TSTP Solution File: SEV021^6 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV021^6 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n017.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 : 300s
% DateTime : Mon Jun 24 15:58:00 EDT 2024
% Result : Theorem 265.96s 71.25s
% Output : Refutation 266.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of formulae : 390 ( 19 unt; 0 typ; 1 def)
% Number of atoms : 1993 ( 353 equ; 6 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 3489 ( 759 ~; 697 |; 156 &;1851 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 221 ( 221 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 44 usr; 27 con; 0-3 aty)
% Number of variables : 717 ( 341 ^ 295 !; 81 ?; 717 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cP_type,type,
cP: ( a > $o ) > $o ).
thf(cQ_type,type,
cQ: a > a > $o ).
thf(cQ_def,definition,
( cQ
= ( ^ [A: a,B: a] :
? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: ( a > $o ) > a ).
thf(sk2_type,type,
sk2: a > a > $o ).
thf(sk3_type,type,
sk3: a > $o ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: a ).
thf(sk6_type,type,
sk6: a ).
thf(sk7_type,type,
sk7: a > a > $o ).
thf(sk8_type,type,
sk8: a > a > a ).
thf(sk9_type,type,
sk9: a > a > a > $o ).
thf(sk10_type,type,
sk10: a > a ).
thf(sk16_type,type,
sk16: a ).
thf(sk21_type,type,
sk21: a ).
thf(sk22_type,type,
sk22: a > $o ).
thf(sk68_type,type,
sk68: a > $o ).
thf(sk77_type,type,
sk77: a ).
thf(sk84_type,type,
sk84: a ).
thf(sk93_type,type,
sk93: a ).
thf(sk94_type,type,
sk94: a ).
thf(sk97_type,type,
sk97: a ).
thf(sk98_type,type,
sk98: a ).
thf(sk101_type,type,
sk101: a ).
thf(sk104_type,type,
sk104: a ).
thf(sk113_type,type,
sk113: a ).
thf(sk114_type,type,
sk114: a ).
thf(sk116_type,type,
sk116: a ).
thf(sk117_type,type,
sk117: a ).
thf(sk120_type,type,
sk120: a > $o ).
thf(sk121_type,type,
sk121: a > $o ).
thf(sk128_type,type,
sk128: a > $o ).
thf(sk129_type,type,
sk129: a > $o ).
thf(sk138_type,type,
sk138: a > $o ).
thf(sk139_type,type,
sk139: a > $o ).
thf(sk140_type,type,
sk140: a > $o ).
thf(sk141_type,type,
sk141: a > $o ).
thf(sk183_type,type,
sk183: a ).
thf(sk184_type,type,
sk184: a ).
thf(sk186_type,type,
sk186: a ).
thf(sk187_type,type,
sk187: a ).
thf(sk202_type,type,
sk202: a > $o ).
thf(sk211_type,type,
sk211: a ).
thf(sk231_type,type,
sk231: a ).
thf(1,conjecture,
( ! [A: a > $o,B: a > $o] :
( ( ( A = B )
& ( cP @ A ) )
=> ( cP @ B ) )
=> ( ( ! [A: a > $o] :
( ( cP @ A )
=> ? [B: a] : ( A @ B ) )
& ! [A: a] :
? [B: a > $o] :
( ( cP @ B )
& ( B @ A ) )
& ! [A: a,B: a,C: a > $o,D: a > $o] :
( ( ( cP @ C )
& ( cP @ D )
& ( C @ A )
& ( D @ A )
& ( C @ B ) )
=> ( D @ B ) ) )
=> ( ( ^ [A: a > $o] :
( ? [B: a] : ( A @ B )
& ! [B: a] :
( ( A @ B )
=> ! [C: a] :
( ( A @ C )
= ( cQ @ B @ C ) ) ) ) )
= cP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM262_D_EXT2_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > $o,B: a > $o] :
( ( ( A = B )
& ( cP @ A ) )
=> ( cP @ B ) )
=> ( ( ! [A: a > $o] :
( ( cP @ A )
=> ? [B: a] : ( A @ B ) )
& ! [A: a] :
? [B: a > $o] :
( ( cP @ B )
& ( B @ A ) )
& ! [A: a,B: a,C: a > $o,D: a > $o] :
( ( ( cP @ C )
& ( cP @ D )
& ( C @ A )
& ( D @ A )
& ( C @ B ) )
=> ( D @ B ) ) )
=> ( ( ^ [A: a > $o] :
( ? [B: a] : ( A @ B )
& ! [B: a] :
( ( A @ B )
=> ! [C: a] :
( ( A @ C )
= ( cQ @ B @ C ) ) ) ) )
= cP ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > $o,B: a > $o] :
( ( ( A = B )
& ( cP @ A ) )
=> ( cP @ B ) )
=> ( ( ! [A: a > $o] :
( ( cP @ A )
=> ? [B: a] : ( A @ B ) )
& ! [A: a] :
? [B: a > $o] :
( ( cP @ B )
& ( B @ A ) )
& ! [A: a,B: a,C: a > $o,D: a > $o] :
( ( ( cP @ C )
& ( cP @ D )
& ( C @ A )
& ( D @ A )
& ( C @ B ) )
=> ( D @ B ) ) )
=> ( ( ^ [A: a > $o] :
( ? [B: a] : ( A @ B )
& ! [B: a] :
( ( A @ B )
=> ! [C: a] :
( ( A @ C )
= ( ? [D: a > $o] :
( ( cP @ D )
& ( D @ B )
& ( D @ C ) ) ) ) ) ) )
= cP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( A @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( A @ ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(70,plain,
( ~ ( cP @ sk3 )
| ( sk3 @ ( sk1 @ sk3 ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( sk3 ))]]) ).
thf(8,plain,
( ( ^ [A: a > $o] :
( ? [B: a] : ( A @ B )
& ! [B: a] :
( ( A @ B )
=> ! [C: a] :
( ( A @ C )
= ( ? [D: a > $o] :
( ( cP @ D )
& ( D @ B )
& ( D @ C ) ) ) ) ) ) )
!= cP ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
( ( ^ [A: a > $o] :
( ? [B: a] : ( A @ B )
& ! [B: a] :
( ( A @ B )
=> ! [C: a] :
( ( A @ C )
= ( ? [D: a > $o] :
( ( cP @ D )
& ( D @ B )
& ( D @ C ) ) ) ) ) ) )
!= cP ),
inference(lifteq,[status(thm)],[8]) ).
thf(20,plain,
( ( ? [A: a] : ( sk3 @ A )
& ! [A: a] :
( ( sk3 @ A )
=> ! [B: a] :
( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) ) )
!= ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[18]) ).
thf(21,plain,
( ~ ( ? [A: a] : ( sk3 @ A )
& ! [A: a] :
( ( sk3 @ A )
=> ! [B: a] :
( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) ) )
| ~ ( cP @ sk3 ) ),
inference(bool_ext,[status(thm)],[20]) ).
thf(23,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( sk3 @ A )
| ( sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[21]) ).
thf(1406,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ( sk3 @ sk4 )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70,23]) ).
thf(1407,plain,
( ~ ( cP @ sk3 )
| ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1406:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(24,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( sk3 @ A )
| ( ( sk3 @ sk5 )
!= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(25,plain,
! [A: a] :
( ( ( sk3 @ sk5 )
!= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ) )
| ~ ( cP @ sk3 )
| ~ ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(29,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( sk3 @ A )
| ~ ( sk3 @ sk5 )
| ~ ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[25]) ).
thf(33,plain,
! [B: a > $o,A: a] :
( ~ ( cP @ B )
| ~ ( B @ sk4 )
| ~ ( B @ sk5 )
| ~ ( sk3 @ sk5 )
| ~ ( sk3 @ A )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[29]) ).
thf(2985,plain,
! [B: a > $o,A: a] :
( ~ ( cP @ sk3 )
| ~ ( cP @ B )
| ~ ( B @ sk5 )
| ~ ( sk3 @ sk5 )
| ~ ( sk3 @ A )
| ( ( sk3 @ sk4 )
!= ( B @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1407,33]) ).
thf(3113,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( cP @ sk3 )
| ~ ( sk3 @ sk5 )
| ~ ( sk3 @ sk5 )
| ~ ( sk3 @ A ) ),
inference(pre_uni,[status(thm)],[2985:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(3236,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( sk3 @ sk5 )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[3113]) ).
