TSTP Solution File: SEV116^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV116^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n020.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 15:58:15 EDT 2024
% Result : Theorem 79.66s 17.93s
% Output : Refutation 80.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 693 ( 36 unt; 0 typ; 1 def)
% Number of atoms : 3724 (1078 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 7342 (1690 ~;1181 |; 70 &;4331 @)
% ( 0 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 289 ( 289 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 66 con; 0-3 aty)
% Number of variables : 1847 (1708 ^ 139 !; 0 ?;1847 :)
% Comments :
%------------------------------------------------------------------------------
thf(cS_type,type,
cS: ( $i > $i > $o ) > $o ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(cSTRANGE_HO_ABBR_type,type,
cSTRANGE_HO_ABBR: ( ( $i > $i > $o ) > $o ) > $i > $i > $o ).
thf(cSTRANGE_HO_ABBR_def,definition,
( cSTRANGE_HO_ABBR
= ( ^ [A: ( $i > $i > $o ) > $o,B: $i,C: $i] :
! [D: $i > $i > $o] :
( ( ( A @ D )
& ( D @ B @ C ) )
=> ( D @ C @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i > $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i > $o ).
thf(sk8_type,type,
sk8: $i > $i > $o ).
thf(sk9_type,type,
sk9: $i > $i > $o ).
thf(sk10_type,type,
sk10: $i > $i > $o ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk13_type,type,
sk13: $i > $i > $o ).
thf(sk14_type,type,
sk14: $i > $i > $o ).
thf(sk17_type,type,
sk17: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk20_type,type,
sk20: $i ).
thf(sk24_type,type,
sk24: $i ).
thf(sk25_type,type,
sk25: $i ).
thf(sk28_type,type,
sk28: $i ).
thf(sk29_type,type,
sk29: $i ).
thf(sk33_type,type,
sk33: $i ).
thf(sk34_type,type,
sk34: $i ).
thf(sk35_type,type,
sk35: $i ).
thf(sk36_type,type,
sk36: $i ).
thf(sk39_type,type,
sk39: $i ).
thf(sk40_type,type,
sk40: $i ).
thf(sk63_type,type,
sk63: $i ).
thf(sk64_type,type,
sk64: $i ).
thf(sk68_type,type,
sk68: $i ).
thf(sk69_type,type,
sk69: $i ).
thf(sk70_type,type,
sk70: $i ).
thf(sk71_type,type,
sk71: $i ).
thf(sk73_type,type,
sk73: $i ).
thf(sk74_type,type,
sk74: $i ).
thf(sk77_type,type,
sk77: $i ).
thf(sk78_type,type,
sk78: $i ).
thf(sk106_type,type,
sk106: $i ).
thf(sk107_type,type,
sk107: $i ).
thf(sk115_type,type,
sk115: $i > $i > $o ).
thf(sk121_type,type,
sk121: $i ).
thf(sk122_type,type,
sk122: $i ).
thf(sk138_type,type,
sk138: $i ).
thf(sk139_type,type,
sk139: $i ).
thf(sk140_type,type,
sk140: $i ).
thf(sk141_type,type,
sk141: $i ).
thf(sk154_type,type,
sk154: $i > $i > $o ).
thf(sk161_type,type,
sk161: $i ).
thf(sk162_type,type,
sk162: $i ).
thf(sk163_type,type,
sk163: $i ).
thf(sk164_type,type,
sk164: $i ).
thf(sk165_type,type,
sk165: $i ).
thf(sk166_type,type,
sk166: $i ).
thf(sk167_type,type,
sk167: $i ).
thf(sk168_type,type,
sk168: $i ).
thf(sk177_type,type,
sk177: $i ).
thf(sk178_type,type,
sk178: $i ).
thf(sk179_type,type,
sk179: $i ).
thf(sk180_type,type,
sk180: $i ).
thf(sk181_type,type,
sk181: $i ).
thf(sk182_type,type,
sk182: $i ).
thf(sk187_type,type,
sk187: $i ).
