%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV273^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:49:51 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 1
% Syntax : Number of formulae : 115 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 725 ( 356 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1608 ( 545 ~; 253 |; 18 &; 773 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 96 ( 96 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 384 ( 113 ^; 263 !; 8 ?; 384 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cR,type,
cR: a > a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_Xz,type,
sK2_Xz: ( a > $o ) > a ).
thf(tp_sK3_Xx,type,
sK3_Xx: a > ( a > $o ) > a ).
thf(1,conjecture,
( ! [X: a > $o] :
( ? [Xz: a] : ( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) )
=> ! [Xx: a] : ( cR @ Xx @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM542_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o] :
( ? [Xz: a] : ( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) )
=> ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o] :
( ? [Xz: a] : ( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) )
=> ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: a > $o] :
( ? [Xz: a] : ( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xx: a] : ( cR @ Xx @ Xx ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( cR @ sK1_Xx @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [X: a > $o] :
( ! [Xz: a] :
~ ( X @ Xz )
| ( ! [SY7: a] :
( ( ( X @ ( sK3_Xx @ SY7 @ X ) )
& ~ ( cR @ SY7 @ ( sK3_Xx @ SY7 @ X ) ) )
| ~ ( X @ SY7 )
| ( SY7
= ( sK2_Xz @ X ) ) )
& ! [SY9: a] :
( ~ ( X @ SY9 )
| ( cR @ ( sK2_Xz @ X ) @ SY9 ) )
& ( X @ ( sK2_Xz @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [X: a > $o] :
( ! [Xz: a] :
~ ( X @ Xz )
| ( ! [SY7: a] :
( ( ( X @ ( sK3_Xx @ SY7 @ X ) )
& ~ ( cR @ SY7 @ ( sK3_Xx @ SY7 @ X ) ) )
| ~ ( X @ SY7 )
| ( SY7
= ( sK2_Xz @ X ) ) )
& ! [SY9: a] :
( ~ ( X @ SY9 )
| ( cR @ ( sK2_Xz @ X ) @ SY9 ) )
& ( X @ ( sK2_Xz @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ( cR @ sK1_Xx @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: a > $o] :
( ! [SX1: a] :
~ ( SX0 @ SX1 )
| ~ ( ~ ! [SX1: a] :
( ~ ( ~ ( SX0 @ ( sK3_Xx @ SX1 @ SX0 ) )
| ~ ~ ( cR @ SX1 @ ( sK3_Xx @ SX1 @ SX0 ) ) )
| ~ ( SX0 @ SX1 )
| ( SX1
= ( sK2_Xz @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: a] :
( ~ ( SX0 @ SX1 )
| ( cR @ ( sK2_Xz @ SX0 ) @ SX1 ) )
| ~ ( SX0 @ ( sK2_Xz @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(12,plain,
( ( cR @ sK1_Xx @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: a > $o] :
( ( ! [SY10: a] :
~ ( SV1 @ SY10 )
| ~ ( ~ ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) )
| ~ ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: a > $o] :
( ( ( ! [SY10: a] :
~ ( SV1 @ SY10 ) )
= $true )
| ( ( ~ ( ~ ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) )
| ~ ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(15,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) )
| ~ ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV2: a,SV1: a > $o] :
( ( ( SV1 @ SV2 )
= $false )
| ( ( ~ ( ~ ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) )
| ~ ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) )
| ~ ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(18,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(19,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ! [SY11: a] :
( ~ ( ~ ( SV1 @ ( sK3_Xx @ SY11 @ SV1 ) )
| ~ ~ ( cR @ SY11 @ ( sK3_Xx @ SY11 @ SV1 ) ) )
| ~ ( SV1 @ SY11 )
| ( SY11
= ( sK2_Xz @ SV1 ) ) ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(22,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) )
| ~ ~ ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) ) )
| ~ ( SV1 @ SV3 )
| ( SV3
= ( sK2_Xz @ SV1 ) ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(23,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) )
| ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) )
| ~ ~ ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) ) )
| ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(25,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK2_Xz @ SV1 ) ) )
= $false )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) )
| ~ ~ ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ! [SY12: a] :
( ~ ( SV1 @ SY12 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SY12 ) ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: a,SV1: a > $o] :
( ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) )
| ~ ~ ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: a,SV4: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV4 )
| ( cR @ ( sK2_Xz @ SV1 ) @ SV4 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: a,SV1: a > $o,SV3: a] :
( ( ( ~ ~ ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: a,SV4: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV4 ) )
= $true )
| ( ( cR @ ( sK2_Xz @ SV1 ) @ SV4 )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: a,SV1: a > $o,SV3: a] :
( ( ( ~ ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) ) )
= $true )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV2: a,SV4: a,SV1: a > $o] :
( ( ( SV1 @ SV4 )
= $false )
| ( ( cR @ ( sK2_Xz @ SV1 ) @ SV4 )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( SV1 @ ( sK3_Xx @ SV3 @ SV1 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV2: a,SV1: a > $o,SV3: a] :
( ( ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) )
= $false )
| ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV2: a,SV3: a,SV1: a > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( cR @ SV3 @ ( sK3_Xx @ SV3 @ SV1 ) )
= $false )
| ( ( SV3
= ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV2: a,SV7: a > $o] :
( ( ( ~ ( SV7
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV1,$thf( ^ [SV6: a] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(44,plain,
! [SV2: a] :
( ( ( ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
= sK1_Xx )
= $true )
| ( ( SV2 = sK1_Xx )
= $false ) ),
inference(prim_subst,[status(thm)],[29:[bind(SV1,$thf( ^ [SV5: a] : ( SV5 = sK1_Xx ) ))]]) ).
