%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEV272^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:49:51 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 3
% Syntax : Number of formulae : 107 ( 20 unt; 0 typ; 2 def)
% Number of atoms : 1104 ( 469 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 4306 (2220 ~; 751 |; 24 &;1291 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 976 ( 976 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 1035 ( 472 ^; 549 !; 14 ?;1035 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cSUCC,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(tp_cZERO,type,
cZERO: ( $i > $o ) > $o ).
thf(tp_sK1_SV1,type,
sK1_SV1: ( $i > $o ) > $o ).
thf(tp_sK2_SY42,type,
sK2_SY42: ( ( $i > $o ) > $o ) > $o ).
thf(tp_sK3_SY49,type,
sK3_SY49: ( ( $i > $o ) > $o ) > $o ).
thf(tp_sK4_SY58,type,
sK4_SY58: ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(tp_sK5_SY49,type,
sK5_SY49: ( ( $i > $o ) > $o ) > $o ).
thf(tp_sK6_SY49,type,
sK6_SY49: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > $o ).
thf(tp_sK7_SY88,type,
sK7_SY88: ( ( ( $i > $o ) > $o ) > $o ) > ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(tp_sK8_SY94,type,
sK8_SY94: ( ( ( $i > $o ) > $o ) > $o ) > ( ( ( $i > $o ) > $o ) > $o ) > ( $i > $o ) > $o ).
thf(cSUCC,definition,
( cSUCC
= ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
? [Xx: $i] :
( ( Xp @ Xx )
& ( Xn
@ ^ [Xt: $i] :
( ( Xt != Xx )
& ( Xp @ Xt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def) ).
thf(cZERO,definition,
( cZERO
= ( ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def) ).
thf(1,conjecture,
( ( ^ [N: ( $i > $o ) > $o] :
! [P: ( ( $i > $o ) > $o ) > $o] :
( ( ( P @ cZERO )
& ! [X: ( $i > $o ) > $o] :
( ( P @ X )
=> ( P @ ( cSUCC @ X ) ) ) )
=> ( P @ N ) ) )
= ( ^ [Xx: ( $i > $o ) > $o] :
! [S: ( ( $i > $o ) > $o ) > $o] :
( ( ( S @ cZERO )
& ! [X: ( $i > $o ) > $o] :
( ( S @ X )
=> ( S @ ( cSUCC @ X ) ) ) )
=> ( S @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX6007A_pme) ).
thf(2,negated_conjecture,
( ( ( ^ [N: ( $i > $o ) > $o] :
! [P: ( ( $i > $o ) > $o ) > $o] :
( ( ( P @ cZERO )
& ! [X: ( $i > $o ) > $o] :
( ( P @ X )
=> ( P @ ( cSUCC @ X ) ) ) )
=> ( P @ N ) ) )
= ( ^ [Xx: ( $i > $o ) > $o] :
! [S: ( ( $i > $o ) > $o ) > $o] :
( ( ( S @ cZERO )
& ! [X: ( $i > $o ) > $o] :
( ( S @ X )
=> ( S @ ( cSUCC @ X ) ) ) )
=> ( S @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ^ [SY0: ( $i > $o ) > $o] :
! [SY1: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY1
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY2: ( $i > $o ) > $o] :
( ( SY1 @ SY2 )
=> ( SY1
@ ^ [SY3: $i > $o] :
? [SY4: $i] :
( ( SY3 @ SY4 )
& ( SY2
@ ^ [Xt: $i] :
( ( Xt != SY4 )
& ( SY3 @ Xt ) ) ) ) ) ) )
=> ( SY1 @ SY0 ) ) )
= ( ^ [SY6: ( $i > $o ) > $o] :
! [SY7: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY7
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY8: ( $i > $o ) > $o] :
( ( SY7 @ SY8 )
=> ( SY7
@ ^ [SY9: $i > $o] :
? [SY10: $i] :
( ( SY9 @ SY10 )
& ( SY8
@ ^ [Xt: $i] :
( ( Xt != SY10 )
& ( SY9 @ Xt ) ) ) ) ) ) )
=> ( SY7 @ SY6 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cSUCC,cZERO]) ).