thf(sk188_type,type,
sk188: $i ).
thf(sk193_type,type,
sk193: $i > $i > $o ).
thf(sk194_type,type,
sk194: $i ).
thf(sk195_type,type,
sk195: $i ).
thf(sk200_type,type,
sk200: $i ).
thf(sk201_type,type,
sk201: $i ).
thf(sk323_type,type,
sk323: $i ).
thf(sk324_type,type,
sk324: $i ).
thf(sk420_type,type,
sk420: $i ).
thf(sk421_type,type,
sk421: $i ).
thf(1,conjecture,
( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSTRANGE_HO_EXAMPLE) ).
thf(2,negated_conjecture,
~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
& ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ x @ y ) )
=> ( A @ y @ x ) ) )
=> ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ y @ x ) )
=> ( A @ x @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
sk1 @ y @ x,
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( A @ y @ x ) ),
inference(cnf,[status(esa)],[3]) ).
thf(27,plain,
! [A: $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] :
~ ( A @ B @ C ) )
| ~ ~ ( A @ x @ y )
| ~ ( A @ y @ x ) ),
inference(prim_subst,[status(thm)],[4:[bind(A,$thf( ^ [C: $i] : ^ [D: $i] : ~ ( B @ C @ D ) ))]]) ).
thf(50,plain,
! [A: $i > $i > $o] :
( ~ ( A @ y @ x )
| ( A @ x @ y )
| ~ ( cS
@ ^ [B: $i,C: $i] :
~ ( A @ B @ C ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(51,plain,
! [A: $i > $i > $o] :
( ~ ( A @ y @ x )
| ( A @ x @ y )
| ~ ( cS
@ ^ [B: $i,C: $i] :
~ ( A @ B @ C ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(4934,plain,
! [A: $i > $i > $o] :
( ( A @ x @ y )
| ~ ( cS
@ ^ [B: $i,C: $i] :
~ ( A @ B @ C ) )
| ( ( sk1 @ y @ x )
!= ( A @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,51]) ).
thf(5040,plain,
( ( sk1 @ y @ y )
| ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ),
inference(pre_uni,[status(thm)],[4934:[bind(A,$thf( ^ [B: $i] : ( sk1 @ y ) ))]]) ).
thf(5,plain,
~ ( sk1 @ x @ y ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( A @ y @ x )
!= ( sk1 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[4,5]) ).
thf(36,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ~ ( sk1 @ y @ y ) ),
inference(pre_uni,[status(thm)],[12:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ y ) ))]]) ).
thf(6975,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[5040,36]) ).
thf(6976,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pattern_uni,[status(thm)],[6975:[]]) ).
thf(8,plain,
cS @ sk1,
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(38,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) )
| ~ ( sk1 @ y @ x ) ),
inference(pre_uni,[status(thm)],[12:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ B ) ))]]) ).
thf(53,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) )
| ~ $true ),
inference(rewrite,[status(thm)],[38,7]) ).
thf(54,plain,
~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ),
inference(simp,[status(thm)],[53]) ).
thf(59,plain,
( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,54]) ).
thf(63,plain,
( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(72,plain,
( ( sk1 @ sk6 @ sk5 )
!= ( ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) ) ) ),
inference(func_ext,[status(esa)],[63]) ).
thf(82,plain,
( ( sk1 @ sk6 @ sk5 )
| ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[72]) ).
thf(90,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ sk5 @ sk6 )
| ( A @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[82]) ).
thf(8181,plain,
! [A: $i > $i > $o] :
( ~ ( A @ sk5 @ sk6 )
| ( A @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk5 )
| ( ( cS @ sk1 )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,90]) ).
thf(8182,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[8181:[bind(A,$thf( sk1 ))]]) ).
thf(8673,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(simp,[status(thm)],[8182]) ).
thf(81,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) ) ),
inference(bool_ext,[status(thm)],[72]) ).
thf(87,plain,
( ~ ( sk7 @ sk6 @ sk5 )
| ~ ( sk1 @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[81]) ).
