TSTP Solution File: SEV222^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEV222^5 : TPTP v8.1.0. Released v4.0.0.
% 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 : Tue Jul 19 17:35:44 EDT 2022
% Result : Theorem 75.41s 75.65s
% Output : CNFRefutation 75.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 18
% Syntax : Number of formulae : 298 ( 54 unt; 17 typ; 0 def)
% Number of atoms : 2608 ( 891 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 3649 ( 606 ~; 888 |; 19 &;2115 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 389 ( 389 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 3 con; 0-2 aty)
% Number of variables : 748 ( 357 ^ 384 !; 7 ?; 748 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cW,type,
cW: ( a > $o ) > $o ).
thf(tp_cZ,type,
cZ: a > $o ).
thf(tp_sK10_SV25,type,
sK10_SV25: ( a > $o ) > a ).
thf(tp_sK11_SV26,type,
sK11_SV26: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK12_E,type,
sK12_E: ( a > $o ) > a ).
thf(tp_sK13_E,type,
sK13_E: ( a > $o ) > a ).
thf(tp_sK14_E,type,
sK14_E: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_SY421,type,
sK2_SY421: a > $o ).
thf(tp_sK3_SY424,type,
sK3_SY424: a > $o ).
thf(tp_sK4_SY420,type,
sK4_SY420: a > $o ).
thf(tp_sK5_SV6,type,
sK5_SV6: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK6_SV21,type,
sK6_SV21: ( a > $o ) > a ).
thf(tp_sK7_SV22,type,
sK7_SV22: ( a > $o ) > a ).
thf(tp_sK8_SV23,type,
sK8_SV23: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK9_SV24,type,
sK9_SV24: ( a > $o ) > a ).
thf(1,conjecture,
! [Xx: a] :
( ( ! [S: a > $o] :
( ( cW @ S )
=> ( S @ Xx ) )
| ( cZ @ Xx ) )
<=> ! [S: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( S
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( S @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM60_pme) ).
thf(2,negated_conjecture,
( ( ! [Xx: a] :
( ( ! [S: a > $o] :
( ( cW @ S )
=> ( S @ Xx ) )
| ( cZ @ Xx ) )
<=> ! [S: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( S
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [SY420: a > $o] :
( ( cW @ SY420 )
=> ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
<=> ! [SY421: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( SY421
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( SY421 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2]) ).
thf(4,plain,
( ( ( ! [SY420: a > $o] :
( ( cW @ SY420 )
=> ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
=> ! [SY421: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( SY421
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( SY421 @ sK1_Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ! [SY421: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( SY421
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( SY421 @ sK1_Xx ) )
=> ( ! [SY420: a > $o] :
( ( cW @ SY420 )
=> ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ( ! [SY420: a > $o] :
( ( cW @ SY420 )
=> ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
=> ! [SY421: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( SY421
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( SY421 @ sK1_Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ! [SY421: a > $o] :
( ? [Xt: a > $o] :
( ( cW @ Xt )
& ( SY421
= ( ^ [Xz: a] :
( ( cZ @ Xz )
| ( Xt @ Xz ) ) ) ) )
=> ( SY421 @ sK1_Xx ) )
=> ( ! [SY420: a > $o] :
( ( cW @ SY420 )
=> ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ! [SY420: a > $o] :
( ~ ( cW @ SY420 )
| ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
& ( sK2_SY421
= ( ^ [SY426: a] :
( ( sK3_SY424 @ SY426 )
| ( cZ @ SY426 ) ) ) )
& ( cW @ sK3_SY424 )
& ~ ( sK2_SY421 @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ! [SY421: a > $o] :
( ! [Xt: a > $o] :
( ( SY421
!= ( ^ [Xz: a] :
( ( Xt @ Xz )
| ( cZ @ Xz ) ) ) )
| ~ ( cW @ Xt ) )
| ( SY421 @ sK1_Xx ) )
& ( cW @ sK4_SY420 )
& ~ ( sK4_SY420 @ sK1_Xx )
& ~ ( cZ @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( ! [SY420: a > $o] :
( ~ ( cW @ SY420 )
| ( SY420 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
& ( sK2_SY421
= ( ^ [SY426: a] :
( ( sK3_SY424 @ SY426 )
| ( cZ @ SY426 ) ) ) )
& ( cW @ sK3_SY424 )
& ~ ( sK2_SY421 @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ( ! [SX0: a > $o] :
( ~ ( cW @ SX0 )
| ( SX0 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) )
| ~ ~ ( sK2_SY421 @ sK1_Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ( ! [SX0: a > $o] :
( ~ ( cW @ SX0 )
| ( SX0 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) )
| ~ ~ ( sK2_SY421 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ( ! [SX0: a > $o] :
( ~ ( cW @ SX0 )
| ( SX0 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) )
| ~ ~ ( sK2_SY421 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SX0: a > $o] :
