TSTP Solution File: SYO378^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO378^5 : 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 : n015.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 : Thu Jul 21 17:33:40 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of formulae : 120 ( 13 unt; 7 typ; 3 def)
% Number of atoms : 1184 ( 554 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 1318 ( 336 ~; 315 |; 8 &; 659 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 354 ( 354 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 372 ( 56 ^ 304 !; 12 ?; 372 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c,type,
c: $i ).
thf(tp_cQDP0,type,
cQDP0: $i > $o ).
thf(tp_cQDP1,type,
cQDP1: ( $i > $o ) > $o ).
thf(tp_cQDP2,type,
cQDP2: ( ( $i > $o ) > $o ) > $o ).
thf(tp_sK1_SV2,type,
sK1_SV2: ( ( $i > $o ) > $o ) > $i > $o ).
thf(tp_sK2_SY18,type,
sK2_SY18: ( ( $i > $o ) > $o ) > $i ).
thf(tp_sK3_SV8,type,
sK3_SV8: ( ( $i > $o ) > $o ) > $i ).
thf(cQDP0,definition,
( cQDP0
= ( ^ [Xz: $i] : ( Xz = c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDP0) ).
thf(cQDP1,definition,
( cQDP1
= ( ^ [Xz: $i > $o] :
( ( Xz = cQDP0 )
& ? [Xt: $i] : ( Xz @ Xt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDP1) ).
thf(cQDP2,definition,
( cQDP2
= ( ^ [Xz: ( $i > $o ) > $o] :
( ( Xz = cQDP1 )
& ? [Xt: $i > $o] : ( Xz @ Xt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDP2) ).
thf(1,conjecture,
? [Xs: ( $i > $o ) > $o] : ( cQDP2 @ Xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDTHM2) ).
thf(2,negated_conjecture,
( ( ? [Xs: ( $i > $o ) > $o] : ( cQDP2 @ Xs ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [SY2: ( $i > $o ) > $o] :
( ( SY2
= ( ^ [SY3: $i > $o] :
( ( SY3
= ( ^ [Xz: $i] : ( Xz = c ) ) )
& ? [Xt: $i] : ( SY3 @ Xt ) ) ) )
& ? [SY1: $i > $o] : ( SY2 @ SY1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cQDP0,cQDP1,cQDP2]) ).
thf(4,plain,
( ( ~ ? [SY2: ( $i > $o ) > $o] :
( ( SY2
= ( ^ [SY3: $i > $o] :
( ( SY3
= ( ^ [Xz: $i] : ( Xz = c ) ) )
& ? [Xt: $i] : ( SY3 @ Xt ) ) ) )
& ? [SY1: $i > $o] : ( SY2 @ SY1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY2: ( $i > $o ) > $o] :
( ( SY2
!= ( ^ [SY3: $i > $o] :
( ( SY3
= ( ^ [Xz: $i] : ( Xz = c ) ) )
& ? [Xt: $i] : ( SY3 @ Xt ) ) ) )
| ! [SY1: $i > $o] :
~ ( SY2 @ SY1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [SY2: ( $i > $o ) > $o] :
( ( SY2
!= ( ^ [SY3: $i > $o] :
( ( SY3
= ( ^ [Xz: $i] : ( Xz = c ) ) )
& ? [Xt: $i] : ( SY3 @ Xt ) ) ) )
| ! [SY1: $i > $o] :
~ ( SY2 @ SY1 ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [SX0: ( $i > $o ) > $o] :
( ( SX0
!= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) )
| ! [SX1: $i > $o] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,cQDP0,cQDP1,cQDP2]) ).
thf(8,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( SV1
!= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) )
| ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( SV1
!= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( SV1
= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SV2: $i > $o] :
( ( SV1 @ SV2 )
= ( ~ ( ( SV2
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY16: $i] :
~ ( SV2 @ SY16 ) ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(12,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( SV1
= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV3: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV3 ) )
= $true )
| ( ( SV1
= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
| ~ ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ~ ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[13]) ).
thf(16,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV3 )
= $false )
| ( ( SV1
= ( ^ [SX1: $i > $o] :
~ ( ( SX1
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SX2: $i] :
~ ( SX1 @ SX2 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ~ ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
! [SV4: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV4 ) )
= $true )
| ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) )
| ~ ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV4: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV4 )
= $false )
| ( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= ( ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ ( sK1_SV2 @ SV1 ) ) )
= $true )
| ( ( ~ ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ~ ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) )
| ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SV5: $i] :
( ( sK1_SV2 @ SV1 @ SV5 )
= ( SV5 = c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( ( sK1_SV2 @ SV1 )
!= ( ^ [SX2: $i] : ( SX2 = c ) ) ) )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 @ SV6 )
= ( SV6 = c ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV7: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV7 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ ( sK2_SY18 @ SV1 ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(41,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 = c ) )
| ~ ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 @ SV6 )
= ( SV6 = c ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV7: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV7 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ ( sK2_SY18 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SV8: $i] :
( ( sK1_SV2 @ SV1 @ SV8 )
= ( SV8 = c ) ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[41]) ).