thf(3789,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( sk3 @ sk5 )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70,3236]) ).
thf(3790,plain,
( ~ ( cP @ sk3 )
| ~ ( sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[3789:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(3877,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( sk3 @ sk5 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3790]) ).
thf(3928,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ~ ( sk3 @ sk5 ) ),
inference(pre_uni,[status(thm)],[3877:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(5061,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( sk3 @ sk5 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,3928]) ).
thf(5116,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ~ ( sk3 @ sk5 ) ),
inference(pre_uni,[status(thm)],[5061:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(993,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ ( sk1 @ sk3 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,70]) ).
thf(1024,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk3 @ ( sk1 @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[993:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(991,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ( ( sk3 @ sk5 )
!= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ) )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70,25]) ).
thf(992,plain,
( ~ ( cP @ sk3 )
| ( ( sk3 @ sk5 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[991:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(1116,plain,
( ~ ( cP @ sk3 )
| ( sk3 @ sk5 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[992]) ).
thf(1171,plain,
( ( cP @ sk22 )
| ( sk3 @ sk5 )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[1116]) ).
thf(3902,plain,
( ( cP @ sk22 )
| ~ ( cP @ sk3 )
| ( ( sk3 @ sk5 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1171,3790]) ).
thf(3903,plain,
( ( cP @ sk22 )
| ~ ( cP @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3902:[]]) ).
thf(78,plain,
( ~ ( cP
@ ^ [A: a] : $false )
| $false ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [B: a] : $false ))]]) ).
thf(96,plain,
~ ( cP
@ ^ [A: a] : $false ),
inference(simp,[status(thm)],[78]) ).
thf(4245,plain,
( ~ ( cP @ sk3 )
| ( ( cP @ sk22 )
!= ( cP
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[3903,96]) ).
thf(4308,plain,
( ~ ( cP @ sk3 )
| ( sk22
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[4245]) ).
thf(4433,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22
!= ( ^ [B: a] : $false ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,4308]) ).
thf(4443,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk22
!= ( ^ [A: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[4433:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(5982,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22
!= ( ^ [B: a] : $false ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,4443]) ).
thf(6003,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( sk22
!= ( ^ [A: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[5982:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(13783,plain,
( ( sk22 @ sk211 )
| ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[6003]) ).
thf(22,plain,
( ( ? [A: a] : ( sk3 @ A )
& ! [A: a] :
( ( sk3 @ A )
=> ! [B: a] :
( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) ) )
| ( cP @ sk3 ) ),
inference(bool_ext,[status(thm)],[20]) ).
thf(27,plain,
( ( cP @ sk3 )
| ( sk3 @ sk6 ) ),
inference(cnf,[status(esa)],[22]) ).
thf(3883,plain,
( ( sk3 @ sk6 )
| ~ ( sk3 @ sk5 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,3790]) ).
thf(3884,plain,
( ( sk3 @ sk6 )
| ~ ( sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[3883:[]]) ).
thf(4082,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ sk6 )
| ( ( A @ ( sk1 @ A ) )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3884]) ).
thf(4146,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( sk3 @ sk6 ) ),
inference(pre_uni,[status(thm)],[4082:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk5 ) ))]]) ).
thf(5197,plain,
( ( sk3 @ sk6 )
| ( ( cP @ sk3 )
!= ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,4146]) ).
thf(5299,plain,
( ( sk3 @ sk6 )
| ( sk3
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5197]) ).
thf(6347,plain,
( ( sk3 @ sk6 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(simp,[status(thm)],[5299]) ).
thf(6544,plain,
( ( sk101 != sk5 )
| ( sk3 @ sk6 ) ),
inference(func_ext,[status(esa)],[6347]) ).
thf(75,plain,
! [A: a > $o] :
( ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ~ ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [C: a] : ~ ( B @ C ) ))]]) ).
thf(93,plain,
! [A: a > $o] :
( ~ ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(94,plain,
! [A: a > $o] :
( ~ ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(20091,plain,
! [A: a > $o] :
( ( sk101 != sk5 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6544,94]) ).
thf(20464,plain,
( ( sk101 != sk5 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20091:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(71,plain,
! [C: a > a,B: a > a,A: a > a] :
( ~ ( cP
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) )
| ( sk9
@ ( A
@ ( sk1
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( sk1
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [E: a] : ( sk9 @ ( B @ E ) @ ( C @ E ) @ ( D @ E ) ) ))]]) ).
thf(88,plain,
! [C: a > a,B: a > a,A: a > a] :
( ~ ( cP
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) )
| ( sk9
@ ( A
@ ( sk1
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( B
@ ( sk1
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) ) )
@ ( C
@ ( sk1
@ ^ [D: a] : ( sk9 @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) ) ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(108,plain,
( ( sk3 @ sk6 )
| ( ( cP @ sk3 )
!= ( cP
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[27,96]) ).
thf(112,plain,
( ( sk3 @ sk6 )
| ( sk3
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(638,plain,
( ( sk3 @ sk21 )
| ( sk3 @ sk6 ) ),
inference(func_ext,[status(esa)],[112]) ).
thf(4096,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ sk21 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[638,3884]) ).
thf(4169,plain,
( ( sk3 @ sk6 )
| ( sk21 != sk5 ) ),
inference(simp,[status(thm)],[4096]) ).
thf(1117,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( sk3 @ sk5 )
!= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,992]) ).
thf(1153,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( ( sk3 @ sk5 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ) ) ),
inference(pre_uni,[status(thm)],[1117:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(1179,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( sk3 @ sk5 )
!= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,1153]) ).
thf(1211,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( ( sk3 @ sk5 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ) ) ),
inference(pre_uni,[status(thm)],[1179:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(3878,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( cP @ sk3 )
| ( ( A @ ( sk1 @ A ) )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3790]) ).
thf(3926,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ~ ( cP @ sk3 ) ),
inference(pre_uni,[status(thm)],[3878:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk5 ) ))]]) ).
thf(5018,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( ( cP @ sk3 )
!= ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[3926]) ).
thf(5026,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( sk3
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5018]) ).
thf(7819,plain,
( ( sk3
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) )
| ~ ( cP
@ ^ [A: a] : $true )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[5299,5026]) ).
thf(7975,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ~ ( cP
@ ^ [A: a] : $true )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[7819]) ).
thf(8105,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : sk5 ) )
| ( sk6 != sk5 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[14,7975]) ).
thf(8129,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : $true ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( sk6 != sk5 ) ),
inference(pre_uni,[status(thm)],[8105:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : $true ) ))]]) ).
thf(26,plain,
! [B: a,A: a] :
( ( cP @ sk3 )
| ~ ( sk3 @ A )
| ( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(28,plain,
! [B: a,A: a] :
( ( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) )
| ( cP @ sk3 )
| ~ ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(1958,plain,
! [B: a,A: a] :
( ( cP @ sk3 )
| ( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,28]) ).
thf(1959,plain,
! [A: a] :
( ( cP @ sk3 )
| ( ( sk3 @ A )
= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1958:[bind(A,$thf( sk6 ))]]) ).
thf(2139,plain,
! [A: a] :
( ( cP @ sk3 )
| ( ( sk3 @ A )
= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) ) ) ) ),
inference(simp,[status(thm)],[1959]) ).
thf(9275,plain,
! [A: a] :
( ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2139,27]) ).
thf(9276,plain,
( ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9275:[bind(A,$thf( sk6 ))]]) ).
thf(9717,plain,
( ( cP @ sk120 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9276]) ).
thf(4229,plain,
( ( sk3 @ sk6 )
| ( cP @ sk22 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,3903]) ).
thf(4230,plain,
( ( sk3 @ sk6 )
| ( cP @ sk22 ) ),
inference(pattern_uni,[status(thm)],[4229:[]]) ).
thf(9343,plain,
! [A: a] :
( ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( cP @ sk22 )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2139,4230]) ).
thf(9344,plain,
( ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) )
| ( cP @ sk22 ) ),
inference(pattern_uni,[status(thm)],[9343:[bind(A,$thf( sk6 ))]]) ).
thf(9759,plain,
( ( cP @ sk22 )
| ( sk138 @ sk6 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9344]) ).
thf(20124,plain,
! [A: a > $o] :
( ~ ( sk3 @ sk5 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3884,94]) ).