( ~ ( cW @ SX0 )
| ( SX0 @ sK1_Xx ) )
| ( cZ @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) )
| ~ ~ ( sK2_SY421 @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ! [SX0: a > $o] :
( ~ ( cW @ SX0 )
| ( SX0 @ sK1_Xx ) ) )
= $true )
| ( ( cZ @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) )
| ~ ~ ( sK2_SY421 @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV1: a > $o] :
( ( ( ~ ( cW @ SV1 )
| ( SV1 @ sK1_Xx ) )
= $true )
| ( ( cZ @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( sK2_SY421 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: a > $o] :
( ( ( ~ ( cW @ SV1 ) )
= $true )
| ( ( SV1 @ sK1_Xx )
= $true )
| ( ( cZ @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( sK2_SY421 @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: a > $o] :
( ( ( cW @ SV1 )
= $false )
| ( ( SV1 @ sK1_Xx )
= $true )
| ( ( cZ @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
| ~ ( cW @ sK3_SY424 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( sK2_SY421 @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ( sK2_SY421
!= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( cW @ sK3_SY424 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( sK2_SY421
= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( cW @ sK3_SY424 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ! [SV2: a] :
( ( sK2_SY421 @ SV2 )
= ( ( sK3_SY424 @ SV2 )
| ( cZ @ SV2 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[30]) ).
thf(33,plain,
( ( sK2_SY421
= ( ^ [SX0: a] :
( ( sK3_SY424 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: a] :
( ( ( sK2_SY421 @ SV3 )
= ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: a] :
( ( ~ ( ( sK2_SY421 @ SV3 )
| ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) )
| ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[34]) ).
thf(36,plain,
! [SV3: a] :
( ( ( sK2_SY421 @ SV3 )
= ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: a] :
( ( ( ~ ( ( sK2_SY421 @ SV3 )
| ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: a] :
( ( ( ( sK2_SY421 @ SV3 )
| ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV3: a] :
( ( ( sK2_SY421 @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(40,plain,
! [SV3: a] :
( ( ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $false )
| ( ( sK2_SY421 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: a] :
( ( ( sK3_SY424 @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV3: a] :
( ( ( cZ @ SV3 )
= $false )
| ( ( ~ ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY421 @ SV3 ) )
= $false )
| ( ( sK2_SY421 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: a] :
( ( ( ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $false )
| ( ( sK2_SY421 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $false )
| ( ( sK3_SY424 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY421 @ SV3 )
| ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $false )
| ( ( cZ @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV3: a] :
( ( ( sK2_SY421 @ SV3 )
= $true )
| ( ( sK2_SY421 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: a] :
( ( ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) )
= $true )
| ( ( sK2_SY421 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY421 @ SV3 ) )
= $false )
| ( ( sK3_SY424 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV3: a] :
( ( ( ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $false )
| ( ( sK3_SY424 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: a] :
( ( ( ~ ( sK2_SY421 @ SV3 ) )
= $false )
| ( ( cZ @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV3: a] :
( ( ( ~ ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) ) )
= $false )
| ( ( cZ @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(54,plain,
! [SV3: a] :
( ( ( sK3_SY424 @ SV3 )
= $true )
| ( ( cZ @ SV3 )
= $true )
| ( ( sK2_SY421 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV3: a] :
( ( ( sK2_SY421 @ SV3 )
= $true )
| ( ( sK3_SY424 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV3: a] :
( ( ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) )
= $true )
| ( ( sK3_SY424 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV3: a] :
( ( ( sK2_SY421 @ SV3 )
= $true )
| ( ( cZ @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: a] :
( ( ( ( sK3_SY424 @ SV3 )
| ( cZ @ SV3 ) )
= $true )
| ( ( cZ @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(59,plain,
! [SV3: a] :
( ( ( sK3_SY424 @ SV3 )
= $true )
| ( ( cZ @ SV3 )
= $true )
| ( ( sK3_SY424 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV3: a] :
( ( ( sK3_SY424 @ SV3 )
= $true )
| ( ( cZ @ SV3 )
= $true )
| ( ( cZ @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,60,59,57,55,54,48,36,33,31,27]) ).