thf(45,plain,
! [SV4: a] :
( ( $true = $false )
| ( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] : $true )
@ SV4 )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV1,$thf( ^ [SV9: a] : $true ))]]) ).
thf(47,plain,
! [SV2: a,SV4: a,SV7: a > $o] :
( ( ( ~ ( SV7 @ SV4 ) )
= $false )
| ( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) )
@ SV4 )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV1,$thf( ^ [SV6: a] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(48,plain,
! [SV2: a,SV4: a] :
( ( ( SV4 = sK1_Xx )
= $false )
| ( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
@ SV4 )
= $true )
| ( ( SV2 = sK1_Xx )
= $false ) ),
inference(prim_subst,[status(thm)],[37:[bind(SV1,$thf( ^ [SV5: a] : ( SV5 = sK1_Xx ) ))]]) ).
thf(51,plain,
! [SV2: a,SV3: a,SV7: a > $o] :
( ( ( ~ ( SV7 @ SV3 ) )
= $false )
| ( ( ~ ( SV7
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) ) )
= $true )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV6: a] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(52,plain,
! [SV2: a,SV3: a] :
( ( ( SV3 = sK1_Xx )
= $false )
| ( ( ( sK3_Xx @ SV3
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
= sK1_Xx )
= $true )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $true )
| ( ( SV2 = sK1_Xx )
= $false ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV1,$thf( ^ [SV5: a] : ( SV5 = sK1_Xx ) ))]]) ).
thf(53,plain,
! [SV3: a] :
( ( $true = $false )
| ( ( cR @ SV3
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] : $true ) )
= $false )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] : $true ) )
= $true )
| ( $true = $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV1,$thf( ^ [SV9: a] : $true ))]]) ).
thf(55,plain,
! [SV2: a,SV3: a,SV7: a > $o] :
( ( ( ~ ( SV7 @ SV3 ) )
= $false )
| ( ( cR @ SV3
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV1,$thf( ^ [SV6: a] : ~ ( SV7 @ SV6 ) ))]]) ).
thf(56,plain,
! [SV2: a,SV3: a] :
( ( ( SV3 = sK1_Xx )
= $false )
| ( ( cR @ SV3
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $false )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $true )
| ( ( SV2 = sK1_Xx )
= $false ) ),
inference(prim_subst,[status(thm)],[40:[bind(SV1,$thf( ^ [SV5: a] : ( SV5 = sK1_Xx ) ))]]) ).
thf(57,plain,
! [SV2: a,SV1: a > $o] :
( ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true )
| ( ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= ( ~ ( SV1 @ SV2 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[29]) ).
thf(58,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( ( SV1 @ ( sK2_Xz @ SV1 ) )
| ~ ( SV1 @ SV2 ) )
| ~ ( ~ ( SV1 @ ( sK2_Xz @ SV1 ) )
| ~ ~ ( SV1 @ SV2 ) ) )
= $false )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[57]) ).
thf(59,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= ( ~ ( SV1 @ SV2 ) ) )
= $false )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ~ ( ( SV1 @ ( sK2_Xz @ SV1 ) )
| ~ ( SV1 @ SV2 ) ) )
= $false )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV2: a,SV1: a > $o] :
( ( ( ( SV1 @ ( sK2_Xz @ SV1 ) )
| ~ ( SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV2: a,SV1: a > $o] :
( ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ SV2 ) )
= $true )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV2: a,SV1: a > $o] :
( ( ( SV1 @ SV2 )
= $false )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV2: a,SV24: a > $o] :
( ( ( ~ ~ ~ ~ ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: a] : ~ ( ~ ( ~ ( ~ ( ~ ( SV24 @ SX0 ) ) ) ) ) ))]]) ).
thf(73,plain,
! [SV2: a,SV21: a > $o] :
( ( ( ~ ~ ~ ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV2 ) )
= $false ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: a] : ~ ( ~ ( ~ ( ~ ( SV21 @ SX0 ) ) ) ) ))]]) ).