thf(20437,plain,
( ~ ( sk3 @ sk5 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20124:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(1496,plain,
( ( sk3 @ sk6 )
| ( sk3 @ sk4 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,1407]) ).
thf(1497,plain,
( ( sk3 @ sk6 )
| ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1496:[]]) ).
thf(4432,plain,
( ( sk22 @ sk77 )
| ~ ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[4308]) ).
thf(4748,plain,
( ( sk3 @ sk6 )
| ( sk22 @ sk77 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,4432]) ).
thf(4749,plain,
( ( sk3 @ sk6 )
| ( sk22 @ sk77 ) ),
inference(pattern_uni,[status(thm)],[4748:[]]) ).
thf(20174,plain,
! [A: a > $o] :
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk22 @ sk77 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4749,94]) ).
thf(20469,plain,
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk22 @ sk77 ) ) ),
inference(pre_uni,[status(thm)],[20174:[bind(A,$thf( ^ [B: a] : ( sk22 @ sk77 ) ))]]) ).
thf(9347,plain,
! [A: a] :
( ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : sk5 ) )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2139,6347]) ).
thf(9348,plain,
( ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(pattern_uni,[status(thm)],[9347:[bind(A,$thf( sk6 ))]]) ).
thf(9764,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( cP @ sk140 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9348]) ).
thf(11009,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( cP @ sk3 )
| ( ( cP @ sk140 )
!= ( cP
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9764,96]) ).
thf(11160,plain,
( ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( sk140
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[11009]) ).
thf(4434,plain,
( ( sk3 @ sk6 )
| ( sk22
!= ( ^ [A: a] : $false ) )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,4308]) ).
thf(4435,plain,
( ( sk3 @ sk6 )
| ( sk22
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[4434:[]]) ).
thf(9,plain,
! [A: a] : ( cP @ ( sk2 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: a] : ( cP @ ( sk2 @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(5,plain,
! [D: a > $o,C: a > $o,B: a,A: a] :
( ~ ( cP @ C )
| ~ ( cP @ D )
| ~ ( C @ A )
| ~ ( D @ A )
| ~ ( C @ B )
| ( D @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [D: a > $o,C: a > $o,B: a,A: a] :
( ~ ( cP @ C )
| ~ ( cP @ D )
| ~ ( C @ A )
| ~ ( D @ A )
| ~ ( C @ B )
| ( D @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(152,plain,
! [E: a > $o,D: a > $o,C: a,B: a,A: a] :
( ~ ( cP @ D )
| ~ ( D @ B )
| ~ ( E @ B )
| ~ ( D @ C )
| ( E @ C )
| ( ( cP @ ( sk2 @ A ) )
!= ( cP @ E ) ) ),
inference(paramod_ordered,[status(thm)],[15,11]) ).
thf(153,plain,
! [D: a > $o,C: a,B: a,A: a] :
( ~ ( cP @ D )
| ~ ( D @ B )
| ~ ( sk2 @ A @ B )
| ~ ( D @ C )
| ( sk2 @ A @ C ) ),
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sk2 @ A ))]]) ).
thf(20118,plain,
! [A: a > $o] :
( ( ( ^ [B: a] : B )
!= ( ^ [B: a] : sk5 ) )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6347,94]) ).
thf(20556,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20118:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(5981,plain,
( ( sk22 @ sk93 )
| ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) ) ),
inference(func_ext,[status(esa)],[4443]) ).
thf(7021,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22 @ sk93 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,5981]) ).
thf(7064,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( sk22 @ sk93 ) ),
inference(pre_uni,[status(thm)],[7021:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(9297,plain,
! [A: a] :
( ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( sk3 @ sk4 )
| ( ( sk3 @ A )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[2139,1497]) ).
thf(9298,plain,
( ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) )
| ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[9297:[bind(A,$thf( sk6 ))]]) ).
thf(9735,plain,
( ( sk3 @ sk4 )
| ( cP @ sk128 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9298]) ).
thf(4218,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( cP @ sk22 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3903]) ).
thf(4310,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( cP @ sk22 ) ),
inference(pre_uni,[status(thm)],[4218:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(5777,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( cP @ sk22 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,4310]) ).
thf(5921,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( cP @ sk22 ) ),
inference(pre_uni,[status(thm)],[5777:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(31,plain,
! [B: a,A: a] :
( ( ( sk3 @ sk5 )
!= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ) )
| ~ ( sk3 @ B )
| ( ( cP @ ( sk2 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[15,25]) ).
thf(32,plain,
! [B: a,A: a] :
( ( ( sk3 @ sk5 )
!= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ) )
| ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[31]) ).
thf(37,plain,
! [B: a,A: a] :
( ( ( sk2 @ A @ ( sk8 @ B @ A ) )
!= ( sk3 @ ( sk8 @ B @ A ) ) )
| ( ( sk3 @ sk5 )
!= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ) )
| ~ ( sk3 @ B ) ),
inference(func_ext,[status(esa)],[32]) ).
thf(7763,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) )
| ( sk3
!= ( ^ [B: a] : $true ) )
| ( ( A @ ( sk1 @ A ) )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[14,5026]) ).
thf(7925,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( sk3
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[7763:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk5 ) ))]]) ).
thf(7999,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( sk3
!= ( ^ [A: a] : $true ) ) ),
inference(simp,[status(thm)],[7925]) ).
thf(8249,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3
!= ( ^ [B: a] : $true ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,7999]) ).
thf(8325,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ( sk3
!= ( ^ [A: a] : $true ) ) ),
inference(pre_uni,[status(thm)],[8249:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(39,plain,
! [B: a,A: a] :
( ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= sk3 )
| ( sk3 @ sk5 )
| ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[32]) ).
thf(42,plain,
! [B: a,A: a] :
( ( sk9 @ B @ A @ sk4 )
| ( sk3 @ sk5 )
| ( ( sk2 @ A )
!= sk3 )
| ~ ( sk3 @ B ) ),
inference(cnf,[status(esa)],[39]) ).
thf(5003,plain,
( ~ ( cP @ sk3 )
| ( ( cP @ sk22 )
!= ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3903,3926]) ).
thf(5047,plain,
( ~ ( cP @ sk3 )
| ( sk22
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5003]) ).
thf(6019,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22
!= ( ^ [B: a] : ( sk3 @ sk5 ) ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,5047]) ).
thf(6034,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk22
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(pre_uni,[status(thm)],[6019:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(9277,plain,
! [A: a] :
( ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,2139]) ).
thf(9278,plain,
( ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9277:[bind(A,$thf( sk6 ))]]) ).
thf(9719,plain,
( ( cP @ sk121 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9278]) ).
thf(10549,plain,
( ( cP @ sk3 )
| ( ( cP @ sk121 )
!= ( cP @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9719]) ).
thf(10606,plain,
( ( cP @ sk3 )
| ( ( cP @ sk121 )
!= ( cP @ sk3 ) ) ),
inference(simp,[status(thm)],[10549]) ).
thf(4741,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22 @ sk77 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,4432]) ).
thf(4771,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk22 @ sk77 ) ),
inference(pre_uni,[status(thm)],[4741:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(6073,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22 @ sk77 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,4771]) ).
thf(6130,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( sk22 @ sk77 ) ),
inference(pre_uni,[status(thm)],[6073:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(65,plain,
! [A: a > $o] :
( ( sk3 @ sk6 )
| ( A @ ( sk1 @ A ) )
| ( ( cP @ sk3 )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,14]) ).
thf(66,plain,
( ( sk3 @ sk6 )
| ( sk3 @ ( sk1 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( sk3 ))]]) ).
thf(4121,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[66,3884]) ).
thf(4179,plain,
( ( sk3 @ sk6 )
| ( ( sk1 @ sk3 )
!= sk5 ) ),
inference(simp,[status(thm)],[4121]) ).
thf(1558,plain,
( ( sk3 @ sk4 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1497]) ).
thf(1572,plain,
( ( sk3 @ sk4 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[1558]) ).
thf(10049,plain,
( ( cP @ sk3 )
| ( ( cP @ sk120 )
!= ( cP @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9717]) ).
thf(10066,plain,
( ( cP @ sk3 )
| ( sk120 != sk3 ) ),
inference(simp,[status(thm)],[10049]) ).
thf(10650,plain,
( ( ( sk120 @ sk183 )
!= ( sk3 @ sk183 ) )
| ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[10066]) ).