thf(62,plain,
( ( ! [SY421: a > $o] :
( ! [Xt: a > $o] :
( ( SY421
!= ( ^ [Xz: a] :
( ( Xt @ Xz )
| ( cZ @ Xz ) ) ) )
| ~ ( cW @ Xt ) )
| ( SY421 @ sK1_Xx ) )
& ( cW @ sK4_SY420 )
& ~ ( sK4_SY420 @ sK1_Xx )
& ~ ( cZ @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(63,plain,
( ( ~ ( ~ ! [SX0: a > $o] :
( ! [SX1: a > $o] :
( ( SX0
!= ( ^ [SX2: a] :
( ( SX1 @ SX2 )
| ( cZ @ SX2 ) ) ) )
| ~ ( cW @ SX1 ) )
| ( SX0 @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) )
| ~ ~ ( cZ @ sK1_Xx ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(64,plain,
( ( ~ ! [SX0: a > $o] :
( ! [SX1: a > $o] :
( ( SX0
!= ( ^ [SX2: a] :
( ( SX1 @ SX2 )
| ( cZ @ SX2 ) ) ) )
| ~ ( cW @ SX1 ) )
| ( SX0 @ sK1_Xx ) )
| ~ ~ ( ~ ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) )
| ~ ~ ( cZ @ sK1_Xx ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(65,plain,
( ( ~ ! [SX0: a > $o] :
( ! [SX1: a > $o] :
( ( SX0
!= ( ^ [SX2: a] :
( ( SX1 @ SX2 )
| ( cZ @ SX2 ) ) ) )
| ~ ( cW @ SX1 ) )
| ( SX0 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(66,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) )
| ~ ~ ( cZ @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(67,plain,
( ( ! [SX0: a > $o] :
( ! [SX1: a > $o] :
( ( SX0
!= ( ^ [SX2: a] :
( ( SX1 @ SX2 )
| ( cZ @ SX2 ) ) ) )
| ~ ( cW @ SX1 ) )
| ( SX0 @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(68,plain,
( ( ~ ( ~ ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) )
| ~ ~ ( cZ @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(69,plain,
! [SV4: a > $o] :
( ( ! [SY427: a > $o] :
( ( SV4
!= ( ^ [SX2: a] :
( ( SY427 @ SX2 )
| ( cZ @ SX2 ) ) ) )
| ~ ( cW @ SY427 ) )
| ( SV4 @ sK1_Xx ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(70,plain,
( ( ~ ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) )
| ~ ~ ( cZ @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV4: a > $o] :
( ( ( ! [SY427: a > $o] :
( ( SV4
!= ( ^ [SX2: a] :
( ( SY427 @ SX2 )
| ( cZ @ SX2 ) ) ) )
| ~ ( cW @ SY427 ) ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(72,plain,
( ( ~ ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(73,plain,
( ( ~ ~ ( cZ @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(74,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ( SV4
!= ( ^ [SY429: a] :
( ( SV5 @ SY429 )
| ( cZ @ SY429 ) ) ) )
| ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(75,plain,
( ( ~ ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(76,plain,
( ( ~ ( cZ @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ( SV4
!= ( ^ [SY429: a] :
( ( SV5 @ SY429 )
| ( cZ @ SY429 ) ) ) ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(78,plain,
( ( ~ ( cW @ sK4_SY420 )
| ~ ~ ( sK4_SY420 @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
( ( cZ @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( SV4
= ( ^ [SY429: a] :
( ( SV5 @ SY429 )
| ( cZ @ SY429 ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(81,plain,
( ( ~ ( cW @ sK4_SY420 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(82,plain,
( ( ~ ~ ( sK4_SY420 @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(83,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ! [SV6: a] :
( ( SV4 @ SV6 )
= ( ( SV5 @ SV6 )
| ( cZ @ SV6 ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( SV4
= ( ^ [SY429: a] :
( ( SV5 @ SY429 )
| ( cZ @ SY429 ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[80]) ).
thf(85,plain,
( ( cW @ sK4_SY420 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(86,plain,
( ( ~ ( sK4_SY420 @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(88,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( SV4
= ( ^ [SY429: a] :
( ( SV5 @ SY429 )
| ( cZ @ SY429 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(89,plain,
( ( sK4_SY420 @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) )
| ~ ( ~ ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ~ ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[87]) ).