thf(74,plain,
! [SV2: a,SV18: a > $o] :
( ( ( ~ ~ ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV2 ) )
= $true ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: a] : ~ ( ~ ( ~ ( SV18 @ SX0 ) ) ) ))]]) ).
thf(77,plain,
! [SV2: a,SV15: a > $o] :
( ( ( ~ ~ ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV15 @ SV2 ) )
= $false ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: a] : ~ ( ~ ( SV15 @ SX0 ) ) ))]]) ).
thf(78,plain,
! [SV2: a,SV12: a > $o] :
( ( ( ~ ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV12 @ SV2 ) )
= $true ) ),
inference(extuni,[status(esa)],[59:[bind(SV1,$thf( ^ [SX0: a] : ~ ( SV12 @ SX0 ) ))]]) ).
thf(81,plain,
! [SV2: a,SV12: a > $o] :
( ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV12 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV2: a,SV15: a > $o] :
( ( ( ~ ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV15 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV2: a,SV18: a > $o] :
( ( ( ~ ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV2: a,SV21: a > $o] :
( ( ( ~ ~ ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV2: a,SV24: a > $o] :
( ( ( ~ ~ ~ ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(91,plain,
! [SV2: a,SV12: a > $o] :
( ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( SV12 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV2: a,SV15: a > $o] :
( ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV15 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(95,plain,
! [SV2: a,SV18: a > $o] :
( ( ( ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV2: a,SV21: a > $o] :
( ( ( ~ ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(99,plain,
! [SV2: a,SV24: a > $o] :
( ( ( ~ ~ ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(101,plain,
! [SV2: a,SV12: a > $o] :
( ( ( ~ ( SV12 @ SV2 ) )
= $false )
| ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV2: a,SV15: a > $o] :
( ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( ~ ~ ( SV15 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(105,plain,
! [SV2: a,SV18: a > $o] :
( ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV18 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV2: a,SV21: a > $o] :
( ( ( ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV2: a,SV24: a > $o] :
( ( ( ~ ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV2: a,SV12: a > $o] :
( ( ( SV12 @ SV2 )
= $true )
| ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false )
| ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(112,plain,
! [SV2: a,SV15: a > $o] :
( ( ( ~ ( SV15 @ SV2 ) )
= $true )
| ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV2: a,SV18: a > $o] :
( ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( SV18 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV2: a,SV21: a > $o] :
( ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) ) )
= $false )
| ( ( ~ ~ ( SV21 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(119,plain,
! [SV2: a,SV24: a > $o] :
( ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(120,plain,
! [SV2: a,SV15: a > $o] :
( ( ( SV15 @ SV2 )
= $false )
| ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true )
| ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV2: a,SV18: a > $o] :
( ( ( ~ ( SV18 @ SV2 ) )
= $false )
| ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV2: a,SV21: a > $o] :
( ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( ~ ~ ( SV21 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(127,plain,
! [SV2: a,SV24: a > $o] :
( ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV2: a,SV18: a > $o] :
( ( ( SV18 @ SV2 )
= $true )
| ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false )
| ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(130,plain,
! [SV2: a,SV21: a > $o] :
( ( ( ~ ( SV21 @ SV2 ) )
= $true )
| ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(133,plain,
! [SV2: a,SV24: a > $o] :
( ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( ~ ~ ( SV24 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV2: a,SV21: a > $o] :
( ( ( SV21 @ SV2 )
= $false )
| ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true )
| ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV2: a,SV24: a > $o] :
( ( ( ~ ( SV24 @ SV2 ) )
= $false )
| ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(139,plain,
! [SV2: a,SV24: a > $o] :
( ( ( SV24 @ SV2 )
= $true )
| ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(140,plain,
! [SV2: a,SV7: a > $o] :
( ( ( SV7
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(141,plain,
! [SV2: a,SV4: a,SV7: a > $o] :
( ( ( SV7 @ SV4 )
= $true )
| ( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) )
@ SV4 )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(142,plain,
! [SV2: a,SV3: a,SV7: a > $o] :
( ( ( SV7 @ SV3 )
= $true )
| ( ( ~ ( SV7
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) ) )
= $true )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(143,plain,
! [SV2: a,SV3: a,SV7: a > $o] :
( ( ( SV7 @ SV3 )
= $true )
| ( ( cR @ SV3
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(144,plain,
! [SV2: a,SV7: a > $o] :
( ( ( SV7 @ SV2 )
= $true )
| ( ( SV7
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(145,plain,
! [SV4: a,SV2: a,SV7: a > $o] :
( ( ( SV7 @ SV2 )
= $true )
| ( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) )
@ SV4 )
= $true )
| ( ( SV7 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(146,plain,
! [SV2: a,SV3: a,SV7: a > $o] :
( ( ( SV7
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false )
| ( ( SV7 @ SV3 )
= $true )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV7 @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV3: a,SV2: a,SV7: a > $o] :
( ( ( SV7 @ SV2 )
= $true )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( cR @ SV3
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false )
| ( ( SV7 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(148,plain,
! [SV3: a,SV2: a,SV7: a > $o] :
( ( ( SV7 @ SV2 )
= $true )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $true )
| ( ( SV7 @ SV3 )
= $true )
| ( ( SV7
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] :
~ ( SV7 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(149,plain,
( ( ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
= sK1_Xx )
= $true ),
inference(extuni,[status(esa)],[44:[bind(SV2,$thf( sK1_Xx ))]]) ).
