%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET600^5 : 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 : n010.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 10:40:29 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 1
% Syntax : Number of formulae : 185 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 1548 ( 513 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 860 ( 220 ~; 329 |; 11 &; 289 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 197 ( 126 ^; 71 !; 0 ?; 197 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY6,type,
sK2_SY6: a > $o ).
thf(tp_sK3_SV3,type,
sK3_SV3: a ).
thf(tp_sK4_SV4,type,
sK4_SV4: a ).
thf(tp_sK5_SV5,type,
sK5_SV5: a ).
thf(tp_sK6_SV6,type,
sK6_SV6: a ).
thf(tp_sK7_SV7,type,
sK7_SV7: a ).
thf(tp_sK8_SV8,type,
sK8_SV8: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o] :
( ( ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xx: a] : $false ) )
<=> ( ( X
= ( ^ [Xx: a] : $false ) )
& ( Y
= ( ^ [Xx: a] : $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_59_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o] :
( ( ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xx: a] : $false ) )
<=> ( ( X
= ( ^ [Xx: a] : $false ) )
& ( Y
= ( ^ [Xx: a] : $false ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ( ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xx: a] : $false ) )
<=> ( ( X
= ( ^ [Xx: a] : $false ) )
& ( Y
= ( ^ [Xx: a] : $false ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY6: a > $o] :
( ( ( ^ [SY7: a] :
( ( sK1_X @ SY7 )
| ( SY6 @ SY7 ) ) )
= ( ^ [Xx: a] : $false ) )
<=> ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( SY6
= ( ^ [Xx: a] : $false ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) )
<=> ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) )
=> ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) )
=> ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ( ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) )
=> ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) )
=> ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ( ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) )
=> ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
!= ( ^ [SX0: a] : $false ) )
| ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
!= ( ^ [SX0: a] : $false ) )
| ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
!= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [SV1: a] :
( ( ( sK1_X @ SV1 )
| ( sK2_SY6 @ SV1 ) )
= $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
= $true )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: a] :
( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 )
| $false )
| ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( ( ! [SV3: a] :
( ( sK1_X @ SV3 )
= $false ) )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(28,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 )
| $false )
= $false )
| ( ( ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ( ( sK1_X @ sK3_SV3 )
| $false )
| ~ ( ~ ( sK1_X @ sK3_SV3 )
| ~ $false ) )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ! [SV4: a] :
( ( sK2_SY6 @ SV4 )
= $false ) )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV2: a] :
( ( $false = $false )
| ( ( ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( ( ~ ( ( sK1_X @ sK3_SV3 )
| $false ) )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(37,plain,
( ( ( ~ ( ~ ( sK1_X @ sK3_SV3 )
| ~ $false ) )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(38,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(39,plain,
( ( ( ( sK2_SY6 @ sK4_SV4 )
= $false )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(40,plain,
! [SV2: a] :
( ( ( sK1_X @ SV2 )
= $false )
| ( ( ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV2: a] :
( ( ( sK2_SY6 @ SV2 )
= $false )
| ( ( ~ ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(42,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(43,plain,
( ( ( ( sK1_X @ sK3_SV3 )
| $false )
= $true )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(44,plain,
( ( ( ~ ( sK1_X @ sK3_SV3 )
| ~ $false )
= $true )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(45,plain,
( ( ( ! [SV5: a] :
( ( sK2_SY6 @ SV5 )
= $false ) )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[38]) ).
thf(46,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[38]) ).
thf(47,plain,
( ( ( ~ ( ( sK2_SY6 @ sK4_SV4 )
| $false )
| ~ ( ~ ( sK2_SY6 @ sK4_SV4 )
| ~ $false ) )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[39]) ).
thf(48,plain,
( ( ( ( sK2_SY6 @ sK4_SV4 )
= $false )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[39]) ).
thf(49,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false )
= $false )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
| ~ $false )
= $false )
| ( ( sK2_SY6 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(52,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(53,plain,
( ( ( sK1_X @ sK3_SV3 )
= $true )
| ( $false = $true )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(54,plain,
( ( ( ~ ( sK1_X @ sK3_SV3 ) )
= $true )
| ( ( ~ $false ) = $true )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(55,plain,
( ( ( ( sK2_SY6 @ sK5_SV5 )
= $false )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(56,plain,
( ( ( ~ ( ( sK2_SY6 @ sK4_SV4 )
| $false ) )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(57,plain,
( ( ( ~ ( ~ ( sK2_SY6 @ sK4_SV4 )
| ~ $false ) )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(58,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) ) )
= $false )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(59,plain,
! [SV2: a] :
( ( ( ~ $false ) = $false )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(60,plain,
! [SV2: a] :
( ( ( ~ ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) ) )
= $false )
| ( ( sK2_SY6 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(61,plain,
! [SV2: a] :
( ( ( ~ $false ) = $false )
| ( ( sK2_SY6 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(62,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(63,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(64,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(65,plain,
( ( ( sK1_X @ sK3_SV3 )
= $false )
| ( ( ~ $false ) = $true )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(66,plain,
( ( ( ~ ( ( sK2_SY6 @ sK5_SV5 )
| $false )
| ~ ( ~ ( sK2_SY6 @ sK5_SV5 )
| ~ $false ) )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[55]) ).