thf(91,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[87]) ).
thf(92,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(93,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ~ ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(94,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ~ ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(97,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) ) )
= $true )
| ( ( ~ ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(100,plain,
! [SV5: a > $o,SV4: a > $o] :
( ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( ~ ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(101,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(102,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
| ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(104,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( ~ ( cW @ SV5 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(105,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( SV5 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
! [SV4: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( SV4 @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( cZ @ ( sK5_SV6 @ SV5 @ SV4 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4
= ( ^ [SX0: a] :
( $true
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[88:[bind(SV5,$thf( ^ [SV10: a] : $true ))]]) ).
thf(108,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4
= ( ^ [SX0: a] :
( $false
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[88:[bind(SV5,$thf( ^ [SV9: a] : $false ))]]) ).
thf(109,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4
= ( ^ [SX0: a] :
( ~ ( SV8 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[88:[bind(SV5,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(111,plain,
! [SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ( ^ [SX0: a] : $false )
= ( ^ [SX0: a] :
( ( SV5 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[88:[bind(SV4,$thf( ^ [SV14: a] : $false ))]]) ).
thf(112,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ( ^ [SX0: a] :
~ ( SV13 @ SX0 ) )
= ( ^ [SX0: a] :
( ( SV5 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(prim_subst,[status(thm)],[88:[bind(SV4,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(113,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[94:[bind(SV5,$thf( ^ [SV10: a] : $true ))]]) ).
thf(114,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[94:[bind(SV5,$thf( ^ [SV9: a] : $false ))]]) ).
thf(115,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[94:[bind(SV5,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(117,plain,
! [SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( $false
= ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) ) ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[94:[bind(SV4,$thf( ^ [SV14: a] : $false ))]]) ).
thf(118,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(prim_subst,[status(thm)],[94:[bind(SV4,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(120,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( $false = $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[101:[bind(SV5,$thf( ^ [SV9: a] : $false ))]]) ).
thf(121,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[101:[bind(SV5,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(123,plain,
! [SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( $false = $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[101:[bind(SV4,$thf( ^ [SV14: a] : $false ))]]) ).
thf(124,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(prim_subst,[status(thm)],[101:[bind(SV4,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(125,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( $true = $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV5,$thf( ^ [SV10: a] : $true ))]]) ).
