%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV239^5 : 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 : n015.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 10:49:48 AM UTC 2026
% Result : Theorem 7.56s 1.70s
% Output : CNFRefutation 7.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 1
% Syntax : Number of formulae : 87 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 786 ( 375 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 885 ( 356 ~; 220 |; 10 &; 299 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 189 ( 59 ^; 120 !; 10 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_SV1,type,
sK1_SV1: a ).
thf(tp_sK2_SY11,type,
sK2_SY11: a > $o ).
thf(tp_sK3_SY14,type,
sK3_SY14: a ).
thf(tp_sK4_SV6,type,
sK4_SV6: a > ( a > $o ) > a ).
thf(tp_y,type,
y: a > $o ).
thf(1,conjecture,
( y
= ( ^ [Xx: a] :
? [S: a > $o] :
( ? [Xx0: a] :
( ( y @ Xx0 )
& ( S
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xx0 ) ) )
& ( S @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5211_pme) ).
thf(2,negated_conjecture,
( ( y
= ( ^ [Xx: a] :
? [S: a > $o] :
( ? [Xx0: a] :
( ( y @ Xx0 )
& ( S
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xx0 ) ) )
& ( S @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( y
= ( ^ [SY0: a] :
? [SY1: a > $o] :
( ? [SY2: a] :
( ( y @ SY2 )
& ( SY1
= ( ^ [SY3: a] : ( SY2 = SY3 ) ) ) )
& ( SY1 @ SY0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( y
!= ( ^ [SY0: a] :
? [SY1: a > $o] :
( ? [SY2: a] :
( ( y @ SY2 )
& ( SY1
= ( ^ [SY3: a] : ( SY2 = SY3 ) ) ) )
& ( SY1 @ SY0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( y
!= ( ^ [SY0: a] :
? [SY1: a > $o] :
( ? [SY2: a] :
( ( y @ SY2 )
& ( SY1
= ( ^ [SY3: a] : ( SY2 = SY3 ) ) ) )
& ( SY1 @ SY0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( y
!= ( ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SX1
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( y
= ( ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SX1
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SV1: a] :
( ( y @ SV1 )
= ( ~ ! [SY8: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY8
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY8 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[7]) ).
thf(9,plain,
( ( y
= ( ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SX1
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ( y @ sK1_SV1 )
= ( ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(11,plain,
( ( ~ ( ( y @ sK1_SV1 )
| ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
| ~ ( ~ ( y @ sK1_SV1 )
| ~ ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(12,plain,
( ( ( y @ sK1_SV1 )
= ( ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ( y @ sK1_SV1 )
| ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ~ ( y @ sK1_SV1 )
| ~ ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
( ( ( y @ sK1_SV1 )
| ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( y @ sK1_SV1 )
| ~ ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( y @ sK1_SV1 )
= $true )
| ( ( ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ( ~ ( y @ sK1_SV1 ) )
= $true )
| ( ( ~ ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( y @ sK1_SV1 )
= $false )
| ( ( ~ ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ~ ~ ( ~ ~ ! [SY14: a] :
~ ~ ( ~ ( y @ SY14 )
| ( sK2_SY11
!= ( ^ [SX3: a] : ( SY14 = SX3 ) ) ) )
| ~ ( sK2_SY11 @ sK1_SV1 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(22,plain,
( ( ( ~ ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(23,plain,
( ( ( ~ ( ~ ~ ! [SY14: a] :
~ ~ ( ~ ( y @ SY14 )
| ( sK2_SY11
!= ( ^ [SX3: a] : ( SY14 = SX3 ) ) ) )
| ~ ( sK2_SY11 @ sK1_SV1 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(24,plain,
( ( ( ! [SY11: a > $o] :
~ ~ ( ~ ~ ! [SX2: a] :
~ ~ ( ~ ( y @ SX2 )
| ( SY11
!= ( ^ [SX3: a] : ( SX2 = SX3 ) ) ) )
| ~ ( SY11 @ sK1_SV1 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ( ~ ~ ! [SY14: a] :
~ ~ ( ~ ( y @ SY14 )
| ( sK2_SY11
!= ( ^ [SX3: a] : ( SY14 = SX3 ) ) ) )
| ~ ( sK2_SY11 @ sK1_SV1 ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: a > $o] :
