TSTP Solution File: NUM812^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM812^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:55:44 EDT 2022
% Result : Theorem 150.33s 150.51s
% Output : CNFRefutation 150.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 7
% Syntax : Number of formulae : 129 ( 28 unt; 5 typ; 1 def)
% Number of atoms : 852 ( 581 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 755 ( 174 ~; 196 |; 7 &; 369 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 288 ( 123 ^ 160 !; 5 ?; 288 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c0,type,
c0: $i ).
thf(tp_cIND,type,
cIND: $o ).
thf(tp_cS,type,
cS: $i > $i ).
thf(tp_sK1_Xn,type,
sK1_Xn: $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: ( $i > $o ) > $i ).
thf(cIND,definition,
( cIND
= ( ! [Xp: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xx: $i] :
( ( Xp @ Xx )
=> ( Xp @ ( cS @ Xx ) ) ) )
=> ! [Xx: $i] : ( Xp @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cIND) ).
thf(1,conjecture,
( cIND
=> ! [Xn: $i] :
( ( Xn = c0 )
| ? [Xm: $i] :
( Xn
= ( cS @ Xm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM578) ).
thf(2,negated_conjecture,
( ( cIND
=> ! [Xn: $i] :
( ( Xn = c0 )
| ? [Xm: $i] :
( Xn
= ( cS @ Xm ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xp: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xx: $i] :
( ( Xp @ Xx )
=> ( Xp @ ( cS @ Xx ) ) ) )
=> ! [Xx: $i] : ( Xp @ Xx ) )
=> ! [Xn: $i] :
( ( Xn = c0 )
| ? [Xm: $i] :
( Xn
= ( cS @ Xm ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cIND]) ).
thf(4,plain,
( ( ! [Xp: $i > $o] :
( ( ( Xp @ c0 )
& ! [Xx: $i] :
( ( Xp @ Xx )
=> ( Xp @ ( cS @ Xx ) ) ) )
=> ! [Xx: $i] : ( Xp @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xn: $i] :
( ( Xn = c0 )
| ? [Xm: $i] :
( Xn
= ( cS @ Xm ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [Xn: $i] :
( ( Xn = c0 )
| ? [Xm: $i] :
( Xn
= ( cS @ Xm ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( sK1_Xn != c0 )
& ! [SY145: $i] :
( sK1_Xn
!= ( cS @ SY145 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xp: $i > $o] :
( ( ( Xp @ ( sK2_Xx @ Xp ) )
& ~ ( Xp @ ( cS @ ( sK2_Xx @ Xp ) ) ) )
| ~ ( Xp @ c0 )
| ! [Xx: $i] : ( Xp @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xp: $i > $o] :
( ( ( Xp @ ( sK2_Xx @ Xp ) )
& ~ ( Xp @ ( cS @ ( sK2_Xx @ Xp ) ) ) )
| ~ ( Xp @ c0 )
| ! [Xx: $i] : ( Xp @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( sK1_Xn != c0 )
& ! [SY145: $i] :
( sK1_Xn
!= ( cS @ SY145 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i > $o] :
( ~ ( ~ ( SX0 @ ( sK2_Xx @ SX0 ) )
| ~ ~ ( SX0 @ ( cS @ ( sK2_Xx @ SX0 ) ) ) )
| ~ ( SX0 @ c0 )
| ! [SX1: $i] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,cIND]) ).
thf(12,plain,
( ( ~ ( ~ ( ( sK1_Xn != c0 ) )
| ~ ! [SX0: $i] :
( sK1_Xn
!= ( cS @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,cIND]) ).
