%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO031^1 : 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 : n012.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 0.10s 0.14s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 96 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 627 ( 183 equ; 0 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 544 ( 200 ~; 129 |; 0 &; 215 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 166 ( 139 ^; 23 !; 4 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_X,type,
sK1_X: ( $o > $o ) > $o ).
thf(1,conjecture,
~ ! [F: $o > $o] :
? [X: $o] :
( ( F @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
( ( ~ ! [F: $o > $o] :
? [X: $o] :
( ( F @ X )
= X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ! [F: $o > $o] :
? [X: $o] :
( ( F @ X )
= X ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [F: $o > $o] :
? [X: $o] :
( ( F @ X )
= X ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [F: $o > $o] :
( ( F @ ( sK1_X @ F ) )
= ( sK1_X @ F ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [F: $o > $o] :
( ( F @ ( sK1_X @ F ) )
= ( sK1_X @ F ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_X @ SV1 ) )
= ( sK1_X @ SV1 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( $true
= ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(9,plain,
( ( $false
= ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(10,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(11,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[6]) ).
thf(12,plain,
! [SV1: $o > $o] :
( ( ~ ( ( SV1 @ ( sK1_X @ SV1 ) )
| ( sK1_X @ SV1 ) )
| ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[7]) ).
thf(13,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_X @ SV1 ) )
= ( sK1_X @ SV1 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ ( $true
| ( sK1_X
@ ^ [SX0: $o] : $true ) )
| ~ ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[8]) ).
thf(15,plain,
( ( $true
= ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ ( $false
| ( sK1_X
@ ^ [SX0: $o] : $false ) )
| ~ ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9]) ).
thf(17,plain,
( ( $false
= ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
| ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[10]) ).
thf(19,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
| ~ ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[11]) ).
thf(21,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[11]) ).
thf(22,plain,
! [SV1: $o > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_X @ SV1 ) )
| ( sK1_X @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(23,plain,
( ( ( ~ ( $true
| ( sK1_X
@ ^ [SX0: $o] : $true ) ) )
= $true )
| ( ( ~ ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(24,plain,
( ( ( ~ ( $false
| ( sK1_X
@ ^ [SX0: $o] : $false ) ) )
= $true )
| ( ( ~ ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(25,plain,
( ( ( ~ ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ( sK1_X
@ ^ [SX0: $o] : SX0 ) ) )
= $true )
| ( ( ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(26,plain,
( ( ( ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV1: $o > $o] :
( ( ( ( SV1 @ ( sK1_X @ SV1 ) )
| ( sK1_X @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(28,plain,
( ( ( $true
| ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $false )
| ( ( ~ ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ( $false
| ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $false )
| ( ( ~ ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_X @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV1: $o > $o] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( ~ ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(35,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $false )
| ( ( ~ ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(36,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(37,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $false )
| ( ( ~ ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(38,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false )
| ( ( ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(39,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false )
| ( ( ~ ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(40,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( ~ ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(41,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false )
| ( ( ~ ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(42,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK1_X @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1 @ ( sK1_X @ SV1 ) )
| ~ ( sK1_X @ SV1 ) )
= $false )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(44,plain,
( ( ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $false )
| ( $true = $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(45,plain,
( ( ( ~ $true
| ~ ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(46,plain,
( ( ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(47,plain,
( ( ( ~ $false
| ~ ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(48,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(49,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(50,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true )
| ( ( ~ ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(51,plain,
( ( ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1 @ ( sK1_X @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK1_X @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(53,plain,
! [SV1: $o > $o] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $false )
| ( ( SV1 @ ( sK1_X @ SV1 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(54,plain,
! [SV1: $o > $o] :
( ( ( ~ ( SV1 @ ( sK1_X @ SV1 ) ) )
= $false )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(55,plain,
! [SV1: $o > $o] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $false )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(56,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(57,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $false )
| ( $true = $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(58,plain,
( ( ( ~ $true ) = $false )
| ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(59,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : $true ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(60,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(61,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(62,plain,
( ( ( ~ $false ) = $false )
| ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(63,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : $false ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(64,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(65,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(66,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(67,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(68,plain,
( ( ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
| ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(69,plain,
( ( ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(70,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(71,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_X @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_X @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(72,plain,
! [SV1: $o > $o] :
( ( ( sK1_X @ SV1 )
= $true )
| ( ( SV1 @ ( sK1_X @ SV1 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(73,plain,
! [SV1: $o > $o] :
( ( ( SV1 @ ( sK1_X @ SV1 ) )
= $true )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(74,plain,
! [SV1: $o > $o] :
( ( ( sK1_X @ SV1 )
= $true )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(75,plain,
( ( $true = $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(76,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $true )
| ( $true = $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(77,plain,
( ( $true = $true )
| ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(78,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : $true )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(79,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(80,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(81,plain,
( ( $false = $true )
| ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(82,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : $false )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(83,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(84,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(85,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(86,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(87,plain,
( ( ( ~ ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(88,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(89,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(90,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(91,plain,
( ( ( ~ ( sK1_X
@ ^ [SX0: $o] : ~ SX0 ) )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(92,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(93,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
( ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $false )
| ( ( sK1_X
@ ^ [SX0: $o] : ~ SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[13,94,93,92,90,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,21,19,17,15]) ).
thf(96,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO031^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 17:30:31 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.14
% 0.10/0.14 No.of.Axioms: 0
% 0.10/0.14
% 0.10/0.14 Length.of.Defs: 0
% 0.10/0.14
% 0.10/0.14 Contains.Choice.Funs: false
% 0.10/0.14
% 0.10/0.14 ********************************
% 0.10/0.14 * All subproblems solved! *
% 0.10/0.14 ********************************
% 0.10/0.14 % 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:95,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.14
% 0.10/0.14 %**** Beginning of derivation protocol ****
% 0.10/0.14 % SZS output start CNFRefutation
% See solution above
% 0.10/0.14
% 0.10/0.14 %**** End of derivation protocol ****
% 0.10/0.14 %**** no. of clauses in derivation: 96 ****
% 0.10/0.14 %**** clause counter: 95 ****
% 0.10/0.14
% 0.10/0.14 % 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:95,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------