thf(3890,plain,
( ~ ( cP @ sk3 )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[70,3790]) ).
thf(3917,plain,
( ~ ( cP @ sk3 )
| ( ( sk1 @ sk3 )
!= sk5 ) ),
inference(simp,[status(thm)],[3890]) ).
thf(4447,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( sk1 @ sk3 )
!= sk5 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3917]) ).
thf(4460,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( ( sk1 @ sk3 )
!= sk5 ) ),
inference(pre_uni,[status(thm)],[4447:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(109,plain,
! [A: a] :
( ( cP @ ( sk2 @ A ) )
!= ( cP
@ ^ [B: a] : $false ) ),
inference(paramod_ordered,[status(thm)],[15,96]) ).
thf(113,plain,
! [A: a] :
( ( sk2 @ A )
!= ( ^ [B: a] : $false ) ),
inference(simp,[status(thm)],[109]) ).
thf(492,plain,
! [A: a] : ( sk2 @ A @ ( sk10 @ A ) ),
inference(func_ext,[status(esa)],[113]) ).
thf(5183,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ sk6 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,4146]) ).
thf(5267,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ( sk3 @ sk6 ) ),
inference(pre_uni,[status(thm)],[5183:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(11502,plain,
( ( sk3 @ sk6 )
| ( ( cP @ sk22 )
!= ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4230,5267]) ).
thf(11676,plain,
( ( sk3 @ sk6 )
| ( sk22
!= ( ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(simp,[status(thm)],[11502]) ).
thf(1133,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ sk5 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ) )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,992]) ).
thf(1134,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ sk5 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1133:[]]) ).
thf(3453,plain,
( ( sk3 @ sk6 )
| ( sk3 @ sk5 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk4 )
& ( A @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[1134]) ).
thf(3621,plain,
( ( cP @ sk68 )
| ( sk3 @ sk5 )
| ( sk3 @ sk6 ) ),
inference(cnf,[status(esa)],[3453]) ).
thf(3905,plain,
( ( sk3
!= ( ^ [A: a] : $false ) )
| ~ ( cP @ sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[112,3790]) ).
thf(3923,plain,
( ( sk3
!= ( ^ [A: a] : $false ) )
| ~ ( cP @ sk3 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[3905]) ).
thf(61,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( ! [B: a] :
( ( sk3 @ B )
=> ! [C: a] :
( ( sk3 @ C )
= ( ? [D: a > $o] :
( ( cP @ D )
& ( D @ B )
& ( D @ C ) ) ) ) ) )
!= ( cP @ sk3 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( ? [B: a] : ( sk3 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,20]) ).
thf(84,plain,
( ~ ( cP
@ ^ [A: a] :
? [B: a] : ( sk3 @ B ) )
| ( ( ! [A: a] :
( ( sk3 @ A )
=> ! [B: a] :
( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) ) )
!= ( cP @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[61:[bind(A,$thf( ^ [B: a] : ? [C: a] : ( sk3 @ C ) ))]]) ).
thf(1169,plain,
( ( sk22 @ sk5 )
| ( sk3 @ sk5 )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[1116]) ).
thf(7759,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(simp,[status(thm)],[5026]) ).
thf(8001,plain,
( ( sk113 != sk5 )
| ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[7759]) ).
thf(6411,plain,
( ( sk3
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) )
| ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[5299,3928]) ).
thf(6498,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[6411]) ).
thf(72,plain,
! [B: a > a,A: a > a] :
( ~ ( cP
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk1
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk1
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [D: a] : ( sk2 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(89,plain,
! [B: a > a,A: a > a] :
( ~ ( cP
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk2
@ ( A
@ ( sk1
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk1
@ ^ [C: a] : ( sk2 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(8002,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : sk5 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,7759]) ).
thf(8093,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(pre_uni,[status(thm)],[8002:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(8443,plain,
( ( sk117 != sk5 )
| ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(func_ext,[status(esa)],[8093]) ).
thf(1293,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ ( sk1 @ sk3 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,1024]) ).
thf(1335,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( sk3 @ ( sk1 @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[1293:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(2395,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ ( sk1 @ sk3 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : ( cP @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,1335]) ).
thf(2441,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : ( cP @ sk3 ) ) ) )
| ( sk3 @ ( sk1 @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[2395:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ ^ [D: a] : ( cP @ sk3 ) ) ) ))]]) ).
thf(6018,plain,
( ( ( sk22 @ sk94 )
!= ( sk3 @ sk5 ) )
| ~ ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[5047]) ).
thf(13916,plain,
( ( sk3 @ sk6 )
| ( ( sk22 @ sk94 )
!= ( sk3 @ sk5 ) )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,6018]) ).
thf(13917,plain,
( ( sk3 @ sk6 )
| ( ( sk22 @ sk94 )
!= ( sk3 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[13916:[]]) ).
thf(20134,plain,
! [A: a > $o] :
( ~ ( cP @ sk3 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk4 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1407,94]) ).
thf(20459,plain,
( ~ ( cP @ sk3 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[20134:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk4 ) ))]]) ).
thf(11957,plain,
! [A: a] :
( ( cP @ sk128 )
| ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9735,2139]) ).
thf(11958,plain,
( ( cP @ sk128 )
| ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[11957:[bind(A,$thf( sk4 ))]]) ).
thf(12215,plain,
( ( sk202 @ sk4 )
| ( cP @ sk3 )
| ( cP @ sk128 ) ),
inference(cnf,[status(esa)],[11958]) ).
thf(9734,plain,
( ( sk3 @ sk4 )
| ( sk128 @ sk6 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9298]) ).
thf(1485,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ sk4 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,1407]) ).
thf(1527,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk3 @ sk4 ) ),
inference(pre_uni,[status(thm)],[1485:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(1645,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ sk4 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,1527]) ).
thf(1676,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( sk3 @ sk4 ) ),
inference(pre_uni,[status(thm)],[1645:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(74,plain,
! [A: a > a > $o] :
( ~ ( cP
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
| ( cP
@ ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [C: a] : ( cP @ ( B @ C ) ) ))]]) ).
thf(92,plain,
! [A: a > a > $o] :
( ~ ( cP
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
| ( cP
@ ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(1170,plain,
( ( sk22 @ sk4 )
| ( sk3 @ sk5 )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[1116]) ).
thf(1364,plain,
( ( sk3 @ sk6 )
| ( sk22 @ sk4 )
| ( sk3 @ sk5 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,1170]) ).
thf(1365,plain,
( ( sk3 @ sk6 )
| ( sk22 @ sk4 )
| ( sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1364:[]]) ).
thf(79,plain,
! [A: a > a] :
( ~ ( cP
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ( A
@ ( sk1
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [C: a] : ( sk3 @ ( B @ C ) ) ))]]) ).
thf(97,plain,
! [A: a > a] :
( ~ ( cP
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) )
| ( sk3
@ ( A
@ ( sk1
@ ^ [B: a] : ( sk3 @ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(8104,plain,
( ( sk114 != sk5 )
| ~ ( cP
@ ^ [A: a] : $true )
| ( sk6 != sk5 ) ),
inference(func_ext,[status(esa)],[7975]) ).
thf(1573,plain,
( ( sk3 @ sk4 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[1558]) ).
thf(9349,plain,
! [A: a] :
( ( ( ^ [B: a] : B )
!= ( ^ [B: a] : sk5 ) )
| ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6347,2139]) ).
thf(9350,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9349:[bind(A,$thf( sk6 ))]]) ).
thf(9766,plain,
( ( cP @ sk141 )
| ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(cnf,[status(esa)],[9350]) ).
thf(12306,plain,
( ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( ( cP @ sk141 )
!= ( cP
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9766,96]) ).
thf(12404,plain,
( ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( sk141
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[12306]) ).
thf(11075,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( cP @ sk3 )
| ( ( cP @ sk140 )
!= ( cP @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9764]) ).
thf(11096,plain,
( ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( sk140 != sk3 ) ),
inference(simp,[status(thm)],[11075]) ).
thf(49,plain,
! [B: a,A: a] :
( ( cP @ sk3 )
| ~ ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) )
| ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[27,32]) ).
thf(52,plain,
! [B: a,A: a] :
( ( cP @ sk3 )
| ~ ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) )
| ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= sk3 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[49]) ).