thf(13,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( SV1 @ ( sK2_Xx @ SV1 ) )
| ~ ~ ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) ) )
| ~ ( SV1 @ c0 )
| ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ( sK1_Xn != c0 ) )
| ~ ! [SX0: $i] :
( sK1_Xn
!= ( cS @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK2_Xx @ SV1 ) )
| ~ ~ ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) ) )
| ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ( sK1_Xn != c0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( sK1_Xn
!= ( cS @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK2_Xx @ SV1 ) )
| ~ ~ ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) ) ) )
= $true )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ( sK1_Xn != c0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ! [SX0: $i] :
( sK1_Xn
!= ( cS @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK2_Xx @ SV1 ) )
| ~ ~ ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) ) )
= $false )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( sK1_Xn = c0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
! [SV2: $i] :
( ( ( sK1_Xn
!= ( cS @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK2_Xx @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i > $o] :
( ( ( ~ ~ ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) ) )
= $false )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i] :
( ( sK1_Xn
= ( cS @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK2_Xx @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) ) )
= $true )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ c0 )
= $false )
| ( ( SV1 @ ( sK2_Xx @ SV1 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ c0 ) )
= $true )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV3: $i,SV1: $i > $o] :
( ( ( SV1 @ SV3 )
= $true )
| ( ( SV1 @ ( sK2_Xx @ SV1 ) )
= $true )
| ( ( SV1 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ c0 )
= $false )
| ( ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) )
= $false )
| ( ( ! [SY146: $i] : ( SV1 @ SY146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV4: $i,SV1: $i > $o] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( SV1 @ ( cS @ ( sK2_Xx @ SV1 ) ) )
= $false )
| ( ( SV1 @ c0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( c0 = c0 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[31:[bind(SV1,$thf( ^ [SV5: $i] : ( SV5 = c0 ) ))]]) ).
thf(35,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(sim,[status(thm)],[34]) ).
thf(36,plain,
! [SV4: $i] :
( ( ( SV4 = c0 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) ) )
= c0 )
= $false )
| ( ( c0 = c0 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[33:[bind(SV1,$thf( ^ [SV6: $i] : ( SV6 = c0 ) ))]]) ).
thf(37,plain,
! [SV4: $i] :
( ( ( SV4 = c0 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) ) )
= c0 )
= $false ) ),
inference(sim,[status(thm)],[36]) ).
thf(40,plain,
! [SV3: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ SV3 ) )
= $true )
| ( ( ~ ( SV8
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV8 @ c0 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[31:[bind(SV1,$thf( ^ [SV7: $i] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( c0 = c0 )
= $false ) ),
inference(prim_subst,[status(thm)],[31:[bind(SV1,$thf( ^ [SV11: $i] : ( SV11 = c0 ) ))]]) ).
thf(45,plain,
! [SV4: $i,SV8: $i > $o] :
( ( ( ~ ( SV8 @ SV4 ) )
= $true )
| ( ( ~ ( SV8
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) ) )
= $false )
| ( ( ~ ( SV8 @ c0 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[33:[bind(SV1,$thf( ^ [SV7: $i] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(48,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[35]) ).
thf(49,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
| ~ ( ( SV3 != c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
!= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[48]) ).
thf(50,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[48]) ).
thf(51,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(53,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(55,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ),
inference(extuni,[status(esa)],[50:[bind(SV3,$thf( sK2_Xx @ ^ [SX0: $i] : ( SX0 = c0 ) ))]]) ).
thf(60,plain,
! [SV3: $i,SV8: $i > $o] :
( ( ( SV8 @ SV3 )
= $false )
| ( ( ~ ( SV8
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV8 @ c0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(61,plain,
! [SV4: $i,SV8: $i > $o] :
( ( ( SV8 @ SV4 )
= $false )
| ( ( ~ ( SV8
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) ) )
= $false )
| ( ( ~ ( SV8 @ c0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(62,plain,
! [SV3: $i,SV8: $i > $o] :
( ( ( SV8
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) )
= $false )
| ( ( SV8 @ SV3 )
= $false )
| ( ( ~ ( SV8 @ c0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV4: $i,SV8: $i > $o] :
( ( ( SV8
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) )
= $true )
| ( ( SV8 @ SV4 )
= $false )
| ( ( ~ ( SV8 @ c0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(64,plain,
! [SV3: $i,SV8: $i > $o] :
( ( ( SV8 @ c0 )
= $true )
| ( ( SV8 @ SV3 )
= $false )
| ( ( SV8
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(65,plain,
! [SV4: $i,SV8: $i > $o] :
( ( ( SV8 @ c0 )
= $true )
| ( ( SV8 @ SV4 )
= $false )
| ( ( SV8
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV8 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( SV3 = c0 )
= $true ) ),
inference(extuni,[status(esa)],[41]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(sim,[status(thm)],[55]) ).
thf(68,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( c0 = c0 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[31:[bind(SV1,$thf( ^ [SV13: $i] : ( SV13 = c0 ) ))]]) ).