thf(127,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV5,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(130,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $false )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(prim_subst,[status(thm)],[105:[bind(SV4,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(131,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[106:[bind(SV5,$thf( ^ [SV10: a] : $true ))]]) ).
thf(132,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $false )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[106:[bind(SV5,$thf( ^ [SV9: a] : $false ))]]) ).
thf(133,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(prim_subst,[status(thm)],[106:[bind(SV5,$thf( ^ [SV7: a] : ~ ( SV8 @ SV7 ) ))]]) ).
thf(136,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $false )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(prim_subst,[status(thm)],[106:[bind(SV4,$thf( ^ [SV12: a] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(137,plain,
! [SV5: a > $o] :
( ( ( ( SV5 @ sK1_Xx )
| ( cZ @ sK1_Xx ) )
= $true )
| ( ( cW @ SV5 )
= $false ) ),
inference(extuni,[status(esa)],[88:[bind(SV4,$thf( ^ [SX0: a] : ( ( SV5 @ SX0 ) | ( cZ @ SX0 ) ) ))]]) ).
thf(138,plain,
! [SV5: a > $o] :
( ( ( SV5 @ sK1_Xx )
= $true )
| ( ( cZ @ sK1_Xx )
= $true )
| ( ( cW @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(139,plain,
! [SV4: a > $o] :
( ( ( ! [SV21: a] :
( ( SV4 @ SV21 )
= ( $true
| ( cZ @ SV21 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[107]) ).
thf(140,plain,
! [SV4: a > $o] :
( ( ( SV4
= ( ^ [SX0: a] :
( $true
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[107]) ).
thf(141,plain,
! [SV4: a > $o] :
( ( ( ! [SV22: a] :
( ( SV4 @ SV22 )
= ( $false
| ( cZ @ SV22 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[108]) ).
thf(142,plain,
! [SV4: a > $o] :
( ( ( SV4
= ( ^ [SX0: a] :
( $false
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[108]) ).
thf(143,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ! [SV23: a] :
( ( SV4 @ SV23 )
= ( ~ ( SV8 @ SV23 )
| ( cZ @ SV23 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[109]) ).
thf(144,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( SV4
= ( ^ [SX0: a] :
( ~ ( SV8 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[109]) ).
thf(147,plain,
! [SV5: a > $o] :
( ( ( ! [SV25: a] :
( $false
= ( ( SV5 @ SV25 )
| ( cZ @ SV25 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[111]) ).
thf(148,plain,
! [SV5: a > $o] :
( ( ( ( ^ [SX0: a] : $false )
= ( ^ [SX0: a] :
( ( SV5 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[111]) ).
thf(149,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ! [SV26: a] :
( ( ~ ( SV13 @ SV26 ) )
= ( ( SV5 @ SV26 )
| ( cZ @ SV26 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[112]) ).
thf(150,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ( ^ [SX0: a] :
~ ( SV13 @ SX0 ) )
= ( ^ [SX0: a] :
( ( SV5 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[112]) ).
thf(151,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
| $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) )
| ~ ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
| ~ ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[113]) ).
thf(153,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
| $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) )
| ~ ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
| ~ ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[114]) ).
thf(155,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
| ~ ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ~ ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[115]) ).
thf(159,plain,
! [SV5: a > $o] :
( ( ( ~ ( $false
| ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) ) )
| ~ ( ~ $false
| ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[117]) ).
thf(161,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
| ~ ( ~ ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[118]) ).
thf(163,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(164,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(165,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(166,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(167,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(168,plain,
! [SV4: a > $o] :
( ( ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
= ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(169,plain,
! [SV4: a > $o] :
( ( ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[141]) ).
thf(170,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(172,plain,
! [SV5: a > $o] :
( ( ( $false
= ( ( SV5 @ ( sK10_SV25 @ SV5 ) )
| ( cZ @ ( sK10_SV25 @ SV5 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(173,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ( ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[149]) ).