thf(4,plain,
( ( ( ^ [SY0: ( $i > $o ) > $o] :
! [SY1: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY1
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY2: ( $i > $o ) > $o] :
( ( SY1 @ SY2 )
=> ( SY1
@ ^ [SY3: $i > $o] :
? [SY4: $i] :
( ( SY3 @ SY4 )
& ( SY2
@ ^ [Xt: $i] :
( ( Xt != SY4 )
& ( SY3 @ Xt ) ) ) ) ) ) )
=> ( SY1 @ SY0 ) ) )
!= ( ^ [SY6: ( $i > $o ) > $o] :
! [SY7: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY7
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY8: ( $i > $o ) > $o] :
( ( SY7 @ SY8 )
=> ( SY7
@ ^ [SY9: $i > $o] :
? [SY10: $i] :
( ( SY9 @ SY10 )
& ( SY8
@ ^ [Xt: $i] :
( ( Xt != SY10 )
& ( SY9 @ Xt ) ) ) ) ) ) )
=> ( SY7 @ SY6 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ^ [SY0: ( $i > $o ) > $o] :
! [SY1: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY1
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY2: ( $i > $o ) > $o] :
( ( SY1 @ SY2 )
=> ( SY1
@ ^ [SY3: $i > $o] :
? [SY4: $i] :
( ( SY3 @ SY4 )
& ( SY2
@ ^ [Xt: $i] :
( ( Xt != SY4 )
& ( SY3 @ Xt ) ) ) ) ) ) )
=> ( SY1 @ SY0 ) ) )
!= ( ^ [SY6: ( $i > $o ) > $o] :
! [SY7: ( ( $i > $o ) > $o ) > $o] :
( ( ( SY7
@ ^ [Xp: $i > $o] :
~ ? [Xx: $i] : ( Xp @ Xx ) )
& ! [SY8: ( $i > $o ) > $o] :
( ( SY7 @ SY8 )
=> ( SY7
@ ^ [SY9: $i > $o] :
? [SY10: $i] :
( ( SY9 @ SY10 )
& ( SY8
@ ^ [Xt: $i] :
( ( Xt != SY10 )
& ( SY9 @ Xt ) ) ) ) ) ) )
=> ( SY7 @ SY6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ^ [SX0: ( $i > $o ) > $o] :
! [SX1: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SX1
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SX1 @ SX2 )
| ( SX1
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SX1 @ SX0 ) ) )
!= ( ^ [SX0: ( $i > $o ) > $o] :
! [SX1: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SX1
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SX1 @ SX2 )
| ( SX1
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,cSUCC,cZERO]) ).
thf(7,plain,
( ( ( ^ [SX0: ( $i > $o ) > $o] :
! [SX1: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SX1
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SX1 @ SX2 )
| ( SX1
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SX1 @ SX0 ) ) )
= ( ^ [SX0: ( $i > $o ) > $o] :
! [SX1: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SX1
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SX1 @ SX2 )
| ( SX1
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SV1: ( $i > $o ) > $o] :
( ( ! [SY28: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY28
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY28 @ SX2 )
| ( SY28
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY28 @ SV1 ) ) )
= ( ! [SY35: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY35
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY35 @ SX2 )
| ( SY35
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY35 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[7]) ).
thf(9,plain,
( ( ( ^ [SX0: ( $i > $o ) > $o] :
! [SX1: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SX1
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SX1 @ SX2 )
| ( SX1
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SX1 @ SX0 ) ) )
= ( ^ [SX0: ( $i > $o ) > $o] :
! [SX1: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SX1
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SX1 @ SX2 )
| ( SX1
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) ) )
= ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(11,plain,
( ( ~ ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) )
| ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
| ~ ( ~ ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) )
| ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(12,plain,
( ( ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) ) )
= ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) )
| ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ~ ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) )
| ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) )
| ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) )
| ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) ) )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ( ~ ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(19,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SV2 @ sK1_SV1 ) )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(20,plain,
( ( ( ! [SY42: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY42 @ SX2 )
| ( SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY42 @ sK1_SV1 ) ) )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ~ ~ ( ~ ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY64: ( $i > $o ) > $o] :
( ~ ( sK2_SY42 @ SY64 )
| ( sK2_SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY64
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( sK2_SY42 @ sK1_SV1 ) )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(23,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( ~ ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(24,plain,
( ( ( ~ ~ ( ~ ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY64: ( $i > $o ) > $o] :