thf(69,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(sim,[status(thm)],[68]) ).
thf(70,plain,
! [SV4: $i] :
( ( ( SV4 = c0 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) ) )
= c0 )
= $false )
| ( ( c0 = c0 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[33:[bind(SV1,$thf( ^ [SV14: $i] : ( SV14 = c0 ) ))]]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( SV4 = c0 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) ) )
= c0 )
= $false ) ),
inference(sim,[status(thm)],[70]) ).
thf(72,plain,
! [SV3: $i] :
( ( ( c0 = SV3 )
= $true )
| ( ( SV3 = SV3 )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV3 ) )
= SV3 )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[64:[bind(SV8,$thf( ^ [SV15: $i] : ( SV15 = SV3 ) ))]]) ).
thf(73,plain,
! [SV3: $i] :
( ( ( c0 = SV3 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV3 ) )
= SV3 )
= $false ) ),
inference(sim,[status(thm)],[72]) ).
thf(74,plain,
! [SV4: $i] :
( ( ( c0 = SV4 )
= $true )
| ( ( SV4 = SV4 )
= $false )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[65:[bind(SV8,$thf( ^ [SV16: $i] : ( SV16 = SV4 ) ))]]) ).
thf(75,plain,
! [SV4: $i] :
( ( ( c0 = SV4 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(sim,[status(thm)],[74]) ).
thf(78,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( ~ ( SV24 @ SV3 ) )
= $true )
| ( ( ~ ( SV24
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24 @ c0 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[31:[bind(SV1,$thf( ^ [SV23: $i] : ~ ( SV24 @ SV23 ) ))]]) ).
thf(79,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( c0 = c0 )
= $false ) ),
inference(prim_subst,[status(thm)],[31:[bind(SV1,$thf( ^ [SV27: $i] : ( SV27 = c0 ) ))]]) ).
thf(83,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( ~ ( SV24 @ SV4 ) )
= $true )
| ( ( ~ ( SV24
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) ) )
= $false )
| ( ( ~ ( SV24 @ c0 ) )
= $false ) ),
inference(prim_subst,[status(thm)],[33:[bind(SV1,$thf( ^ [SV23: $i] : ~ ( SV24 @ SV23 ) ))]]) ).
thf(88,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ c0 ) )
= $true )
| ( ( ~ ( SV18 @ SV3 ) )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[64:[bind(SV8,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).
thf(93,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( ~ ( SV18 @ c0 ) )
= $true )
| ( ( ~ ( SV18 @ SV4 ) )
= $false )
| ( ( ~ ( SV18
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) ) )
= $true ) ),
inference(prim_subst,[status(thm)],[65:[bind(SV8,$thf( ^ [SV17: $i] : ~ ( SV18 @ SV17 ) ))]]) ).
thf(95,plain,
! [SV4: $i] :
( ( ( c0 = sK1_Xn )
= $true )
| ( ( SV4 = sK1_Xn )
= $false )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != sK1_Xn ) ) )
= sK1_Xn )
= $true ) ),
inference(prim_subst,[status(thm)],[65:[bind(SV8,$thf( ^ [SV22: $i] : ( SV22 = sK1_Xn ) ))]]) ).
thf(96,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[69]) ).
thf(97,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[35]) ).
thf(98,plain,
! [SV4: $i] :
( ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true )
| ( ( ( c0 = SV4 )
= ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[75]) ).
thf(99,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= ( SV3 = c0 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[66]) ).
thf(100,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[67]) ).
thf(101,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
| ~ ( ( SV3 != c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
!= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[96]) ).
thf(102,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
| ~ ( ( SV3 != c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
!= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[97]) ).
thf(105,plain,
! [SV4: $i] :
( ( ( ~ ( ( c0 = SV4 )
| ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 ) )
| ~ ( ( c0 != SV4 )
| ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
!= SV4 ) ) )
= $false )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV3: $i] :
( ( ( ~ ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
| ( SV3 = c0 ) )
| ~ ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
!= c0 )
| ( SV3 != c0 ) ) )
= $false )
| ( ( SV3 = c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[99]) ).
thf(108,plain,
! [SV3: $i] :
( ( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= ( SV3 = c0 ) )
= $false )
| ( ( SV3 = c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[99]) ).