thf(174,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ( ^ [SX0: a] :
~ ( SV13 @ SX0 ) )
= ( ^ [SX0: a] :
( ( SV5 @ SX0 )
| ( cZ @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(176,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
| ~ ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(177,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
| $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(178,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
| ~ ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(179,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(180,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ~ ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(183,plain,
! [SV5: a > $o] :
( ( ( ~ ( $false
| ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(185,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(186,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( ~ ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(188,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(189,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
| $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) )
| ~ ( ~ ( SV4 @ ( sK6_SV21 @ SV4 ) )
| ~ ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[168]) ).
thf(193,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
| $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) )
| ~ ( ~ ( SV4 @ ( sK7_SV22 @ SV4 ) )
| ~ ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[169]) ).
thf(195,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
| ~ ( ~ ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ~ ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[170]) ).
thf(199,plain,
! [SV5: a > $o] :
( ( ( ~ ( $false
| ( SV5 @ ( sK10_SV25 @ SV5 ) )
| ( cZ @ ( sK10_SV25 @ SV5 ) ) )
| ~ ( ~ $false
| ~ ( ( SV5 @ ( sK10_SV25 @ SV5 ) )
| ( cZ @ ( sK10_SV25 @ SV5 ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[172]) ).
thf(201,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
| ~ ( ~ ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ~ ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[173]) ).
thf(204,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
| ~ ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(205,plain,
! [SV4: a > $o] :
( ( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
| $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(206,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
| ~ ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(207,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(208,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ~ ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(211,plain,
! [SV5: a > $o] :
( ( ( $false
| ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(213,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(214,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(216,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK6_SV21 @ SV4 ) )
| ~ ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(217,plain,
! [SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
| $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(218,plain,
! [SV4: a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK7_SV22 @ SV4 ) )
| ~ ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(219,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(220,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ~ ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(223,plain,
! [SV5: a > $o] :
( ( ( ~ ( $false
| ( SV5 @ ( sK10_SV25 @ SV5 ) )
| ( cZ @ ( sK10_SV25 @ SV5 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(225,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(226,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( ~ ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ~ ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(229,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) )
= $true )
| ( ( ~ ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(230,plain,
! [SV4: a > $o] :
( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(231,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) )
= $true )
| ( ( ~ ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(232,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(233,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(236,plain,
! [SV5: a > $o] :
( ( $false = $true )
| ( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(238,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true )
| ( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(239,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true )
| ( ( ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(241,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK6_SV21 @ SV4 ) )
| ~ ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(242,plain,
! [SV4: a > $o] :
( ( ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
| $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(243,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK7_SV22 @ SV4 ) )
| ~ ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(244,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(245,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ~ ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(248,plain,
! [SV5: a > $o] :
( ( ( $false
| ( SV5 @ ( sK10_SV25 @ SV5 ) )
| ( cZ @ ( sK10_SV25 @ SV5 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(250,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(251,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ~ ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(253,plain,
! [SV4: a > $o] :
( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( ~ ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(254,plain,
! [SV4: a > $o] :
( ( $false = $true )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(255,plain,
! [SV4: a > $o] :
( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $false )
| ( ( ~ ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(256,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $true )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(257,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( ~ ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(260,plain,
! [SV5: a > $o] :
( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( $false = $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(262,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(263,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $false )
| ( ( ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(265,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK6_SV21 @ SV4 ) ) )
= $true )
| ( ( ~ ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(266,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= $true )
| ( ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(267,plain,
! [SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK7_SV22 @ SV4 ) ) )