( ~ ( sK2_SY42 @ SY64 )
| ( sK2_SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY64
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(25,plain,
( ( ( sK2_SY42 @ sK1_SV1 )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ( ~ ( ~ ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY64: ( $i > $o ) > $o] :
( ~ ( sK2_SY42 @ SY64 )
| ( sK2_SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY64
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $true )
| ( ( ~ ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY64: ( $i > $o ) > $o] :
( ~ ( sK2_SY42 @ SY64 )
| ( sK2_SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY64
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ~ ~ ( ~ ( sK3_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY70: ( $i > $o ) > $o] :
( ~ ( sK3_SY49 @ SY70 )
| ( sK3_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY70
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( sK3_SY49 @ sK1_SV1 ) )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(32,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( ~ ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ~ ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ( ~ ! [SY64: ( $i > $o ) > $o] :
( ~ ( sK2_SY42 @ SY64 )
| ( sK2_SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY64
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ( ~ ~ ( ~ ( sK3_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY70: ( $i > $o ) > $o] :
( ~ ( sK3_SY49 @ SY70 )
| ( sK3_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY70
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ( sK3_SY49 @ sK1_SV1 )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ! [SY58: ( $i > $o ) > $o] :
( ~ ( SV2 @ SY58 )
| ( SV2
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY58
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( ( ! [SY64: ( $i > $o ) > $o] :
( ~ ( sK2_SY42 @ SY64 )
| ( sK2_SY42
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY64
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( ( ~ ( ~ ( sK3_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY70: ( $i > $o ) > $o] :
( ~ ( sK3_SY49 @ SY70 )
| ( sK3_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY70
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK4_SY58 @ SV2 ) )
| ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) ) )
= $false )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(42,plain,
( ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ( sK2_SY42 @ SV3 )
| ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ~ ( sK3_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY70: ( $i > $o ) > $o] :
( ~ ( sK3_SY49 @ SY70 )
| ( sK3_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY70
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV2 @ ( sK4_SY58 @ SV2 ) ) )
= $false )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(47,plain,
( ( ( ~ ~ ( ~ ( sK5_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY82: ( $i > $o ) > $o] :
( ~ ( sK5_SY49 @ SY82 )
| ( sK5_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY82
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( sK5_SY49 @ sK1_SV1 ) )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(48,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ( sK2_SY42 @ SV3 ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( ( ~ ( sK3_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(50,plain,
( ( ( ~ ! [SY70: ( $i > $o ) > $o] :
( ~ ( sK3_SY49 @ SY70 )
| ( sK3_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY70
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(51,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SV4 @ sK1_SV1 ) )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
( ( ( ~ ~ ( ~ ( sK5_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY82: ( $i > $o ) > $o] :
( ~ ( sK5_SY49 @ SY82 )
| ( sK5_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY82
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(54,plain,
( ( ( sK5_SY49 @ sK1_SV1 )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(55,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( sK2_SY42 @ SV3 )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( ~ ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(56,plain,
( ( ( sK3_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(57,plain,
( ( ( ! [SY70: ( $i > $o ) > $o] :
( ~ ( sK3_SY49 @ SY70 )
| ( sK3_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY70
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(58,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SV5 @ sK1_SV1 ) )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(60,plain,
( ( ( ~ ( ~ ( sK5_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY82: ( $i > $o ) > $o] :
( ~ ( sK5_SY49 @ SY82 )
| ( sK5_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY82
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(61,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ! [SY49: ( ( $i > $o ) > $o ) > $o] :
( ~ ~ ( ~ ( SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SX2: ( $i > $o ) > $o] :
( ~ ( SY49 @ SX2 )
| ( SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SX2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( SY49 @ sK1_SV1 ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV6: ( $i > $o ) > $o] :
( ( ( ~ ( sK3_SY49 @ SV6 )
| ( sK3_SY49
@ ^ [SY98: $i > $o] :
~ ! [SY99: $i] :
~ ~ ( ~ ( SY98 @ SY99 )
| ~ ( SV6
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY99 ) )
| ~ ( SY98 @ SX5 ) ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ~ ( ~ ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( ~ ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
( ( ( ~ ( sK5_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY82: ( $i > $o ) > $o] :
( ~ ( sK5_SY49 @ SY82 )
| ( sK5_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY82
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ~ ( ~ ( sK6_SY49 @ SV3
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY103: ( $i > $o ) > $o] :
( ~ ( sK6_SY49 @ SV3 @ SY103 )
| ( sK6_SY49 @ SV3
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY103
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
| ( sK6_SY49 @ SV3 @ sK1_SV1 ) )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(67,plain,
! [SV6: ( $i > $o ) > $o] :
( ( ( ~ ( sK3_SY49 @ SV6 ) )
= $true )
| ( ( sK3_SY49
@ ^ [SY98: $i > $o] :
~ ! [SY99: $i] :
~ ~ ( ~ ( SY98 @ SY99 )
| ~ ( SV6
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY99 ) )
| ~ ( SY98 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( ~ ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(70,plain,
( ( ( ~ ( sK5_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(71,plain,
( ( ( ~ ! [SY82: ( $i > $o ) > $o] :
( ~ ( sK5_SY49 @ SY82 )
| ( sK5_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY82
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ~ ( ~ ( sK6_SY49 @ SV3
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY103: ( $i > $o ) > $o] :
( ~ ( sK6_SY49 @ SV3 @ SY103 )
| ( sK6_SY49 @ SV3
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY103
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( sK6_SY49 @ SV3 @ sK1_SV1 )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
! [SV6: ( $i > $o ) > $o] :
( ( ( sK3_SY49 @ SV6 )
= $false )
| ( ( sK3_SY49
@ ^ [SY98: $i > $o] :
~ ! [SY99: $i] :
~ ~ ( ~ ( SY98 @ SY99 )
| ~ ( SV6
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY99 ) )
| ~ ( SY98 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ sK1_SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(75,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $true )
| ( ( ~ ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(77,plain,
( ( ( sK5_SY49
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(78,plain,
( ( ( ! [SY82: ( $i > $o ) > $o] :
( ~ ( sK5_SY49 @ SY82 )
| ( sK5_SY49
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY82
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(79,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ( ~ ( sK6_SY49 @ SV3
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY103: ( $i > $o ) > $o] :
( ~ ( sK6_SY49 @ SV3 @ SY103 )
| ( sK6_SY49 @ SV3
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY103
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(80,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $true )
| ( ( ~ ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( ~ ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV7: ( $i > $o ) > $o] :
( ( ( ~ ( sK5_SY49 @ SV7 )
| ( sK5_SY49
@ ^ [SY107: $i > $o] :
~ ! [SY108: $i] :
~ ~ ( ~ ( SY107 @ SY108 )
| ~ ( SV7
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY108 ) )
| ~ ( SY107 @ SX5 ) ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ( sK6_SY49 @ SV3
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
| ~ ! [SY103: ( $i > $o ) > $o] :
( ~ ( sK6_SY49 @ SV3 @ SY103 )
| ( sK6_SY49 @ SV3
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY103
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( ~ ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ! [SY88: ( $i > $o ) > $o] :
( ~ ( SV4 @ SY88 )
| ( SV4
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY88
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV7: ( $i > $o ) > $o] :
( ( ( ~ ( sK5_SY49 @ SV7 ) )
= $true )
| ( ( sK5_SY49
@ ^ [SY107: $i > $o] :
~ ! [SY108: $i] :
~ ~ ( ~ ( SY107 @ SY108 )
| ~ ( SV7
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY108 ) )
| ~ ( SY107 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ( sK6_SY49 @ SV3
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ~ ! [SY103: ( $i > $o ) > $o] :
( ~ ( sK6_SY49 @ SV3 @ SY103 )
| ( sK6_SY49 @ SV3
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY103
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ! [SY94: ( $i > $o ) > $o] :
( ~ ( SV5 @ SY94 )
| ( SV5
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY94
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY88 @ SV2 @ SV4 ) )
| ( SV4
@ ^ [SY110: $i > $o] :
~ ! [SY111: $i] :
~ ~ ( ~ ( SY110 @ SY111 )
| ~ ( sK7_SY88 @ SV2 @ SV4
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY111 ) )
| ~ ( SY110 @ SX5 ) ) ) ) ) )
= $false )
| ( ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[85]) ).
