%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET636^5 : 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 : n001.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 10:40:41 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 1
% Syntax : Number of formulae : 96 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 629 ( 181 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 726 ( 311 ~; 152 |; 22 &; 230 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 40 ^; 55 !; 11 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY5,type,
sK2_SY5: a > $o ).
thf(tp_sK3_SV1,type,
sK3_SV1: a ).
thf(tp_sK4_SX0,type,
sK4_SX0: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o] :
( ~ ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) )
<=> ( ( ^ [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) ) )
= ( ^ [Xx: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_118_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o] :
( ~ ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) )
<=> ( ( ^ [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ~ ? [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) )
<=> ( ( ^ [Xx: a] :
( ( X @ Xx )
& ( Y @ Xx ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY5: a > $o] :
( ~ ? [SY6: a] :
( ( sK1_X @ SY6 )
& ( SY5 @ SY6 ) )
<=> ( ( ^ [SY7: a] :
( ( sK1_X @ SY7 )
& ( SY5 @ SY7 ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) )
<=> ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) )
=> ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) )
=> ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ( ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) )
=> ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) )
=> ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) )
=> ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) )
| ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) )
| ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SV1: a] :
( ( ~ ( ~ ( sK1_X @ SV1 )
| ~ ( sK2_SY5 @ SV1 ) ) )
= $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) ) )
= $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
( ( ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
| $false )
| ~ ( ~ ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
| ~ $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) ) )
= $false )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: a] :
( ( ~ ~ ( ~ ( sK1_X @ SV2 )
| ~ ( sK2_SY5 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( ~ ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
| ~ $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: a] :
( ( ~ ( ~ ( sK1_X @ SV2 )
| ~ ( sK2_SY5 @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
| ~ $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: a] :
( ( ~ ( sK1_X @ SV2 )
| ~ ( sK2_SY5 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: a] :
( ( ( ~ ( sK1_X @ SV2 ) )
= $true )
| ( ( ~ ( sK2_SY5 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ~ ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) ) )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV2: a] :
( ( ( sK1_X @ SV2 )
= $false )
| ( ( ~ ( sK2_SY5 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ~ ( sK1_X @ sK3_SV1 ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
( ( ( ~ ( sK2_SY5 @ sK3_SV1 ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( ( ~ ( sK1_X @ sK3_SV1 )
| ~ ( sK2_SY5 @ sK3_SV1 ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: a] :
( ( ( sK2_SY5 @ SV2 )
= $false )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ( sK1_X @ sK3_SV1 )
= $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
( ( ( sK2_SY5 @ sK3_SV1 )
= $true )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
( ( ( ~ ( sK1_X @ sK3_SV1 ) )
= $true )
| ( ( ~ ( sK2_SY5 @ sK3_SV1 ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( ~ ( sK2_SY5 @ sK3_SV1 ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
( ( ( sK2_SY5 @ sK3_SV1 )
= $false )
| ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
( ( $false = $false )
| ( ( sK1_X @ sK3_SV1 )
= $false )
| ( ( sK2_SY5 @ sK3_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,45,41,40,39,22]) ).
thf(47,plain,
( ( ~ ( ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( sK2_SY5 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) )
=> ~ ? [SY9: a] :
( ( sK1_X @ SY9 )
& ( sK2_SY5 @ SY9 ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(48,plain,
( ( ~ ( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
!= ( ^ [SX0: a] : $false ) )
| ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(49,plain,
( ( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
!= ( ^ [SX0: a] : $false ) )
| ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(50,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
!= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(51,plain,
( ( ~ ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(52,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(53,plain,
( ( ~ ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(54,plain,
( ( ! [SV3: a] :
( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK2_SY5 @ SV3 ) ) )
= $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[52]) ).
thf(55,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[52]) ).
thf(56,plain,
( ( ! [SX0: a] :
~ ~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK2_SY5 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(58,plain,
( ( ~ ~ ( ~ ( sK1_X @ sK4_SX0 )
| ~ ( sK2_SY5 @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(59,plain,
! [SV4: a] :
( ( ~ ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| $false )
| ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( ~ ( ~ ( sK1_X @ sK4_SX0 )
| ~ ( sK2_SY5 @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
( ( ~ ( sK1_X @ sK4_SX0 )
| ~ ( sK2_SY5 @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
( ( ~ ( sK1_X @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ( sK2_SY5 @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV4: a] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( sK1_X @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( sK2_SY5 @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV4: a] :
( ( ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV4: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV4: a] :
( ( ( ~ ( sK1_X @ SV4 ) )
= $true )
| ( ( ~ ( sK2_SY5 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV4: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV4: a] :
( ( ( sK1_X @ SV4 )
= $false )
| ( ( ~ ( sK2_SY5 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(79,plain,
! [SV4: a] :
( ( ( sK2_SY5 @ SV4 )
= $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV4: a] :
( ( ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(81,plain,
! [SV4: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
| ~ $false )
= $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(82,plain,
! [SV4: a] :
( ( ( ~ ( sK1_X @ SV4 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(83,plain,
! [SV4: a] :
( ( ( ~ ( sK2_SY5 @ SV4 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV4: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(85,plain,
! [SV4: a] :
( ( ( ~ $false ) = $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV4: a] :
( ( ( sK1_X @ SV4 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV4: a] :
( ( ( sK2_SY5 @ SV4 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV4: a] :
( ( ( ~ ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) ) )
= $true )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV4: a] :
( ( $false = $true )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV4: a] :
( ( ( ~ ( sK1_X @ SV4 )
| ~ ( sK2_SY5 @ SV4 ) )
= $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV4: a] :
( ( ( ~ ( sK1_X @ SV4 ) )
= $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(92,plain,
! [SV4: a] :
( ( ( ~ ( sK2_SY5 @ SV4 ) )
= $false )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(93,plain,
! [SV4: a] :
( ( ( sK1_X @ SV4 )
= $true )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(94,plain,
! [SV4: a] :
( ( ( sK2_SY5 @ SV4 )
= $true )
| ( ( sK1_X @ SV4 )
= $false )
| ( ( sK2_SY5 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(95,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,94,93,89,87,86,78,70,69,60]) ).
thf(96,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[95,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET636^5 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n001.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 14:53:54 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.24
% 0.06/0.24 No.of.Axioms: 0
% 0.06/0.24
% 0.06/0.24 Length.of.Defs: 0
% 0.06/0.24
% 0.06/0.24 Contains.Choice.Funs: false
% 0.06/0.24 .
% 0.06/0.24
% 0.06/0.24 ********************************
% 0.06/0.24 * All subproblems solved! *
% 0.06/0.24 ********************************
% 0.06/0.24 % 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:95,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.24
% 0.06/0.24 %**** Beginning of derivation protocol ****
% 0.06/0.24 % SZS output start CNFRefutation
% See solution above
% 0.06/0.24
% 0.06/0.24 %**** End of derivation protocol ****
% 0.06/0.24 %**** no. of clauses in derivation: 96 ****
% 0.06/0.24 %**** clause counter: 95 ****
% 0.06/0.24
% 0.06/0.24 % 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:95,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------