thf(53,plain,
! [C: a > $o,B: a,A: a] :
( ( sk6 != sk5 )
| ( ( sk2 @ A )
!= sk3 )
| ~ ( sk3 @ B )
| ~ ( cP @ C )
| ~ ( C @ sk4 )
| ~ ( C @ sk5 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[52]) ).
thf(560,plain,
( ~ ( cP
@ ^ [A: a] :
? [B: a] : ( sk3 @ B ) )
| ~ ! [A: a] :
( ( sk3 @ A )
=> ! [B: a] :
( ( sk3 @ B )
= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ A )
& ( C @ B ) ) ) ) )
| ~ ( cP @ sk3 ) ),
inference(bool_ext,[status(thm)],[84]) ).
thf(591,plain,
( ~ ( cP @ sk3 )
| ( ( sk3 @ sk16 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk15 )
& ( A @ sk16 ) ) ) )
| ~ ( cP
@ ^ [A: a] :
? [B: a] : ( sk3 @ B ) ) ),
inference(cnf,[status(esa)],[560]) ).
thf(593,plain,
( ( ( sk3 @ sk16 )
!= ( ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk15 )
& ( A @ sk16 ) ) ) )
| ~ ( cP @ sk3 )
| ~ ( cP
@ ^ [A: a] :
? [B: a] : ( sk3 @ B ) ) ),
inference(lifteq,[status(thm)],[591]) ).
thf(193,plain,
! [C: a > $o,B: a,A: a] :
( ~ ( cP @ C )
| ~ ( cP @ sk3 )
| ~ ( C @ A )
| ~ ( sk3 @ A )
| ~ ( C @ B )
| ( sk3 @ B ) ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk3 ))]]) ).
thf(678,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ sk21 )
!= ( sk3 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[638]) ).
thf(686,plain,
( ( sk3 @ sk6 )
| ( sk21 != sk6 ) ),
inference(simp,[status(thm)],[678]) ).
thf(20153,plain,
! [A: a > $o] :
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( cP @ sk3 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,94]) ).
thf(20493,plain,
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [A: a] :
~ ( cP @ sk3 ) ) ),
inference(pre_uni,[status(thm)],[20153:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(9345,plain,
! [A: a] :
( ( cP @ sk22 )
| ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4230,2139]) ).
thf(9346,plain,
( ( cP @ sk22 )
| ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9345:[bind(A,$thf( sk6 ))]]) ).
thf(9761,plain,
( ( sk139 @ sk6 )
| ( cP @ sk3 )
| ( cP @ sk22 ) ),
inference(cnf,[status(esa)],[9346]) ).
thf(10454,plain,
! [A: a > $o] :
( ( cP @ sk3 )
| ( A @ ( sk1 @ A ) )
| ( ( cP @ sk121 )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9719,14]) ).
thf(10455,plain,
( ( cP @ sk3 )
| ( sk121 @ ( sk1 @ sk121 ) ) ),
inference(pattern_uni,[status(thm)],[10454:[bind(A,$thf( sk121 ))]]) ).
thf(10,plain,
! [C: a > $o,B: a,A: a] :
( ~ ( cP @ C )
| ~ ( cP @ ( (=) @ a @ A ) )
| ~ ( C @ A )
| ( A != A )
| ~ ( C @ B )
| ( A = B ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( (=) @ a @ A ))]]) ).
thf(12,plain,
! [C: a > $o,B: a,A: a] :
( ( A != A )
| ( A = B )
| ~ ( cP @ C )
| ~ ( cP @ ( (=) @ a @ A ) )
| ~ ( C @ A )
| ~ ( C @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
! [C: a > $o,B: a,A: a] :
( ( A = B )
| ~ ( cP @ C )
| ~ ( cP @ ( (=) @ a @ A ) )
| ~ ( C @ A )
| ~ ( C @ B ) ),
inference(simp,[status(thm)],[12]) ).
thf(5207,plain,
( ( sk3 @ sk6 )
| ( ( cP @ sk22 )
!= ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4230,4146]) ).
thf(5295,plain,
( ( sk3 @ sk6 )
| ( sk22
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) ) ),
inference(simp,[status(thm)],[5207]) ).
thf(6346,plain,
( ( ( sk22 @ sk97 )
!= ( sk3 @ sk5 ) )
| ( sk3 @ sk6 ) ),
inference(func_ext,[status(esa)],[5295]) ).
thf(3896,plain,
( ~ ( cP @ sk3 )
| ( ( sk3 @ sk5 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1407,3790]) ).
thf(3921,plain,
( ~ ( cP @ sk3 )
| ( sk5 != sk4 ) ),
inference(simp,[status(thm)],[3896]) ).
thf(4330,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk5 != sk4 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3921]) ).
thf(4347,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk5 != sk4 ) ),
inference(pre_uni,[status(thm)],[4330:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(3911,plain,
! [A: a] :
( ~ ( sk3 @ sk5 )
| ( ( cP @ ( sk2 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[15,3790]) ).
thf(3920,plain,
! [A: a] :
( ~ ( sk3 @ sk5 )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[3911]) ).
thf(41,plain,
! [B: a,A: a] :
( ( sk9 @ B @ A @ sk5 )
| ( sk3 @ sk5 )
| ( ( sk2 @ A )
!= sk3 )
| ~ ( sk3 @ B ) ),
inference(cnf,[status(esa)],[39]) ).
thf(9989,plain,
( ( cP @ sk3 )
| ( ( cP @ sk120 )
!= ( cP
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9717,96]) ).
thf(10073,plain,
( ( cP @ sk3 )
| ( sk120
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[9989]) ).
thf(10651,plain,
( ( sk120 @ sk184 )
| ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[10073]) ).
thf(62,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( cP @ A )
| ~ ? [D: a > $o] :
( ( cP @ D )
& ( D @ sk4 )
& ( D @ sk5 ) )
| ~ ( sk3 @ C )
| ( ( sk2 @ B )
!= sk3 )
| ( ( A @ ( sk1 @ A ) )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[14,32]) ).
thf(87,plain,
! [B: a,A: a] :
( ~ ( cP
@ ^ [C: a] : ( sk3 @ sk5 ) )
| ~ ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) )
| ~ ( sk3 @ B )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(pre_uni,[status(thm)],[62:[bind(A,$thf( ^ [D: a] : ( sk3 @ sk5 ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(104,plain,
! [C: a > $o,B: a,A: a] :
( ( ( sk2 @ A )
!= sk3 )
| ~ ( sk3 @ B )
| ~ ( cP @ C )
| ~ ( C @ sk4 )
| ~ ( C @ sk5 )
| ~ ( cP
@ ^ [D: a] : ( sk3 @ sk5 ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(105,plain,
! [C: a > $o,B: a,A: a] :
( ( ( sk2 @ A )
!= sk3 )
| ~ ( sk3 @ B )
| ~ ( cP @ C )
| ~ ( C @ sk4 )
| ~ ( C @ sk5 )
| ~ ( cP
@ ^ [D: a] : ( sk3 @ sk5 ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(9716,plain,
( ( sk120 @ sk6 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9276]) ).
thf(12376,plain,
( ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( ( cP @ sk141 )
!= ( cP @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9766]) ).
thf(12389,plain,
( ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( sk141 != sk3 ) ),
inference(simp,[status(thm)],[12376]) ).
thf(5939,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk5 != sk4 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( cP @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,4347]) ).
thf(5969,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( cP @ sk3 ) ) )
| ( sk5 != sk4 ) ),
inference(pre_uni,[status(thm)],[5939:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ sk3 ) ) ))]]) ).
thf(10607,plain,
( ( cP @ sk3 )
| ( sk121 != sk3 ) ),
inference(simp,[status(thm)],[10549]) ).
thf(9765,plain,
( ( sk141 @ sk6 )
| ( cP @ sk3 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(cnf,[status(esa)],[9350]) ).
thf(30,plain,
! [A: a] :
( ~ ( cP @ sk3 )
| ~ ( sk3 @ A )
| ( sk3 @ sk5 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[25]) ).
thf(34,plain,
! [A: a] :
( ( sk7 @ A @ sk5 )
| ( sk3 @ sk5 )
| ~ ( sk3 @ A )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(3898,plain,
( ( sk21 != sk6 )
| ~ ( cP @ sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[686,3790]) ).
thf(3925,plain,
( ( sk21 != sk6 )
| ~ ( cP @ sk3 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[3898]) ).