thf(91,plain,
! [SV7: ( $i > $o ) > $o] :
( ( ( sK5_SY49 @ SV7 )
= $false )
| ( ( sK5_SY49
@ ^ [SY107: $i > $o] :
~ ! [SY108: $i] :
~ ~ ( ~ ( SY107 @ SY108 )
| ~ ( SV7
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY108 ) )
| ~ ( SY107 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( sK6_SY49 @ SV3
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(93,plain,
! [SV3: ( $i > $o ) > $o] :
( ( ( ! [SY103: ( $i > $o ) > $o] :
( ~ ( sK6_SY49 @ SV3 @ SY103 )
| ( sK6_SY49 @ SV3
@ ^ [SX3: $i > $o] :
~ ! [SX4: $i] :
~ ~ ( ~ ( SX3 @ SX4 )
| ~ ( SY103
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SX4 ) )
| ~ ( SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK8_SY94 @ SV2 @ SV5 ) )
| ( SV5
@ ^ [SY113: $i > $o] :
~ ! [SY114: $i] :
~ ~ ( ~ ( SY113 @ SY114 )
| ~ ( sK8_SY94 @ SV2 @ SV5
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY114 ) )
| ~ ( SY113 @ SX5 ) ) ) ) ) )
= $false )
| ( ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(95,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY88 @ SV2 @ SV4 ) ) )
= $false )
| ( ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(96,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV4
@ ^ [SY110: $i > $o] :
~ ! [SY111: $i] :
~ ~ ( ~ ( SY110 @ SY111 )
| ~ ( sK7_SY88 @ SV2 @ SV4
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY111 ) )
| ~ ( SY110 @ SX5 ) ) ) ) )
= $false )
| ( ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(97,plain,
! [SV8: ( $i > $o ) > $o,SV3: ( $i > $o ) > $o] :
( ( ( ~ ( sK6_SY49 @ SV3 @ SV8 )
| ( sK6_SY49 @ SV3
@ ^ [SY116: $i > $o] :
~ ! [SY117: $i] :
~ ~ ( ~ ( SY116 @ SY117 )
| ~ ( SV8
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY117 ) )
| ~ ( SY116 @ SX5 ) ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( ~ ( SV5 @ ( sK8_SY94 @ SV2 @ SV5 ) ) )
= $false )
| ( ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(99,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV5
@ ^ [SY113: $i > $o] :
~ ! [SY114: $i] :
~ ~ ( ~ ( SY113 @ SY114 )
| ~ ( sK8_SY94 @ SV2 @ SV5
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY114 ) )
| ~ ( SY113 @ SX5 ) ) ) ) )
= $false )
| ( ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV4: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV4 @ ( sK7_SY88 @ SV2 @ SV4 ) )
= $true )
| ( ( SV4
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV4 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2
@ ^ [SY74: $i > $o] :
~ ! [SY75: $i] :
~ ~ ( ~ ( SY74 @ SY75 )
| ~ ( sK4_SY58 @ SV2
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY75 ) )
| ~ ( SY74 @ SX5 ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV8: ( $i > $o ) > $o,SV3: ( $i > $o ) > $o] :
( ( ( ~ ( sK6_SY49 @ SV3 @ SV8 ) )
= $true )
| ( ( sK6_SY49 @ SV3
@ ^ [SY116: $i > $o] :
~ ! [SY117: $i] :
~ ~ ( ~ ( SY116 @ SY117 )
| ~ ( SV8
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY117 ) )
| ~ ( SY116 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV2: ( ( $i > $o ) > $o ) > $o,SV5: ( ( $i > $o ) > $o ) > $o] :
( ( ( SV5 @ ( sK8_SY94 @ SV2 @ SV5 ) )
= $true )
| ( ( SV5
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV5 @ sK1_SV1 )
= $true )
| ( ( SV2 @ sK1_SV1 )
= $true )
| ( ( SV2
@ ^ [SX2: $i > $o] :
~ ~ ! [SX3: $i] :
~ ( SX2 @ SX3 ) )
= $false )
| ( ( SV2 @ ( sK4_SY58 @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(103,plain,
! [SV8: ( $i > $o ) > $o,SV3: ( $i > $o ) > $o] :
( ( ( sK6_SY49 @ SV3 @ SV8 )
= $false )
| ( ( sK6_SY49 @ SV3
@ ^ [SY116: $i > $o] :
~ ! [SY117: $i] :
~ ~ ( ~ ( SY116 @ SY117 )
| ~ ( SV8
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY117 ) )
| ~ ( SY116 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42
@ ^ [SY77: $i > $o] :
~ ! [SY78: $i] :
~ ~ ( ~ ( SY77 @ SY78 )
| ~ ( SV3
@ ^ [SX5: $i] :
~ ( ~ ( ( SX5 != SY78 ) )
| ~ ( SY77 @ SX5 ) ) ) ) )
= $true )
| ( ( sK2_SY42 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9,103,102,100,99,96,92,91,77,74,73,56,54,36,12]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV272^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n013.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 15:44:17 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 0
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 342
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .....
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 105 ****
% 0.08/0.23 %**** clause counter: 104 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:0,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------