thf(150,plain,
( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
@ sK1_Xx )
= $true ),
inference(extuni,[status(esa)],[48:[bind(SV2,$thf( sK1_Xx )),bind(SV4,$thf( sK1_Xx ))]]) ).
thf(151,plain,
( ( ( sK1_Xx
= ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $true )
| ( ( ( sK3_Xx @ sK1_Xx
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) )
= sK1_Xx )
= $true ) ),
inference(extuni,[status(esa)],[52:[bind(SV2,$thf( sK1_Xx )),bind(SV3,$thf( sK1_Xx ))]]) ).
thf(152,plain,
( ( ( sK1_Xx
= ( sK2_Xz
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $true )
| ( ( cR @ sK1_Xx
@ ( sK3_Xx @ sK1_Xx
@ ^ [SX0: a] : ( SX0 = sK1_Xx ) ) )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV2,$thf( sK1_Xx )),bind(SV3,$thf( sK1_Xx ))]]) ).
thf(153,plain,
! [SV2: a,SV1: a > $o] :
( ( ( SV1 @ SV2 )
= $false )
| ( ( SV1 @ ( sK2_Xz @ SV1 ) )
= $true ) ),
inference(sim,[status(thm)],[66]) ).
thf(154,plain,
! [SV2: a,SV12: a > $o] :
( ( ( SV12 @ SV2 )
= $true )
| ( ( SV12
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ( SV12 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[111]) ).
thf(155,plain,
! [SV2: a,SV15: a > $o] :
( ( ( SV15 @ SV2 )
= $false )
| ( ( SV15
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ( SV15 @ SX0 ) ) )
= $true ) ),
inference(sim,[status(thm)],[120]) ).
thf(156,plain,
! [SV2: a,SV18: a > $o] :
( ( ( SV18 @ SV2 )
= $true )
| ( ( SV18
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ( SV18 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[129]) ).
thf(157,plain,
! [SV2: a,SV21: a > $o] :
( ( ( SV21 @ SV2 )
= $false )
| ( ( SV21
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ( SV21 @ SX0 ) ) )
= $true ) ),
inference(sim,[status(thm)],[134]) ).
thf(158,plain,
! [SV2: a,SV24: a > $o] :
( ( ( SV24 @ SV2 )
= $true )
| ( ( SV24
@ ( sK2_Xz
@ ^ [SX0: a] :
~ ~ ~ ~ ~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(sim,[status(thm)],[139]) ).
thf(159,plain,
! [SV4: a] :
( ( cR
@ ( sK2_Xz
@ ^ [SX0: a] : $true )
@ SV4 )
= $true ),
inference(sim,[status(thm)],[45]) ).
thf(160,plain,
! [SV3: a] :
( ( ( cR @ SV3
@ ( sK3_Xx @ SV3
@ ^ [SX0: a] : $true ) )
= $false )
| ( ( SV3
= ( sK2_Xz
@ ^ [SX0: a] : $true ) )
= $true ) ),
inference(sim,[status(thm)],[53]) ).
thf(161,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,160,159,158,157,156,155,154,153,152,151,150,149,148,147,145,144,40,38,37,29]) ).
thf(162,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV273^5 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:46:50 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25
% 0.09/0.25 No.of.Axioms: 0
% 0.09/0.25
% 0.09/0.25 Length.of.Defs: 0
% 0.09/0.25
% 0.09/0.25 Contains.Choice.Funs: false
% 0.09/0.25 ..
% 0.09/0.25
% 0.09/0.25 ********************************
% 0.09/0.25 * All subproblems solved! *
% 0.09/0.25 ********************************
% 0.09/0.25 % 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:161,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.09/0.25
% 0.09/0.25 %**** Beginning of derivation protocol ****
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 %**** End of derivation protocol ****
% 0.09/0.25 %**** no. of clauses in derivation: 115 ****
% 0.09/0.25 %**** clause counter: 161 ****
% 0.09/0.25
% 0.09/0.25 % 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:161,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------