= $true )
| ( ( ~ ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(268,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $true )
| ( ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(269,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( ~ ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(272,plain,
! [SV5: a > $o] :
( ( $false = $true )
| ( ( ( SV5 @ ( sK10_SV25 @ SV5 ) )
| ( cZ @ ( sK10_SV25 @ SV5 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(274,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $true )
| ( ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(275,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $true )
| ( ( ~ ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(276,plain,
! [SV4: a > $o] :
( ( ( $true
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(277,plain,
! [SV4: a > $o] :
( ( ( $false
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(278,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(279,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
| ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(282,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(283,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( ~ ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(285,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
= $false )
| ( ( ~ ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(286,plain,
! [SV4: a > $o] :
( ( $false = $true )
| ( ( cZ @ ( sK7_SV22 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(287,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= $false )
| ( ( ~ ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(288,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
= $true )
| ( ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(289,plain,
! [SV8: a > $o,SV4: a > $o] :
( ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(292,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK10_SV25 @ SV5 ) )
= $true )
| ( ( cZ @ ( sK10_SV25 @ SV5 ) )
= $true )
| ( $false = $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(294,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false )
| ( ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(295,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $false )
| ( ( ~ ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(296,plain,
! [SV4: a > $o] :
( ( $true = $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(297,plain,
! [SV4: a > $o] :
( ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(299,plain,
! [SV4: a > $o] :
( ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(300,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(301,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(306,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(307,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
| ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) ) )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(308,plain,
! [SV4: a > $o] :
( ( ( $true
| ( cZ @ ( sK6_SV21 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(309,plain,
! [SV4: a > $o] :
( ( ( $false
| ( cZ @ ( sK7_SV22 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(310,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(311,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
| ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(314,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(315,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( ~ ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(316,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( SV8
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] :
~ ( SV8 @ SX0 )
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(317,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(318,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(319,plain,
! [SV4: a > $o] :
( ( $true = $false )
| ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(320,plain,
! [SV4: a > $o] :
( ( ( cZ @ ( sK6_SV21 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(322,plain,
! [SV4: a > $o] :
( ( ( cZ @ ( sK7_SV22 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(323,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( ~ ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(324,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( cZ @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(329,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false )
| ( ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(330,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
| ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) ) )
= $false )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(331,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(332,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] :
~ ( SV13 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(333,plain,
! [SV4: a > $o,SV8: a > $o] :
( ( ( SV8 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK8_SV23 @ SV8 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(334,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(335,plain,
! [SV13: a > $o,SV5: a > $o] :
( ( ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( ~ ( SV13 @ sK1_Xx ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(336,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( SV5 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(337,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( SV13 @ sK1_Xx )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13 @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $true )
| ( ( cZ @ ( sK11_SV26 @ SV5 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(338,plain,
( ( ( $true
| ( cZ @ sK1_Xx ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false ) ),
inference(extuni,[status(esa)],[140:[bind(SV4,$thf( ^ [SX0: a] : ( $true | ( cZ @ SX0 ) ) ))]]) ).
thf(339,plain,
( ( ( $false
| ( cZ @ sK1_Xx ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false ) ),
inference(extuni,[status(esa)],[142:[bind(SV4,$thf( ^ [SX0: a] : ( $false | ( cZ @ SX0 ) ) ))]]) ).
thf(340,plain,
! [SV8: a > $o] :
( ( ( ~ ( SV8 @ sK1_Xx )
| ( cZ @ sK1_Xx ) )
= $true )
| ( ( cW
@ ^ [SX0: a] :
~ ( SV8 @ SX0 ) )
= $false ) ),
inference(extuni,[status(esa)],[144:[bind(SV4,$thf( ^ [SX0: a] : ( ~ ( SV8 @ SX0 ) | ( cZ @ SX0 ) ) ))]]) ).
thf(343,plain,
! [SV5: a > $o] :
( ( $false = $true )
| ( ( cW @ SV5 )
= $false )
| ( $false = $true )
| ( ( ( SV5 @ ( sK13_E @ SV5 ) )
| ( cZ @ ( sK13_E @ SV5 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[148]) ).
thf(345,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13 @ ( sK14_E @ SV5 @ SV13 ) ) )
= $true )
| ( ( ( SV5 @ ( sK14_E @ SV5 @ SV13 ) )
| ( cZ @ ( sK14_E @ SV5 @ SV13 ) ) )
= $true )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13 @ sK1_Xx )
= $false ) ),
inference(extuni,[status(esa)],[174]) ).