thf(12216,plain,
( ( sk202 @ sk6 )
| ( cP @ sk3 )
| ( cP @ sk128 ) ),
inference(cnf,[status(esa)],[11958]) ).
thf(20092,plain,
! [A: a > $o] :
( ( sk21 != sk5 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4169,94]) ).
thf(20486,plain,
( ( sk21 != sk5 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20092:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(4973,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( cP @ sk3 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,3926]) ).
thf(5030,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ~ ( cP @ sk3 ) ),
inference(pre_uni,[status(thm)],[4973:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(9020,plain,
( ~ ( cP @ sk3 )
| ( ( cP @ sk22 )
!= ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3903,5030]) ).
thf(9057,plain,
( ~ ( cP @ sk3 )
| ( sk22
!= ( ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(simp,[status(thm)],[9020]) ).
thf(4900,plain,
( ( sk22 @ sk84 )
| ( sk3 @ sk6 ) ),
inference(func_ext,[status(esa)],[4435]) ).
thf(20188,plain,
! [A: a > $o] :
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk22 @ sk84 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4900,94]) ).
thf(20475,plain,
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk22 @ sk84 ) ) ),
inference(pre_uni,[status(thm)],[20188:[bind(A,$thf( ^ [B: a] : ( sk22 @ sk84 ) ))]]) ).
thf(4216,plain,
! [A: a > $o] :
( ~ ( cP @ sk3 )
| ( A @ ( sk1 @ A ) )
| ( ( cP @ sk22 )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3903,14]) ).
thf(4217,plain,
( ~ ( cP @ sk3 )
| ( sk22 @ ( sk1 @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[4216:[bind(A,$thf( sk22 ))]]) ).
thf(5720,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk22 @ ( sk1 @ sk22 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,4217]) ).
thf(5752,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ( sk22 @ ( sk1 @ sk22 ) ) ),
inference(pre_uni,[status(thm)],[5720:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(10488,plain,
( ( cP @ sk3 )
| ( ( cP @ sk121 )
!= ( cP
@ ^ [A: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[9719,96]) ).
thf(10611,plain,
( ( cP @ sk3 )
| ( sk121
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[10488]) ).
thf(10728,plain,
( ( sk121 @ sk187 )
| ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[10611]) ).
thf(3619,plain,
( ( sk68 @ sk5 )
| ( sk3 @ sk5 )
| ( sk3 @ sk6 ) ),
inference(cnf,[status(esa)],[3453]) ).
thf(144,plain,
! [H: a > $o,G: a > $o,F: a,E: a,D: a > $o,C: a > $o,B: a,A: a] :
( ~ ( cP @ C )
| ~ ( cP @ D )
| ~ ( C @ A )
| ~ ( D @ A )
| ~ ( C @ B )
| ~ ( cP @ G )
| ~ ( cP @ H )
| ~ ( H @ E )
| ~ ( G @ F )
| ( H @ F )
| ( ( D @ B )
!= ( G @ E ) ) ),
inference(paramod_ordered,[status(thm)],[11,11]) ).
thf(218,plain,
! [G: a > $o,F: a,E: a,D: a > $o,C: a > $o,B: a,A: a] :
( ~ ( cP @ C )
| ~ ( cP @ D )
| ~ ( C @ A )
| ~ ( D @ A )
| ~ ( C @ B )
| ~ ( cP @ G )
| ~ ( cP @ ( (=) @ a @ E ) )
| ( E != E )
| ~ ( G @ F )
| ( E = F )
| ( ( D @ B )
!= ( G @ E ) ) ),
inference(replace_leibeq,[status(thm)],[144:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( (=) @ a @ E ))]]) ).
thf(263,plain,
! [G: a > $o,F: a,E: a,D: a > $o,C: a > $o,B: a,A: a] :
( ( E != E )
| ( E = F )
| ~ ( cP @ C )
| ~ ( cP @ D )
| ~ ( C @ A )
| ~ ( D @ A )
| ~ ( C @ B )
| ~ ( cP @ G )
| ~ ( cP @ ( (=) @ a @ E ) )
| ~ ( G @ F )
| ( ( D @ B )
!= ( G @ E ) ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(274,plain,
! [G: a > $o,F: a,E: a,D: a > $o,C: a > $o,B: a,A: a] :
( ~ ( G @ F )
| ~ ( cP @ ( (=) @ a @ E ) )
| ~ ( cP @ G )
| ~ ( C @ B )
| ~ ( D @ A )
| ~ ( C @ A )
| ~ ( cP @ D )
| ~ ( cP @ C )
| ( E = F )
| ( ( D @ B )
!= ( G @ E ) ) ),
inference(pre_uni,[status(thm)],[263:[]]) ).
thf(58,plain,
! [B: a > $o,A: a > $o] :
( ~ ( cP @ A )
| ( B @ ( sk1 @ B ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,14]) ).
thf(86,plain,
! [A: a > a > $o] :
( ~ ( cP
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
| ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
@ ( sk1
@ ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[58:[bind(A,$thf( ^ [D: a] : ( cP @ ( C @ D ) ) )),bind(B,$thf( C @ ( sk1 @ ^ [D: a] : ( cP @ ( C @ D ) ) ) ))]]) ).
thf(103,plain,
! [A: a > a > $o] :
( ~ ( cP
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
| ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
@ ( sk1
@ ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(15420,plain,
( ~ ( sk3 @ sk231 )
| ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(func_ext,[status(esa)],[8325]) ).
thf(6965,plain,
( ( sk101 != sk5 )
| ~ ( cP @ sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6544,3790]) ).
thf(6989,plain,
( ( sk101 != sk5 )
| ~ ( cP @ sk3 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[6965]) ).
thf(611,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ sk6 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[66]) ).
thf(621,plain,
( ( sk3 @ sk6 )
| ( ( sk1 @ sk3 )
!= sk6 ) ),
inference(simp,[status(thm)],[611]) ).
thf(73,plain,
! [B: a > $o,A: a > $o] :
( ~ ( cP
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) )
| ( A
@ ( sk1
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk1
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [D: a] : ( ( B @ D ) | ( C @ D ) ) ))]]) ).
thf(90,plain,
! [B: a > $o,A: a > $o] :
( ( A
@ ( sk1
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk1
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( cP
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(91,plain,
! [B: a > $o,A: a > $o] :
( ( A
@ ( sk1
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ( B
@ ( sk1
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
| ~ ( cP
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(685,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ sk21 )
!= ( sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[678]) ).
thf(25986,plain,
! [A: a > a > $o] :
( ~ ( cP
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
| ( ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) )
@ ( sk1
@ ( A
@ ( sk1
@ ^ [B: a] : ( cP @ ( A @ B ) ) ) ) ) )
!= ( cP
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[103,96]) ).
thf(26519,plain,
~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : $false ) ) ),
inference(pre_uni,[status(thm)],[25986:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ( cP @ ^ [D: a] : $false ) ))]]) ).
thf(26985,plain,
~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : $false ) ),
inference(rewrite,[status(thm)],[26519,96]) ).
thf(1504,plain,
! [A: a] :
( ( sk3 @ sk4 )
| ( ( cP @ ( sk2 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[15,1407]) ).
thf(1528,plain,
! [A: a] :
( ( sk3 @ sk4 )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[1504]) ).
thf(4975,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,3926]) ).
thf(5042,plain,
( ~ ( cP
@ ^ [A: a] : ( cP @ sk3 ) )
| ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[4975:[bind(A,$thf( ^ [B: a] : ( cP @ sk3 ) ))]]) ).
thf(134,plain,
! [D: a > $o,C: a > $o,B: a,A: a] :
( ( sk3 @ sk6 )
| ~ ( cP @ C )
| ~ ( C @ A )
| ~ ( D @ A )
| ~ ( C @ B )
| ( D @ B )
| ( ( cP @ sk3 )
!= ( cP @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27,11]) ).
thf(135,plain,
! [C: a > $o,B: a,A: a] :
( ( sk3 @ sk6 )
| ~ ( cP @ C )
| ~ ( C @ A )
| ~ ( sk3 @ A )
| ~ ( C @ B )
| ( sk3 @ B ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk3 ))]]) ).
thf(69,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( A @ ( sk1 @ A ) )
!= ( ~ ( cP @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(80,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( A @ ( sk1 @ A ) )
!= ( ~ ( cP @ A ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(9762,plain,
( ( cP @ sk139 )
| ( cP @ sk3 )
| ( cP @ sk22 ) ),
inference(cnf,[status(esa)],[9346]) ).