( ( ( ~ ~ ( ~ ~ ! [SY16: a] :
~ ~ ( ~ ( y @ SY16 )
| ( SV2
!= ( ^ [SX3: a] : ( SY16 = SX3 ) ) ) )
| ~ ( SV2 @ sK1_SV1 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ( ~ ~ ! [SY14: a] :
~ ~ ( ~ ( y @ SY14 )
| ( sK2_SY11
!= ( ^ [SX3: a] : ( SY14 = SX3 ) ) ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ( ~ ( sK2_SY11 @ sK1_SV1 ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: a > $o] :
( ( ( ~ ( ~ ~ ! [SY16: a] :
~ ~ ( ~ ( y @ SY16 )
| ( SV2
!= ( ^ [SX3: a] : ( SY16 = SX3 ) ) ) )
| ~ ( SV2 @ sK1_SV1 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ! [SY14: a] :
~ ~ ( ~ ( y @ SY14 )
| ( sK2_SY11
!= ( ^ [SX3: a] : ( SY14 = SX3 ) ) ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ( sK2_SY11 @ sK1_SV1 )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: a > $o] :
( ( ( ~ ~ ! [SY16: a] :
~ ~ ( ~ ( y @ SY16 )
| ( SV2
!= ( ^ [SX3: a] : ( SY16 = SX3 ) ) ) )
| ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ! [SY14: a] :
~ ~ ( ~ ( y @ SY14 )
| ( sK2_SY11
!= ( ^ [SX3: a] : ( SY14 = SX3 ) ) ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: a > $o] :
( ( ( ~ ~ ! [SY16: a] :
~ ~ ( ~ ( y @ SY16 )
| ( SV2
!= ( ^ [SX3: a] : ( SY16 = SX3 ) ) ) ) )
= $true )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ( ~ ~ ( ~ ( y @ sK3_SY14 )
| ( sK2_SY11
!= ( ^ [SY18: a] : ( sK3_SY14 = SY18 ) ) ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(36,plain,
! [SV2: a > $o] :
( ( ( ~ ! [SY16: a] :
~ ~ ( ~ ( y @ SY16 )
| ( SV2
!= ( ^ [SX3: a] : ( SY16 = SX3 ) ) ) ) )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
( ( ( ~ ( ~ ( y @ sK3_SY14 )
| ( sK2_SY11
!= ( ^ [SY18: a] : ( sK3_SY14 = SY18 ) ) ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV2: a > $o] :
( ( ( ! [SY16: a] :
~ ~ ( ~ ( y @ SY16 )
| ( SV2
!= ( ^ [SX3: a] : ( SY16 = SX3 ) ) ) ) )
= $true )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
( ( ( ~ ( y @ sK3_SY14 )
| ( sK2_SY11
!= ( ^ [SY18: a] : ( sK3_SY14 = SY18 ) ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV2: a > $o,SV3: a] :
( ( ( ~ ~ ( ~ ( y @ SV3 )
| ( SV2
!= ( ^ [SY19: a] : ( SV3 = SY19 ) ) ) ) )
= $true )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
( ( ( ~ ( y @ sK3_SY14 ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(42,plain,
( ( ( sK2_SY11
!= ( ^ [SY18: a] : ( sK3_SY14 = SY18 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV2: a > $o,SV3: a] :
( ( ( ~ ( ~ ( y @ SV3 )
| ( SV2
!= ( ^ [SY19: a] : ( SV3 = SY19 ) ) ) ) )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
( ( ( y @ sK3_SY14 )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
( ( ( sK2_SY11
= ( ^ [SY18: a] : ( sK3_SY14 = SY18 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV2: a > $o,SV3: a] :
( ( ( ~ ( y @ SV3 )
| ( SV2
!= ( ^ [SY19: a] : ( SV3 = SY19 ) ) ) )
= $true )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(47,plain,
( ( ( ! [SV4: a] :
( ( sK2_SY11 @ SV4 )
= ( sK3_SY14 = SV4 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[45]) ).
thf(48,plain,
( ( ( sK2_SY11
= ( ^ [SY18: a] : ( sK3_SY14 = SY18 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV2: a > $o,SV3: a] :
( ( ( ~ ( y @ SV3 ) )
= $true )
| ( ( SV2
!= ( ^ [SY19: a] : ( SV3 = SY19 ) ) )
= $true )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV5: a] :
( ( ( ( sK2_SY11 @ SV5 )
= ( sK3_SY14 = SV5 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: a > $o,SV3: a] :
( ( ( y @ SV3 )
= $false )
| ( ( SV2
!= ( ^ [SY19: a] : ( SV3 = SY19 ) ) )
= $true )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV5: a] :
( ( ( ~ ( ( sK2_SY11 @ SV5 )
| ( sK3_SY14 = SV5 ) )
| ~ ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV5: a] :
( ( ( ( sK2_SY11 @ SV5 )
= ( sK3_SY14 = SV5 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2
= ( ^ [SY19: a] : ( SV3 = SY19 ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV5: a] :
( ( ( ~ ( ( sK2_SY11 @ SV5 )
| ( sK3_SY14 = SV5 ) ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ! [SV6: a] :
( ( SV2 @ SV6 )
= ( SV3 = SV6 ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[54]) ).