thf(67,plain,
( ( ( ( sK2_SY6 @ sK5_SV5 )
= $false )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[55]) ).
thf(68,plain,
( ( ( ( sK2_SY6 @ sK4_SV4 )
| $false )
= $true )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(69,plain,
( ( ( ~ ( sK2_SY6 @ sK4_SV4 )
| ~ $false )
= $true )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(70,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $true )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(71,plain,
! [SV2: a] :
( ( $false = $true )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(72,plain,
! [SV2: a] :
( ( ( ( sK1_X @ SV2 )
| ( sK2_SY6 @ SV2 ) )
= $true )
| ( ( sK2_SY6 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(73,plain,
! [SV2: a] :
( ( $false = $true )
| ( ( sK2_SY6 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(74,plain,
! [SV2: a] :
( ( ( sK1_X @ SV2 )
= $true )
| ( ( sK2_SY6 @ SV2 )
= $true )
| ( $false = $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(75,plain,
( ( ( ! [SV6: a] :
( ( sK2_SY6 @ SV6 )
= $false ) )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[64]) ).
thf(76,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[64]) ).
thf(77,plain,
( ( $false = $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
( ( ( ~ ( ( sK2_SY6 @ sK5_SV5 )
| $false ) )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(79,plain,
( ( ( ~ ( ~ ( sK2_SY6 @ sK5_SV5 )
| ~ $false ) )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(80,plain,
( ( ( sK2_SY6 @ sK4_SV4 )
= $true )
| ( $false = $true )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(81,plain,
( ( ( ~ ( sK2_SY6 @ sK4_SV4 ) )
= $true )
| ( ( ~ $false ) = $true )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV2: a] :
( ( ( sK1_X @ SV2 )
= $true )
| ( ( sK2_SY6 @ SV2 )
= $true )
| ( ( sK1_X @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV2: a] :
( ( ( sK1_X @ SV2 )
= $true )
| ( ( sK2_SY6 @ SV2 )
= $true )
| ( ( sK2_SY6 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(84,plain,
( ( ( ( sK2_SY6 @ sK6_SV6 )
= $false )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[75]) ).
thf(85,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
( ( ( ( sK2_SY6 @ sK5_SV5 )
| $false )
= $true )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(87,plain,
( ( ( ~ ( sK2_SY6 @ sK5_SV5 )
| ~ $false )
= $true )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(88,plain,
( ( ( sK2_SY6 @ sK4_SV4 )
= $false )
| ( ( ~ $false ) = $true )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
( ( ( ~ ( ( sK2_SY6 @ sK6_SV6 )
| $false )
| ~ ( ~ ( sK2_SY6 @ sK6_SV6 )
| ~ $false ) )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[84]) ).
thf(90,plain,
( ( ( ( sK2_SY6 @ sK6_SV6 )
= $false )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[84]) ).
thf(91,plain,
( ( ( ! [SV7: a] :
( ( sK2_SY6 @ SV7 )
= $false ) )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[85]) ).
thf(92,plain,
( ( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[85]) ).
thf(93,plain,
( ( ( sK2_SY6 @ sK5_SV5 )
= $true )
| ( $false = $true )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
( ( ( ~ ( sK2_SY6 @ sK5_SV5 ) )
= $true )
| ( ( ~ $false ) = $true )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
( ( $false = $false )
| ( ( sK2_SY6 @ sK4_SV4 )
= $false )
| ( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
( ( ( ~ ( ( sK2_SY6 @ sK6_SV6 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(97,plain,
( ( ( ~ ( ~ ( sK2_SY6 @ sK6_SV6 )
| ~ $false ) )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(98,plain,
( ( ( ( sK2_SY6 @ sK7_SV7 )
= $false )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(99,plain,
( ( ( sK2_SY6 @ sK5_SV5 )
= $false )
| ( ( ~ $false ) = $true )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
( ( ( ( sK2_SY6 @ sK6_SV6 )
| $false )
= $true )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(101,plain,
( ( ( ~ ( sK2_SY6 @ sK6_SV6 )
| ~ $false )
= $true )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(102,plain,
( ( ( ~ ( ( sK2_SY6 @ sK7_SV7 )
| $false )
| ~ ( ~ ( sK2_SY6 @ sK7_SV7 )
| ~ $false ) )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[98]) ).