thf(48,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 = c ) ) )
= $true )
| ( ( ~ ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV6: $i,SV9: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV9 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 @ SV6 )
= ( SV6 = c ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV10: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV10 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(52,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 = c ) )
= $false )
| ( ( ~ ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV6: $i,SV9: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV9 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 @ SV6 )
= ( SV6 = c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV10: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV10 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK2_SY18 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
| ( ( sK3_SV8 @ SV1 )
= c ) )
| ~ ( ~ ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
| ( ( sK3_SV8 @ SV1 )
!= c ) ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[51]) ).
thf(58,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(59,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( ~ ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(60,plain,
! [SV1: ( $i > $o ) > $o,SV6: $i] :
( ( ( SV6 = c )
= $false )
| ( ( ~ ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(61,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
| ( ( sK3_SV8 @ SV1 )
= c ) ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( ~ ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
| ( ( sK3_SV8 @ SV1 )
!= c ) ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV11: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV11 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV6 )
| ( SV6 != c ) )
= $false )
| ( ( SV6 = c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
| ( ( sK3_SV8 @ SV1 )
= c ) )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(68,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
| ( ( sK3_SV8 @ SV1 )
!= c ) )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV11: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV11 )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV6 ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV1: ( $i > $o ) > $o,SV6: $i] :
( ( ( ( SV6 != c ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(73,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV6 ) )
= $false )
| ( ( SV6 = c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV1: ( $i > $o ) > $o,SV6: $i] :
( ( ( ( SV6 != c ) )
= $false )
| ( ( SV6 = c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) ) )
= $true )
| ( ( ( ( sK3_SV8 @ SV1 )
!= c ) )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV12: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV12 ) )
= $true )
| ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV11: $i,SV13: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV13 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV6 )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV1: ( $i > $o ) > $o,SV6: $i] :
( ( ( SV6 = c )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(81,plain,
! [SV6: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV6 )
= $true )
| ( ( SV6 = c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV1: ( $i > $o ) > $o,SV6: $i] :
( ( ( SV6 = c )
= $true )
| ( ( SV6 = c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(83,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( ( ( sK3_SV8 @ SV1 )
!= c ) )
= $true )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(85,plain,
! [SV12: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV12 )
= $false )
| ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(86,plain,
! [SV11: $i,SV13: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV13 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 )
= ( ^ [SX2: $i] : ( SX2 = c ) ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(87,plain,
! [SV6: $i,SV14: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV14 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV6: $i,SV15: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV15 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV6 = c )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV6: $i,SV16: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV16 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( SV6 = c )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV6: $i,SV17: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV17 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( SV6 = c )
= $false )
| ( ( SV6 = c )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(92,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( ~ ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV12: $i,SV18: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV18 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV6: $i,SV14: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV14 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV6: $i,SV15: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV15 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $false )
| ( ( SV6 = c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV6: $i,SV16: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV16 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( SV6 = c )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV6: $i,SV17: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV17 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $true )
| ( ( SV6 = c )
= $false )
| ( ( SV6 = c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV19: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV19 ) )
= $true )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ~ ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV12: $i,SV18: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV18 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= ( ( sK3_SV8 @ SV1 )
= c ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV19: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV19 )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV1: ( $i > $o ) > $o] :
( ( ( ! [SY18: $i] :
~ ( sK1_SV2 @ SV1 @ SY18 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(103,plain,
! [SV19: $i,SV20: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV20 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(104,plain,
! [SV21: $i,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( sK1_SV2 @ SV1 @ SV21 ) )
= $true )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(105,plain,
! [SV19: $i,SV20: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV20 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $true )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $true )
| ( ( sK1_SV2 @ SV1 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(106,plain,
! [SV21: $i,SV1: ( $i > $o ) > $o] :
( ( ( sK1_SV2 @ SV1 @ SV21 )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ! [SY14: $i > $o] :
~ ( SV1 @ SY14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV21: $i,SV22: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( ~ ( SV1 @ SV22 ) )
= $true )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(108,plain,
! [SV21: $i,SV22: $i > $o,SV1: ( $i > $o ) > $o] :
( ( ( SV1 @ SV22 )
= $false )
| ( ( SV1 @ ( sK1_SV2 @ SV1 ) )
= $false )
| ( ( ( sK3_SV8 @ SV1 )
= c )
= $false )
| ( ( sK1_SV2 @ SV1 @ ( sK3_SV8 @ SV1 ) )
= $false )
| ( ( sK1_SV2 @ SV1 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(109,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[17,108,105,100,97,96,95,94,86,55,54,44,23]) ).
thf(110,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO378^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 08:58:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 436
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.19/0.34 (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)....
% 0.19/0.41
% 0.19/0.41 ********************************
% 0.19/0.41 * All subproblems solved! *
% 0.19/0.41 ********************************
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:109,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.42
% 0.19/0.42 %**** Beginning of derivation protocol ****
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
% 0.19/0.42
% 0.19/0.42 %**** End of derivation protocol ****
% 0.19/0.42 %**** no. of clauses in derivation: 110 ****
% 0.19/0.42 %**** clause counter: 109 ****
% 0.19/0.42
% 0.19/0.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:109,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------