%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV245^6 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 10:49:49 AM UTC 2026
% Result : Theorem 90.58s 15.40s
% Output : CNFRefutation 90.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 60 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 393 ( 116 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 704 ( 126 ~; 102 |; 18 &; 426 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 203 ( 42 ^; 149 !; 12 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cK,type,
cK: ( a > $o ) > a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY10,type,
sK2_SY10: a > $o ).
thf(tp_sK3_Xx,type,
sK3_Xx: ( a > $o ) > ( a > $o ) > a ).
thf(1,conjecture,
( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM116_2S) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) )
=> ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: a] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: a] :
( ? [S: a > $o] :
( ! [Xx0: a] :
( ( S @ Xx0 )
=> ( cK @ S @ Xx0 ) )
& ( S @ Xx ) )
=> ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SY15: a] :
( ~ ( sK2_SY10 @ SY15 )
| ( cK @ sK2_SY10 @ SY15 ) )
& ( sK2_SY10 @ sK1_Xx )
& ~ ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ( ( X @ ( sK3_Xx @ Y @ X ) )
& ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
| ! [Xx: a] :
( ~ ( cK @ X @ Xx )
| ( cK @ Y @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [X: a > $o,Y: a > $o] :
( ( ( X @ ( sK3_Xx @ Y @ X ) )
& ~ ( Y @ ( sK3_Xx @ Y @ X ) ) )
| ! [Xx: a] :
( ~ ( cK @ X @ Xx )
| ( cK @ Y @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [SY15: a] :
( ~ ( sK2_SY10 @ SY15 )
| ( cK @ sK2_SY10 @ SY15 ) )
& ( sK2_SY10 @ sK1_Xx )
& ~ ( cK
@ ^ [Xx0: a] :
? [S: a > $o] :
( ! [Xx1: a] :
( ( S @ Xx1 )
=> ( cK @ S @ Xx1 ) )
& ( S @ Xx0 ) )
@ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ( ~ ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) )
| ~ ~ ( SX1 @ ( sK3_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: a] :
( ~ ( cK @ SX0 @ SX2 )
| ( cK @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) )
| ~ ( sK2_SY10 @ sK1_Xx ) )
| ~ ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: a > $o] :
( ( ! [SY16: a > $o] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY16 @ SV1 ) )
| ~ ~ ( SY16 @ ( sK3_Xx @ SY16 @ SV1 ) ) )
| ! [SY17: a] :
( ~ ( cK @ SV1 @ SY17 )
| ( cK @ SY16 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) )
| ~ ( sK2_SY10 @ sK1_Xx ) )
| ~ ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
| ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) )
| ~ ( sK2_SY10 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( ~ ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) )
| ~ ( sK2_SY10 @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
| ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) )
| ~ ( sK2_SY10 @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( cK
@ ^ [SX0: a] :
~ ! [SX1: a > $o] :
~ ~ ( ~ ! [SX2: a] :
( ~ ( SX1 @ SX2 )
| ( cK @ SX1 @ SX2 ) )
| ~ ( SX1 @ SX0 ) )
@ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( ~ ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( sK2_SY10 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( ~ ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) ) )
= $true )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SX0: a] :
( ~ ( sK2_SY10 @ SX0 )
| ( cK @ sK2_SY10 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( sK2_SY10 @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV2: a > $o,SV3: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV3 )
| ( cK @ SV2 @ SV3 ) )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: a > $o,SV2: a > $o] :
( ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false )
| ( ( ! [SY18: a] :
( ~ ( cK @ SV1 @ SY18 )
| ( cK @ SV2 @ SY18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: a] :
( ( ~ ( sK2_SY10 @ SV4 )
| ( cK @ sK2_SY10 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: a > $o,SV3: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV3 ) )
= $true )
| ( ( cK @ SV2 @ SV3 )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: a > $o,SV5: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV5 )
| ( cK @ SV2 @ SV5 ) )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: a] :
( ( ( ~ ( sK2_SY10 @ SV4 ) )
= $true )
| ( ( cK @ sK2_SY10 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: a > $o,SV3: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV3 )
= $false )
| ( ( cK @ SV2 @ SV3 )
= $true )
| ( ( SV1 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV2: a > $o,SV5: a,SV1: a > $o] :
( ( ( ~ ( cK @ SV1 @ SV5 ) )
= $true )
| ( ( cK @ SV2 @ SV5 )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV4: a] :
( ( ( sK2_SY10 @ SV4 )
= $false )
| ( ( cK @ sK2_SY10 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV2: a > $o,SV5: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK @ SV2 @ SV5 )
= $true )
| ( ( SV2 @ ( sK3_Xx @ SV2 @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV3 )
= $false )
| ( ( cK
@ ^ [SX0: a] : $true
@ SV3 )
= $true )
| ( ( SV1
@ ( sK3_Xx
@ ^ [SX0: a] : $true
@ SV1 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV10: a] : $true ))]]) ).
thf(43,plain,
! [SV3: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV3 )
= $false )
| ( ( cK
@ ^ [SX0: a] : $false
@ SV3 )
= $true )
| ( ( SV1
@ ( sK3_Xx
@ ^ [SX0: a] : $false
@ SV1 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV9: a] : $false ))]]) ).