thf(35,plain,
! [A: a] :
( ( sk7 @ A @ sk4 )
| ( sk3 @ sk5 )
| ~ ( sk3 @ A )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(4335,plain,
( ( sk3 @ sk6 )
| ( sk5 != sk4 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,3921]) ).
thf(4336,plain,
( ( sk3 @ sk6 )
| ( sk5 != sk4 ) ),
inference(pattern_uni,[status(thm)],[4335:[]]) ).
thf(8248,plain,
( ~ ( sk3 @ sk116 )
| ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ),
inference(func_ext,[status(esa)],[7999]) ).
thf(8644,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( ( sk3 @ sk116 )
!= ( sk3 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[4146,8248]) ).
thf(8710,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) )
| ( sk116 != sk6 ) ),
inference(simp,[status(thm)],[8644]) ).
thf(8878,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk116 != sk6 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8710]) ).
thf(8954,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ( sk116 != sk6 ) ),
inference(pre_uni,[status(thm)],[8878:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(20156,plain,
! [A: a > $o] :
( ( cP @ sk3 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk121 @ sk187 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10728,94]) ).
thf(20467,plain,
( ( cP @ sk3 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk121 @ sk187 ) ) ),
inference(pre_uni,[status(thm)],[20156:[bind(A,$thf( ^ [B: a] : ( sk121 @ sk187 ) ))]]) ).
thf(6682,plain,
! [A: a > $o] :
( ( sk3 @ sk5 )
| ( sk3 @ sk6 )
| ( A @ ( sk1 @ A ) )
| ( ( cP @ sk68 )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3621,14]) ).
thf(6683,plain,
( ( sk3 @ sk5 )
| ( sk3 @ sk6 )
| ( sk68 @ ( sk1 @ sk68 ) ) ),
inference(pattern_uni,[status(thm)],[6682:[bind(A,$thf( sk68 ))]]) ).
thf(8446,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : sk5 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8093]) ).
thf(8537,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : ( sk3 @ sk5 ) ) ) )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) ) ),
inference(pre_uni,[status(thm)],[8446:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ ^ [D: a] : ( sk3 @ sk5 ) ) ) ))]]) ).
thf(76,plain,
! [B: a > a,A: a > a] :
( ~ ( cP
@ ^ [C: a] : ( sk7 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk7
@ ( A
@ ( sk1
@ ^ [C: a] : ( sk7 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk1
@ ^ [C: a] : ( sk7 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [D: a] : ( sk7 @ ( B @ D ) @ ( C @ D ) ) ))]]) ).
thf(95,plain,
! [B: a > a,A: a > a] :
( ~ ( cP
@ ^ [C: a] : ( sk7 @ ( A @ C ) @ ( B @ C ) ) )
| ( sk7
@ ( A
@ ( sk1
@ ^ [C: a] : ( sk7 @ ( A @ C ) @ ( B @ C ) ) ) )
@ ( B
@ ( sk1
@ ^ [C: a] : ( sk7 @ ( A @ C ) @ ( B @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(20095,plain,
! [A: a > $o] :
( ( sk3 @ sk4 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1497,94]) ).
thf(20438,plain,
( ( sk3 @ sk4 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20095:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(20173,plain,
! [A: a > $o] :
( ( sk5 != sk4 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4336,94]) ).
thf(20506,plain,
( ( sk5 != sk4 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20173:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(6417,plain,
( ( sk3
!= ( ^ [A: a] : ( sk3 @ sk5 ) ) )
| ~ ( cP @ sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[5299,3790]) ).
thf(6436,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ~ ( cP @ sk3 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[6417]) ).
thf(1256,plain,
( ( sk3 @ sk6 )
| ( sk22 @ sk5 )
| ( sk3 @ sk5 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,1169]) ).
thf(1257,plain,
( ( sk3 @ sk6 )
| ( sk22 @ sk5 )
| ( sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1256:[]]) ).
thf(20136,plain,
! [A: a > $o] :
( ( sk21 != sk6 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[686,94]) ).
thf(20442,plain,
( ( sk21 != sk6 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20136:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(43,plain,
! [B: a,A: a] :
( ( cP @ ( sk9 @ B @ A ) )
| ( sk3 @ sk5 )
| ( ( sk2 @ A )
!= sk3 )
| ~ ( sk3 @ B ) ),
inference(cnf,[status(esa)],[39]) ).
thf(10727,plain,
( ( ( sk121 @ sk186 )
!= ( sk3 @ sk186 ) )
| ( cP @ sk3 ) ),
inference(func_ext,[status(esa)],[10607]) ).
thf(64,plain,
! [C: a,B: a,A: a > $o] :
( ~ ( cP @ A )
| ( ( sk3 @ sk5 )
!= ( ? [D: a > $o] :
( ( cP @ D )
& ( D @ sk4 )
& ( D @ sk5 ) ) ) )
| ( ( sk2 @ B )
!= sk3 )
| ( ( A @ ( sk1 @ A ) )
!= ( sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,32]) ).
thf(82,plain,
! [B: a > a,A: a] :
( ~ ( cP
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
| ( ( sk3 @ sk5 )
!= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ) )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(pre_uni,[status(thm)],[64:[bind(A,$thf( ^ [E: a] : ( sk3 @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ ( sk1 @ ^ [E: a] : ( sk3 @ ( D @ E ) ) ) ))]]) ).
thf(99,plain,
! [B: a > a,A: a] :
( ~ ( cP
@ ^ [C: a] : ( sk3 @ ( B @ C ) ) )
| ( ( sk3 @ sk5 )
!= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ) )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[82]) ).
thf(9760,plain,
( ( cP @ sk22 )
| ( cP @ sk138 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9344]) ).
thf(3620,plain,
( ( sk68 @ sk4 )
| ( sk3 @ sk5 )
| ( sk3 @ sk6 ) ),
inference(cnf,[status(esa)],[3453]) ).
thf(20116,plain,
! [A: a > $o] :
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( cP @ sk22 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4230,94]) ).
thf(20487,plain,
( ( sk3 @ sk6 )
| ~ ( cP
@ ^ [A: a] :
~ ( cP @ sk22 ) ) ),
inference(pre_uni,[status(thm)],[20116:[bind(A,$thf( ^ [B: a] : ( cP @ sk22 ) ))]]) ).
thf(20143,plain,
! [A: a > $o] :
( ( cP @ sk3 )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk120 @ sk184 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10651,94]) ).
thf(20446,plain,
( ( cP @ sk3 )
| ~ ( cP
@ ^ [A: a] :
~ ( sk120 @ sk184 ) ) ),
inference(pre_uni,[status(thm)],[20143:[bind(A,$thf( ^ [B: a] : ( sk120 @ sk184 ) ))]]) ).
thf(9299,plain,
! [A: a] :
( ( sk3 @ sk4 )
| ( cP @ sk3 )
| ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk6 )
& ( B @ A ) )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1497,2139]) ).
thf(9300,plain,
( ( sk3 @ sk4 )
| ( cP @ sk3 )
| ? [A: a > $o] :
( ( cP @ A )
& ( A @ sk6 )
& ( A @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9299:[bind(A,$thf( sk6 ))]]) ).
thf(9736,plain,
( ( sk129 @ sk6 )
| ( cP @ sk3 )
| ( sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[9300]) ).
thf(9718,plain,
( ( sk121 @ sk6 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9278]) ).
thf(10065,plain,
( ( cP @ sk3 )
| ( ( cP @ sk120 )
!= ( cP @ sk3 ) ) ),
inference(simp,[status(thm)],[10049]) ).
thf(11551,plain,
( ( sk3 @ sk6 )
| ( ( cP @ sk3 )
!= ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,5267]) ).
thf(11685,plain,
( ( sk3 @ sk6 )
| ( sk3
!= ( ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ) ),
inference(simp,[status(thm)],[11551]) ).
thf(9954,plain,
! [A: a > $o] :
( ( cP @ sk3 )
| ( A @ ( sk1 @ A ) )
| ( ( cP @ sk120 )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9717,14]) ).
thf(9955,plain,
( ( cP @ sk3 )
| ( sk120 @ ( sk1 @ sk120 ) ) ),
inference(pattern_uni,[status(thm)],[9954:[bind(A,$thf( sk120 ))]]) ).