thf(109,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
| ~ ( ( SV3 != c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
!= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[100]) ).
thf(110,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
= ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[100]) ).
thf(111,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(113,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(115,plain,
! [SV4: $i] :
( ( ( ~ ( ( c0 = SV4 )
| ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 ) ) )
= $false )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(117,plain,
! [SV3: $i] :
( ( ( ~ ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
| ( SV3 = c0 ) ) )
= $false )
| ( ( SV3 = c0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV3: $i] :
( ( ( ~ ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) ) )
= $false )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(121,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(123,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(125,plain,
! [SV4: $i] :
( ( ( ( c0 = SV4 )
| ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 ) )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(127,plain,
! [SV3: $i] :
( ( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
| ( SV3 = c0 ) )
= $true )
| ( ( SV3 = c0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(129,plain,
! [SV3: $i] :
( ( ( ( SV3 = c0 )
| ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 ) )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(131,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV4: $i] :
( ( ( c0 = SV4 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( SV3 = c0 )
= $true )
| ( ( SV3 = c0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(151,plain,
( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ),
inference(extuni,[status(esa)],[102:[bind(SV3,$thf( sK2_Xx @ ^ [SX0: $i] : ( SX0 = c0 ) ))]]) ).
thf(152,plain,
( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ),
inference(extuni,[status(esa)],[104:[bind(SV3,$thf( sK2_Xx @ ^ [SX0: $i] : ( SX0 = c0 ) ))]]) ).
thf(153,plain,
( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ),
inference(extuni,[status(esa)],[108:[bind(SV3,$thf( sK2_Xx @ ^ [SX0: $i] : ( SX0 = c0 ) ))]]) ).
thf(154,plain,
( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ),
inference(extuni,[status(esa)],[110:[bind(SV3,$thf( sK2_Xx @ ^ [SX0: $i] : ( SX0 = c0 ) ))]]) ).
thf(155,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24 @ SV3 )
= $false )
| ( ( ~ ( SV24
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( SV24 @ c0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(156,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( SV24 @ SV4 )
= $false )
| ( ( ~ ( SV24
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) ) )
= $false )
| ( ( ~ ( SV24 @ c0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(157,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18 @ c0 )
= $false )
| ( ( ~ ( SV18 @ SV3 ) )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(158,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( SV18 @ c0 )
= $false )
| ( ( ~ ( SV18 @ SV4 ) )
= $false )
| ( ( ~ ( SV18
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(159,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) )
= $false )
| ( ( SV24 @ SV3 )
= $false )
| ( ( ~ ( SV24 @ c0 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(160,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( SV24
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true )
| ( ( SV24 @ SV4 )
= $false )
| ( ( ~ ( SV24 @ c0 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(161,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18 @ SV3 )
= $true )
| ( ( SV18 @ c0 )
= $false )
| ( ( ~ ( SV18
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(162,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( SV18 @ SV4 )
= $true )
| ( ( SV18 @ c0 )
= $false )
| ( ( ~ ( SV18
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV3: $i,SV24: $i > $o] :
( ( ( SV24 @ c0 )
= $true )
| ( ( SV24 @ SV3 )
= $false )
| ( ( SV24
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV4: $i,SV24: $i > $o] :
( ( ( SV24 @ c0 )
= $true )
| ( ( SV24 @ SV4 )
= $false )
| ( ( SV24
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ( SV24 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV3: $i,SV18: $i > $o] :
( ( ( SV18
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) )
= $true )
| ( ( SV18 @ c0 )
= $false )
| ( ( SV18 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(166,plain,
! [SV4: $i,SV18: $i > $o] :
( ( ( SV18
@ ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] :
~ ~ ( SV18 @ SX0 ) ) ) )
= $false )
| ( ( SV18 @ c0 )
= $false )
| ( ( SV18 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( SV3 = c0 )
= $true ) ),
inference(extuni,[status(esa)],[79]) ).
thf(169,plain,
( ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != sK1_Xn ) ) )
= sK1_Xn )
= $true )
| ( ( c0 = sK1_Xn )
= $true ) ),
inference(extuni,[status(esa)],[95:[bind(SV4,$thf( sK1_Xn ))]]) ).
thf(170,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(sim,[status(thm)],[131]) ).