thf(103,plain,
( ( ( ( sK2_SY6 @ sK7_SV7 )
= $false )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[98]) ).
thf(104,plain,
( ( $false = $false )
| ( ( sK2_SY6 @ sK5_SV5 )
= $false )
| ( ( ( sK1_X @ sK3_SV3 )
= $false )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(105,plain,
( ( ( sK2_SY6 @ sK6_SV6 )
= $true )
| ( $false = $true )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
( ( ( ~ ( sK2_SY6 @ sK6_SV6 ) )
= $true )
| ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
( ( ( ~ ( ( sK2_SY6 @ sK7_SV7 )
| $false ) )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(108,plain,
( ( ( ~ ( ~ ( sK2_SY6 @ sK7_SV7 )
| ~ $false ) )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(109,plain,
( ( ( sK2_SY6 @ sK6_SV6 )
= $false )
| ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(110,plain,
( ( ( ( sK2_SY6 @ sK7_SV7 )
| $false )
= $true )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(111,plain,
( ( ( ~ ( sK2_SY6 @ sK7_SV7 )
| ~ $false )
= $true )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(112,plain,
( ( $false = $false )
| ( ( sK2_SY6 @ sK6_SV6 )
= $false )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
( ( ( sK2_SY6 @ sK7_SV7 )
= $true )
| ( $false = $true )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(114,plain,
( ( ( ~ ( sK2_SY6 @ sK7_SV7 ) )
= $true )
| ( ( ~ $false ) = $true )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(115,plain,
( ( ( sK2_SY6 @ sK7_SV7 )
= $false )
| ( ( ~ $false ) = $true )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(116,plain,
( ( $false = $false )
| ( ( sK2_SY6 @ sK7_SV7 )
= $false )
| ( ( sK1_X @ sK3_SV3 )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(117,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,116,113,112,105,104,103,95,93,92,90,83,82,80,76,74,73,71,67,63,48,46,33,23]) ).
thf(118,plain,
( ( ~ ( ( ( sK1_X
= ( ^ [Xx: a] : $false ) )
& ( sK2_SY6
= ( ^ [Xx: a] : $false ) ) )
=> ( ( ^ [SY11: a] :
( ( sK1_X @ SY11 )
| ( sK2_SY6 @ SY11 ) ) )
= ( ^ [Xx: a] : $false ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(119,plain,
( ( ~ ( ~ ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) )
| ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(120,plain,
( ( ~ ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) )
| ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(121,plain,
( ( ~ ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(122,plain,
( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(123,plain,
( ( ~ ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(124,plain,
( ( ! [SV8: a] :
( ( ( sK1_X @ SV8 )
| ( sK2_SY6 @ SV8 ) )
= $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[122]) ).
thf(125,plain,
( ( ( ^ [SX0: a] :
( ( sK1_X @ SX0 )
| ( sK2_SY6 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[122]) ).
thf(126,plain,
( ( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
| ( sK2_SY6
!= ( ^ [SX0: a] : $false ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(127,plain,
( ( ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
= $false )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(128,plain,
( ( sK1_X
!= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(129,plain,
( ( sK2_SY6
!= ( ^ [SX0: a] : $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(130,plain,
( ( ~ ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 )
| $false )
| ~ ( ~ ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
| ~ $false ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[127]) ).
thf(131,plain,
( ( ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
= $false )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[127]) ).
thf(132,plain,
( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(133,plain,
( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(134,plain,
( ( ~ ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(135,plain,
( ( ~ ( ~ ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
| ~ $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(136,plain,
( ( ! [SV9: a] :
( ( sK1_X @ SV9 )
= $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[132]) ).
thf(137,plain,
( ( sK1_X
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[132]) ).
thf(138,plain,
( ( ! [SV10: a] :
( ( sK2_SY6 @ SV10 )
= $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[133]) ).
thf(139,plain,
( ( sK2_SY6
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[133]) ).
thf(140,plain,
( ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(141,plain,
( ( ~ ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
| ~ $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV11: a] :
( ( ( sK1_X @ SV11 )
= $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV12: a] :
( ( ( sK2_SY6 @ SV12 )
= $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(144,plain,
( ( ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(145,plain,
( ( ( ~ ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) ) )
= $true )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV11: a] :
( ( ~ ( ( sK1_X @ SV11 )
| $false )
| ~ ( ~ ( sK1_X @ SV11 )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV11: a] :
( ( ( sK1_X @ SV11 )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV12: a] :
( ( ~ ( ( sK2_SY6 @ SV12 )
| $false )
| ~ ( ~ ( sK2_SY6 @ SV12 )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV12: a] :
( ( ( sK2_SY6 @ SV12 )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[143]) ).