thf(8343,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk113 != sk5 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8001]) ).
thf(8399,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ( sk113 != sk5 ) ),
inference(pre_uni,[status(thm)],[8343:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(20172,plain,
! [A: a > $o] :
( ( sk3
!= ( ^ [B: a] : $false ) )
| ~ ( cP
@ ^ [B: a] :
~ ( A @ B ) )
| ( ( sk3 @ sk6 )
!= ( A
@ ( sk1
@ ^ [B: a] :
~ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[112,94]) ).
thf(20495,plain,
( ( sk3
!= ( ^ [A: a] : $false ) )
| ~ ( cP
@ ^ [A: a] :
~ ( sk3 @ sk6 ) ) ),
inference(pre_uni,[status(thm)],[20172:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk6 ) ))]]) ).
thf(620,plain,
( ( sk3 @ sk6 )
| ( ( sk3 @ ( sk1 @ sk3 ) )
!= ( sk3 @ sk6 ) ) ),
inference(simp,[status(thm)],[611]) ).
thf(8568,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) )
| ( ( A @ ( sk1 @ A ) )
!= ( sk3 @ sk116 ) ) ),
inference(paramod_ordered,[status(thm)],[14,8248]) ).
thf(8660,plain,
( ~ ( cP
@ ^ [A: a] : ( sk3 @ sk116 ) )
| ~ ( cP
@ ^ [A: a] : ( sk3 @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[8568:[bind(A,$thf( ^ [B: a] : ( sk3 @ sk116 ) ))]]) ).
thf(36,plain,
! [A: a] :
( ( cP @ ( sk7 @ A ) )
| ( sk3 @ sk5 )
| ~ ( sk3 @ A )
| ~ ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(50,plain,
! [B: a,A: a] :
( ( cP @ sk3 )
| ( ( sk3 @ sk5 )
!= ( ? [C: a > $o] :
( ( cP @ C )
& ( C @ sk4 )
& ( C @ sk5 ) ) ) )
| ( ( sk2 @ A )
!= sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,32]) ).
thf(51,plain,
! [A: a] :
( ( cP @ sk3 )
| ( ( sk3 @ sk5 )
!= ( ? [B: a > $o] :
( ( cP @ B )
& ( B @ sk4 )
& ( B @ sk5 ) ) ) )
| ( ( sk2 @ A )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).
thf(1772,plain,
( ( sk3 @ sk6 )
| ( cP @ sk22 )
| ( sk3 @ sk5 )
| ( ( cP @ sk3 )
!= ( cP @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,1171]) ).
thf(1773,plain,
( ( sk3 @ sk6 )
| ( cP @ sk22 )
| ( sk3 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[1772:[]]) ).
thf(2795,plain,
( ( cP @ sk22 )
| ( sk3 @ sk5 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1773]) ).
thf(2815,plain,
( ( cP @ sk22 )
| ( sk3 @ sk5 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[2795]) ).
thf(4471,plain,
! [A: a > $o] :
( ( sk3 @ sk6 )
| ( A @ ( sk1 @ A ) )
| ( ( cP @ sk22 )
!= ( cP @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4230,14]) ).
thf(4472,plain,
( ( sk3 @ sk6 )
| ( sk22 @ ( sk1 @ sk22 ) ) ),
inference(pattern_uni,[status(thm)],[4471:[bind(A,$thf( sk22 ))]]) ).
thf(4383,plain,
( ( sk21 != sk5 )
| ~ ( cP @ sk3 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4169,3790]) ).
thf(4399,plain,
( ( sk21 != sk5 )
| ~ ( cP @ sk3 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[4383]) ).
thf(4,plain,
! [A: a] : ( sk2 @ A @ A ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [A: a] : ( sk2 @ A @ A ),
inference(simp,[status(thm)],[4]) ).
thf(2266,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ( sk3 @ sk4 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : ( cP @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,1676]) ).
thf(2340,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] :
( cP
@ ^ [C: a] : ( cP @ sk3 ) ) ) )
| ( sk3 @ sk4 ) ),
inference(pre_uni,[status(thm)],[2266:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( cP @ ^ [D: a] : ( cP @ sk3 ) ) ) ))]]) ).
thf(6644,plain,
( ( sk104 != sk5 )
| ~ ( cP @ sk3 )
| ( sk6 != sk5 ) ),
inference(func_ext,[status(esa)],[6436]) ).
thf(8569,plain,
! [A: a > $o] :
( ~ ( cP @ A )
| ~ ( sk3 @ sk116 )
| ( ( A @ ( sk1 @ A ) )
!= ( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8248]) ).
thf(8706,plain,
( ~ ( cP
@ ^ [A: a] :
( cP
@ ^ [B: a] : ( sk3 @ sk5 ) ) )
| ~ ( sk3 @ sk116 ) ),
inference(pre_uni,[status(thm)],[8569:[bind(A,$thf( ^ [B: a] : ( cP @ ^ [C: a] : ( sk3 @ sk5 ) ) ))]]) ).
thf(6348,plain,
( ( ( sk3 @ sk98 )
!= ( sk3 @ sk5 ) )
| ( sk3 @ sk6 ) ),
inference(func_ext,[status(esa)],[5299]) ).
thf(15012,plain,
( ( sk3 @ sk6 )
| ( sk98 != sk5 ) ),
inference(simp,[status(thm)],[6348]) ).
thf(9763,plain,
( ( ( ^ [A: a] : A )
!= ( ^ [A: a] : sk5 ) )
| ( sk140 @ sk6 )
| ( cP @ sk3 ) ),
inference(cnf,[status(esa)],[9348]) ).
thf(67,plain,
! [B: a > $o,A: a] :
( ( B @ ( sk1 @ B ) )
| ( ( cP @ ( sk2 @ A ) )
!= ( cP @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,14]) ).
thf(68,plain,
! [A: a] : ( sk2 @ A @ ( sk1 @ ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( A )),bind(B,$thf( sk2 @ A ))]]) ).
thf(9737,plain,
( ( cP @ sk129 )
| ( cP @ sk3 )
| ( sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[9300]) ).
thf(195735,plain,
$false,
inference(e,[status(thm)],[5116,1024,13783,20464,88,6544,4169,1211,8129,9717,9759,20437,1497,20469,11160,4435,153,20556,7064,9735,5921,37,8325,42,14,6034,10606,6130,638,20,4179,1572,10650,4460,4771,4432,492,4443,11676,3621,3923,84,1169,8001,4230,6347,6498,89,8443,9764,1153,7999,2441,13917,20459,70,3884,12215,9734,28,1676,92,1365,97,3926,1407,8104,1573,12404,11096,53,593,193,686,96,20493,9761,10455,13,6346,4347,3920,41,5026,10651,3903,105,9716,1170,5295,4308,12389,5969,10607,9765,32,34,3925,12216,20486,9719,9057,20475,5752,27,10611,10728,3619,113,274,10066,5267,103,66,15420,6989,621,91,685,26985,1528,3917,2139,5042,135,3,5299,80,9762,35,7975,1134,112,3921,4336,8954,20467,4749,5047,6683,18,8537,95,9766,20438,5030,20506,6436,8248,1257,11,20442,43,4217,10727,99,9760,3928,4310,3620,5981,20487,6003,20446,4900,9736,9718,6018,10065,11685,8710,9955,8399,20495,620,8660,7759,36,51,2815,10073,4472,4399,3790,1527,19,4146,2340,94,6644,1335,8706,15012,9763,8093,6348,15,68,9737,992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV021^6 : TPTP v8.2.0. Released v5.5.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 21 19:13:25 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.92/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (107ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.65/1.19 % [INFO] eprover registered as external prover.
% 1.65/1.19 % [INFO] Scanning for conjecture ...
% 1.93/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.93/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.29 % [INFO] Type checking passed.
% 1.93/1.29 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 265.96/71.25 % External prover 'e' found a proof!
% 265.96/71.25 % [INFO] Killing All external provers ...
% 265.96/71.25 % Time passed: 70733ms (effective reasoning time: 70277ms)
% 265.96/71.25 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 265.96/71.25 % Axioms used in derivation (0):
% 265.96/71.25 % No. of inferences in proof: 389
% 265.96/71.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 70733 ms resp. 70277 ms w/o parsing
% 266.30/71.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 266.30/71.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------