ( sK1_SY1 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : $true )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(95,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : $false )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $o] : SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $false )
| ( ( ~ ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
( ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $false )
| ( ( sK1_SY1
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(99,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,98,96,95,94,93,91,84,83,82,80,79,78,77,75,74,73,72,70,69,68,67,65,64,63]) ).
thf(100,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO030^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.15 % Computer : n002.cluster.edu
% 0.11/0.15 % Model : x86_64 x86_64
% 0.11/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.15 % Memory : 8046.5625MB
% 0.11/0.15 % OS : Linux 6.8.0-71-generic
% 0.11/0.15 % CPULimit : 300
% 0.11/0.15 % WCLimit : 300
% 0.11/0.15 % DateTime : Tue Oct 6 17:33:42 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.19
% 0.11/0.19 No.of.Axioms: 0
% 0.11/0.19
% 0.11/0.19 Length.of.Defs: 151
% 0.11/0.19
% 0.11/0.19 Contains.Choice.Funs: false
% 0.11/0.19
% 0.11/0.19 ********************************
% 0.11/0.19 * All subproblems solved! *
% 0.11/0.19 ********************************
% 0.11/0.19 % 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:99,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.19
% 0.11/0.19 %**** Beginning of derivation protocol ****
% 0.11/0.19 % SZS output start CNFRefutation
% See solution above
% 0.11/0.19
% 0.11/0.19 %**** End of derivation protocol ****
% 0.11/0.19 %**** no. of clauses in derivation: 100 ****
% 0.11/0.19 %**** clause counter: 99 ****
% 0.11/0.19
% 0.11/0.19 % 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:99,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------