thf(44,plain,
! [SV8: a > $o,SV3: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV3 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV3 )
= $true )
| ( ( SV1
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(45,plain,
! [SV3: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV3 )
= $false )
| ( ( cK
@ ^ [SX0: a] : ( SX0 = sK1_Xx )
@ SV3 )
= $true )
| ( ( SV1
@ ( sK3_Xx
@ ^ [SX0: a] : ( SX0 = sK1_Xx )
@ SV1 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV2,$thf( ^ [SV6: a] : ( SV6 = sK1_Xx ) ))]]) ).
thf(47,plain,
! [SV2: a > $o,SV3: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV3 )
= $false )
| ( ( cK @ SV2 @ SV3 )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV14: a] : $false ))]]) ).
thf(48,plain,
! [SV2: a > $o,SV3: a,SV13: a > $o] :
( ( ( cK
@ ^ [SX0: a] :
~ ( SV13 @ SX0 )
@ SV3 )
= $false )
| ( ( cK @ SV2 @ SV3 )
= $true )
| ( ( ~ ( SV13
@ ( sK3_Xx @ SV2
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(49,plain,
! [SV2: a > $o,SV3: a] :
( ( ( cK
@ ^ [SX0: a] : ( SX0 = sK1_Xx )
@ SV3 )
= $false )
| ( ( cK @ SV2 @ SV3 )
= $true )
| ( ( ( sK3_Xx @ SV2
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
= sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV11: a] : ( SV11 = sK1_Xx ) ))]]) ).
thf(50,plain,
! [SV5: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK
@ ^ [SX0: a] : $true
@ SV5 )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[41:[bind(SV2,$thf( ^ [SV10: a] : $true ))]]) ).
thf(52,plain,
! [SV8: a > $o,SV5: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV5 )
= $true )
| ( ( ~ ( SV8
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[41:[bind(SV2,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(54,plain,
! [SV2: a > $o,SV5: a] :
( ( ( cK
@ ^ [SX0: a] : $true
@ SV5 )
= $false )
| ( ( cK @ SV2 @ SV5 )
= $true )
| ( ( SV2
@ ( sK3_Xx @ SV2
@ ^ [SX0: a] : $true ) )
= $false ) ),
inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV15: a] : $true ))]]) ).
thf(55,plain,
! [SV2: a > $o,SV5: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV5 )
= $false )
| ( ( cK @ SV2 @ SV5 )
= $true )
| ( ( SV2
@ ( sK3_Xx @ SV2
@ ^ [SX0: a] : $false ) )
= $false ) ),
inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV14: a] : $false ))]]) ).
thf(56,plain,
! [SV2: a > $o,SV5: a,SV13: a > $o] :
( ( ( cK
@ ^ [SX0: a] :
~ ( SV13 @ SX0 )
@ SV5 )
= $false )
| ( ( cK @ SV2 @ SV5 )
= $true )
| ( ( SV2
@ ( sK3_Xx @ SV2
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(57,plain,
! [SV2: a > $o,SV5: a] :
( ( ( cK
@ ^ [SX0: a] : ( SX0 = sK1_Xx )
@ SV5 )
= $false )
| ( ( cK @ SV2 @ SV5 )
= $true )
| ( ( SV2
@ ( sK3_Xx @ SV2
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[41:[bind(SV1,$thf( ^ [SV11: a] : ( SV11 = sK1_Xx ) ))]]) ).
thf(58,plain,
! [SV3: a,SV2: a > $o,SV13: a > $o] :
( ( ( SV13
@ ( sK3_Xx @ SV2
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cK @ SV2 @ SV3 )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV13 @ SX0 )
@ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV5: a,SV1: a > $o,SV8: a > $o] :
( ( ( SV8
@ ( sK3_Xx
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV1 ) )
= $true )
| ( ( cK
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV5 )
= $true )
| ( ( cK @ SV1 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(60,plain,
! [SV2: a > $o,SV3: a] :
( ( ( cK
@ ^ [SX0: a] : $false
@ SV3 )
= $false )
| ( ( cK @ SV2 @ SV3 )
= $true ) ),
inference(sim,[status(thm)],[47]) ).
thf(61,plain,
! [SV5: a,SV1: a > $o] :
( ( ( cK @ SV1 @ SV5 )
= $false )
| ( ( cK
@ ^ [SX0: a] : $true
@ SV5 )
= $true ) ),
inference(sim,[status(thm)],[50]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,61,60,59,58,57,56,55,54,49,45,44,43,42,41,40,38,31]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV245^6 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n006.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:43:07 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 90.58/15.40
% 90.58/15.40 No.of.Axioms: 0
% 90.58/15.40
% 90.58/15.40 Length.of.Defs: 0
% 90.58/15.40
% 90.58/15.40 Contains.Choice.Funs: false
% 90.58/15.40 .eprover: CPU time limit exceeded, terminating
% 90.58/15.40
% 90.58/15.40
% 90.58/15.40 ********************************
% 90.58/15.40 * All subproblems solved! *
% 90.58/15.40 ********************************
% 90.58/15.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:62,loop_count:0,foatp_calls:2,translation:fof_experiment)
% 90.58/15.40
% 90.58/15.40 %**** Beginning of derivation protocol ****
% 90.58/15.40 % SZS output start CNFRefutation
% See solution above
% 90.58/15.41
% 90.58/15.41 %**** End of derivation protocol ****
% 90.58/15.41 %**** no. of clauses in derivation: 60 ****
% 90.58/15.41 %**** clause counter: 62 ****
% 90.58/15.41
% 90.58/15.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:62,loop_count:0,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------