thf(346,plain,
! [SV5: a > $o,SV13: a > $o] :
( ( ( ~ ( SV13 @ ( sK14_E @ SV5 @ SV13 ) ) )
= $false )
| ( ( ( SV5 @ ( sK14_E @ SV5 @ SV13 ) )
| ( cZ @ ( sK14_E @ SV5 @ SV13 ) ) )
= $false )
| ( ( cW @ SV5 )
= $false )
| ( ( SV13 @ sK1_Xx )
= $false ) ),
inference(extuni,[status(esa)],[174]) ).
thf(347,plain,
! [SV4: a > $o] :
( ( ( SV4 @ ( sK6_SV21 @ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(sim,[status(thm)],[319]) ).
thf(348,plain,
! [SV4: a > $o] :
( ( ( cZ @ ( sK7_SV22 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SV22 @ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(sim,[status(thm)],[286]) ).
thf(349,plain,
! [SV5: a > $o] :
( ( ( SV5 @ ( sK10_SV25 @ SV5 ) )
= $true )
| ( ( cZ @ ( sK10_SV25 @ SV5 ) )
= $true )
| ( ( cW @ SV5 )
= $false ) ),
inference(sim,[status(thm)],[292]) ).
thf(350,plain,
! [SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( ( SV5 @ ( sK13_E @ SV5 ) )
| ( cZ @ ( sK13_E @ SV5 ) ) )
= $true ) ),
inference(sim,[status(thm)],[343]) ).
thf(351,plain,
! [SV4: a > $o] :
( ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(sim,[status(thm)],[296]) ).
thf(352,plain,
! [SV4: a > $o] :
( ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(sim,[status(thm)],[254]) ).
thf(353,plain,
! [SV5: a > $o] :
( ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( ( cW @ SV5 )
= $false ) ),
inference(sim,[status(thm)],[260]) ).
thf(354,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $false )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( cZ
@ ( sK5_SV6
@ ^ [SX0: a] : $false
@ SV4 ) )
= $true )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(sim,[status(thm)],[120]) ).
thf(355,plain,
! [SV5: a > $o] :
( ( ( cW @ SV5 )
= $false )
| ( ( cZ
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true )
| ( ( SV5
@ ( sK5_SV6 @ SV5
@ ^ [SX0: a] : $false ) )
= $true ) ),
inference(sim,[status(thm)],[123]) ).
thf(356,plain,
! [SV4: a > $o] :
( ( ( cW
@ ^ [SX0: a] : $true )
= $false )
| ( ( SV4
@ ( sK5_SV6
@ ^ [SX0: a] : $true
@ SV4 ) )
= $false )
| ( ( SV4 @ sK1_Xx )
= $true ) ),
inference(sim,[status(thm)],[125]) ).
thf(357,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[79,356,355,354,353,352,351,350,349,348,347,346,345,340,339,338,337,336,333,332,331,329,324,322,320,316,310,306,301,299,297,278,190,189,188,165,163,138,133,132,131,106,105,101,94,89,88,85]) ).
thf(358,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[357,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV222^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 28 02:09:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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)................
% 75.10/75.28 (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).......
% 75.41/75.65
% 75.41/75.65 ********************************
% 75.41/75.65 * All subproblems solved! *
% 75.41/75.65 ********************************
% 75.41/75.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:357,loop_count:0,foatp_calls:2,translation:fof_full)
% 75.51/75.71
% 75.51/75.71 %**** Beginning of derivation protocol ****
% 75.51/75.71 % SZS output start CNFRefutation
% See solution above
% 75.51/75.71
% 75.51/75.71 %**** End of derivation protocol ****
% 75.51/75.71 %**** no. of clauses in derivation: 281 ****
% 75.51/75.71 %**** clause counter: 357 ****
% 75.51/75.71
% 75.51/75.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:357,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------