thf(171,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(sim,[status(thm)],[133]) ).
thf(172,plain,
! [SV4: $i] :
( ( ( c0 = SV4 )
= $true )
| ( ( ( cS
@ ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 != SV4 ) ) )
= SV4 )
= $true ) ),
inference(sim,[status(thm)],[135]) ).
thf(173,plain,
! [SV3: $i] :
( ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true )
| ( ( SV3 = c0 )
= $true ) ),
inference(sim,[status(thm)],[137]) ).
thf(174,plain,
! [SV3: $i] :
( ( ( SV3 = c0 )
= $true )
| ( ( ( sK2_Xx
@ ^ [SX0: $i] : ( SX0 = c0 ) )
= c0 )
= $true ) ),
inference(sim,[status(thm)],[139]) ).
thf(175,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,174,173,172,171,170,169,167,166,165,164,163,154,153,152,151,75,73,71,69,67,66,65,64,59,37,35,33,31,26]) ).
thf(176,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM812^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 01:34:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 0
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 188
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.20/0.49
% 0.20/0.49 Prim_subst applied to clause
% 0.20/0.49
% 0.20/0.49 70:[ 0:<SV15@SV14 = $true>-w(1)-i() 1:<SV15@(sK2_Xx@SV15) = $true>-w(1)-i() 2:<SV15@c0 = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 31)-o(AXIOM)-fv([ SV14 SV15 ])
% 0.20/0.52
% 0.20/0.52 Prim_subst applied to clause
% 0.20/0.52
% 0.20/0.52 70:[ 0:<SV15@SV14 = $true>-w(1)-i() 1:<SV15@(sK2_Xx@SV15) = $true>-w(1)-i() 2:<SV15@c0 = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 31)-o(AXIOM)-fv([ SV14 SV15 ])
% 0.20/0.55 .
% 0.20/0.55
% 0.20/0.55 Prim_subst applied to clause
% 0.20/0.55
% 0.20/0.55 70:[ 0:<SV15@SV14 = $true>-w(1)-i() 1:<SV15@(sK2_Xx@SV15) = $true>-w(1)-i() 2:<SV15@c0 = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 31)-o(AXIOM)-fv([ SV14 SV15 ])
% 0.90/1.07 ......................
% 75.21/75.37 (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 75.25/75.46
% 75.25/75.46 Prim_subst applied to clause
% 75.25/75.46
% 75.25/75.46 63:[ 0:<SV15@SV14 = $true>-w(1)-i() 1:<SV15@c0 = $false>-w(1)-i() 2:<SV15@(cS@(sK2_SY86@SV15)) = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 30)-o(AXIOM)-fv([ SV14 SV15 ])
% 75.25/75.47
% 75.25/75.47 Prim_subst applied to clause
% 75.25/75.47
% 75.25/75.47 63:[ 0:<SV15@SV14 = $true>-w(1)-i() 1:<SV15@c0 = $false>-w(1)-i() 2:<SV15@(cS@(sK2_SY86@SV15)) = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 30)-o(AXIOM)-fv([ SV14 SV15 ])
% 75.25/75.48
% 75.25/75.48 Prim_subst applied to clause
% 75.25/75.48
% 75.25/75.48 63:[ 0:<SV15@SV14 = $true>-w(1)-i() 1:<SV15@c0 = $false>-w(1)-i() 2:<SV15@(cS@(sK2_SY86@SV15)) = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 30)-o(AXIOM)-fv([ SV14 SV15 ])
% 75.25/75.49 ..............................................
% 150.06/150.29 (rf:0,axioms:0,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).....
% 150.33/150.51
% 150.33/150.51 ********************************
% 150.33/150.51 * All subproblems solved! *
% 150.33/150.51 ********************************
% 150.33/150.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:175,loop_count:0,foatp_calls:3,translation:fof_full)
% 150.36/150.51
% 150.36/150.51 %**** Beginning of derivation protocol ****
% 150.36/150.51 % SZS output start CNFRefutation
% See solution above
% 150.36/150.52
% 150.36/150.52 %**** End of derivation protocol ****
% 150.36/150.52 %**** no. of clauses in derivation: 123 ****
% 150.36/150.52 %**** clause counter: 175 ****
% 150.36/150.52
% 150.36/150.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:175,loop_count:0,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------