thf(150,plain,
( ( ( sK1_X @ sK8_SV8 )
= $true )
| ( ( sK2_SY6 @ sK8_SV8 )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(151,plain,
( ( ( ( sK1_X @ sK8_SV8 )
| ( sK2_SY6 @ sK8_SV8 ) )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV11: a] :
( ( ( ~ ( ( sK1_X @ SV11 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( sK1_X @ SV11 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV12: a] :
( ( ( ~ ( ( sK2_SY6 @ SV12 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(154,plain,
( ( ( sK1_X @ sK8_SV8 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(155,plain,
( ( ( sK2_SY6 @ sK8_SV8 )
= $false )
| ( ( ~ $false ) = $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(156,plain,
! [SV11: a] :
( ( ( ( sK1_X @ SV11 )
| $false )
= $false )
| ( ( ~ ( ~ ( sK1_X @ SV11 )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(157,plain,
! [SV12: a] :
( ( ( ( sK2_SY6 @ SV12 )
| $false )
= $false )
| ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(158,plain,
( ( $false = $false )
| ( ( sK1_X @ sK8_SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(159,plain,
( ( $false = $false )
| ( ( sK2_SY6 @ sK8_SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(160,plain,
! [SV11: a] :
( ( ( sK1_X @ SV11 )
= $false )
| ( ( ~ ( ~ ( sK1_X @ SV11 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(161,plain,
! [SV11: a] :
( ( $false = $false )
| ( ( ~ ( ~ ( sK1_X @ SV11 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(162,plain,
! [SV12: a] :
( ( ( sK2_SY6 @ SV12 )
= $false )
| ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(163,plain,
! [SV12: a] :
( ( $false = $false )
| ( ( ~ ( ~ ( sK2_SY6 @ SV12 )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(164,plain,
! [SV11: a] :
( ( ( ~ ( sK1_X @ SV11 )
| ~ $false )
= $false )
| ( ( sK1_X @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV11: a] :
( ( ( ~ ( sK1_X @ SV11 )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV12: a] :
( ( ( ~ ( sK2_SY6 @ SV12 )
| ~ $false )
= $false )
| ( ( sK2_SY6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV12: a] :
( ( ( ~ ( sK2_SY6 @ SV12 )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(168,plain,
! [SV11: a] :
( ( ( ~ ( sK1_X @ SV11 ) )
= $false )
| ( ( sK1_X @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(169,plain,
! [SV11: a] :
( ( ( ~ $false ) = $false )
| ( ( sK1_X @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(170,plain,
! [SV11: a] :
( ( ( ~ ( sK1_X @ SV11 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(171,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(172,plain,
! [SV12: a] :
( ( ( ~ ( sK2_SY6 @ SV12 ) )
= $false )
| ( ( sK2_SY6 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(173,plain,
! [SV12: a] :
( ( ( ~ $false ) = $false )
| ( ( sK2_SY6 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(174,plain,
! [SV12: a] :
( ( ( ~ ( sK2_SY6 @ SV12 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(175,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(176,plain,
! [SV11: a] :
( ( ( sK1_X @ SV11 )
= $true )
| ( ( sK1_X @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(177,plain,
! [SV11: a] :
( ( $false = $true )
| ( ( sK1_X @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(178,plain,
! [SV11: a] :
( ( ( sK1_X @ SV11 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(179,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(180,plain,
! [SV12: a] :
( ( ( sK2_SY6 @ SV12 )
= $true )
| ( ( sK2_SY6 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(181,plain,
! [SV12: a] :
( ( $false = $true )
| ( ( sK2_SY6 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(182,plain,
! [SV12: a] :
( ( ( sK2_SY6 @ SV12 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(183,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(184,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[125,183,182,181,180,179,178,177,176,159,158,150,149,147,139,137,131]) ).
thf(185,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[184,117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET600^5 : 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
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 14:47:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24
% 0.08/0.24 No.of.Axioms: 0
% 0.08/0.24
% 0.08/0.24 Length.of.Defs: 0
% 0.08/0.24
% 0.08/0.24 Contains.Choice.Funs: false
% 0.08/0.24 .
% 0.08/0.24
% 0.08/0.24 ********************************
% 0.08/0.24 * All subproblems solved! *
% 0.08/0.24 ********************************
% 0.08/0.24 % 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:184,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.24
% 0.08/0.24 %**** Beginning of derivation protocol ****
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 185 ****
% 0.08/0.25 %**** clause counter: 184 ****
% 0.08/0.25
% 0.08/0.25 % 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:184,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------