thf(57,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2
= ( ^ [SY19: a] : ( SV3 = SY19 ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV5: a] :
( ( ( ( sK2_SY11 @ SV5 )
| ( sK3_SY14 = SV5 ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(60,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ sK1_SV1 )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( SV2
= ( ^ [SY19: a] : ( SV3 = SY19 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV5: a] :
( ( ( sK2_SY11 @ SV5 )
= $false )
| ( ( ~ ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV5: a] :
( ( ( sK3_SY14 = SV5 )
= $false )
| ( ( ~ ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) ) )
= $true )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
| ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) ) )
| ~ ( ~ ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
| ( SV3
!= ( sK4_SV6 @ SV3 @ SV2 ) ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[59]) ).
thf(64,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[59]) ).
thf(65,plain,
! [SV5: a] :
( ( ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) )
= $false )
| ( ( sK2_SY11 @ SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: a] :
( ( ( ~ ( sK2_SY11 @ SV5 )
| ( sK3_SY14 != SV5 ) )
= $false )
| ( ( sK3_SY14 = SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
| ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( ~ ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
| ( SV3
!= ( sK4_SV6 @ SV3 @ SV2 ) ) ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ sK1_SV1 )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) ) )
= $false )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV5: a] :
( ( ( ~ ( sK2_SY11 @ SV5 ) )
= $false )
| ( ( sK2_SY11 @ SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(71,plain,
! [SV5: a] :
( ( ( sK3_SY14 != SV5 )
= $false )
| ( ( sK2_SY11 @ SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV5: a] :
( ( ( ~ ( sK2_SY11 @ SV5 ) )
= $false )
| ( ( sK3_SY14 = SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV5: a] :
( ( ( sK3_SY14 != SV5 )
= $false )
| ( ( sK3_SY14 = SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
| ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) ) )
= $true )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(75,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
| ( SV3
!= ( sK4_SV6 @ SV3 @ SV2 ) ) )
= $true )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
! [SV5: a] :
( ( ( sK2_SY11 @ SV5 )
= $true )
| ( ( sK2_SY11 @ SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV5: a] :
( ( ( sK3_SY14 = SV5 )
= $true )
| ( ( sK2_SY11 @ SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(78,plain,
! [SV5: a] :
( ( ( sK2_SY11 @ SV5 )
= $true )
| ( ( sK3_SY14 = SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(79,plain,
! [SV5: a] :
( ( ( sK3_SY14 = SV5 )
= $true )
| ( ( sK3_SY14 = SV5 )
= $false )
| ( ( y @ sK1_SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= $true )
| ( ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) )
= $true )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV3: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) ) )
= $true )
| ( ( SV3
!= ( sK4_SV6 @ SV3 @ SV2 ) )
= $true )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ sK1_SV1 )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) )
= $true )
| ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= $false )
| ( ( SV3
!= ( sK4_SV6 @ SV3 @ SV2 ) )
= $true )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV2: a > $o,SV3: a] :
( ( ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) )
= $false )
| ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( ~ ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(85,plain,
! [SV3: a,SV2: a > $o] :
( ( ( SV2 @ sK1_SV1 )
= $false )
| ( ( y @ SV3 )
= $false )
| ( ( SV2 @ ( sK4_SV6 @ SV3 @ SV2 ) )
= $false )
| ( ( SV3
= ( sK4_SV6 @ SV3 @ SV2 ) )
= $false )
| ( ( y @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(86,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,85,82,79,78,77,76,69,60,53,48,44,31,12]) ).
thf(87,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV239^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.19 % Computer : n015.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Oct 6 15:46:58 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.56/1.70
% 7.56/1.70 No.of.Axioms: 0
% 7.56/1.70
% 7.56/1.70 Length.of.Defs: 0
% 7.56/1.70
% 7.56/1.70 Contains.Choice.Funs: false
% 7.56/1.70 .
% 7.56/1.70
% 7.56/1.70 ********************************
% 7.56/1.70 * All subproblems solved! *
% 7.56/1.70 ********************************
% 7.56/1.70 % 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:86,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.56/1.70
% 7.56/1.70 %**** Beginning of derivation protocol ****
% 7.56/1.70 % SZS output start CNFRefutation
% See solution above
% 7.56/1.70
% 7.56/1.70 %**** End of derivation protocol ****
% 7.56/1.70 %**** no. of clauses in derivation: 87 ****
% 7.56/1.70 %**** clause counter: 86 ****
% 7.56/1.70
% 7.56/1.70 % 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:86,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------