thf(10266,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk7 @ sk6 @ sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,87]) ).
thf(10267,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ~ ( sk7 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[10266:[]]) ).
thf(60,plain,
! [A: $i > $i > $o] :
( ~ ( A @ x @ y )
| ( A @ y @ x )
| ( ( cS
@ ^ [B: $i,C: $i] :
! [D: $i > $i > $o] :
( ( ( cS @ D )
& ( D @ B @ C ) )
=> ( D @ C @ B ) ) )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,4]) ).
thf(61,plain,
( ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ x @ y ) )
=> ( A @ y @ x ) )
| ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ y @ x ) )
=> ( A @ x @ y ) ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ! [D: $i > $i > $o] : ( ( ( cS @ D ) & ( D @ B @ C ) ) => ( D @ C @ B ) ) ))]]) ).
thf(64,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ y @ x )
| ( A @ x @ y )
| ( cS @ sk2 ) ),
inference(cnf,[status(esa)],[61]) ).
thf(5482,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ( A @ x @ y )
| ( cS @ sk2 )
| ( ( sk1 @ y @ x )
!= ( A @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,64]) ).
thf(5675,plain,
( ~ ( cS @ sk1 )
| ( sk1 @ x @ y )
| ( cS @ sk2 ) ),
inference(pre_uni,[status(thm)],[5482:[bind(A,$thf( sk1 ))]]) ).
thf(7789,plain,
( ~ $true
| $false
| ( cS @ sk2 ) ),
inference(rewrite,[status(thm)],[5675,5,8]) ).
thf(7790,plain,
cS @ sk2,
inference(simp,[status(thm)],[7789]) ).
thf(65,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ y @ x )
| ( A @ x @ y )
| ( sk2 @ x @ y ) ),
inference(cnf,[status(esa)],[61]) ).
thf(7808,plain,
! [A: $i > $i > $o] :
( ~ ( A @ y @ x )
| ( A @ x @ y )
| ( sk2 @ x @ y )
| ( ( cS @ sk2 )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7790,65]) ).
thf(7809,plain,
( ~ ( sk2 @ y @ x )
| ( sk2 @ x @ y )
| ( sk2 @ x @ y ) ),
inference(pattern_uni,[status(thm)],[7808:[bind(A,$thf( sk2 ))]]) ).
thf(7922,plain,
( ~ ( sk2 @ y @ x )
| ( sk2 @ x @ y ) ),
inference(simp,[status(thm)],[7809]) ).
thf(5041,plain,
( ( sk1 @ x @ y )
| ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ),
inference(pre_uni,[status(thm)],[4934:[bind(A,$thf( sk1 ))]]) ).
thf(5349,plain,
( $false
| ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ),
inference(rewrite,[status(thm)],[5041,5]) ).
thf(5350,plain,
~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[5349]) ).
thf(5351,plain,
( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6,5350]) ).
thf(5376,plain,
( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[5351]) ).
thf(5383,plain,
( ( ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk106 @ sk107 ) )
=> ( A @ sk107 @ sk106 ) ) )
!= ( ~ ( sk1 @ sk106 @ sk107 ) ) ),
inference(func_ext,[status(esa)],[5376]) ).
thf(5771,plain,
( ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk106 @ sk107 ) )
=> ( A @ sk107 @ sk106 ) )
| ~ ~ ( sk1 @ sk106 @ sk107 ) ),
inference(bool_ext,[status(thm)],[5383]) ).
thf(5864,plain,
( ( sk1 @ sk106 @ sk107 )
| ( cS @ sk115 ) ),
inference(cnf,[status(esa)],[5771]) ).
thf(5947,plain,
( ( sk1 @ sk106 @ sk107 )
| ( ( cS @ sk115 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5864,5350]) ).
thf(6042,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk115
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5947]) ).
thf(5948,plain,
( ( sk1 @ sk106 @ sk107 )
| ( ( cS @ sk115 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[5864,54]) ).
thf(6074,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk115
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[5948]) ).
thf(13,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ( A @ y @ x )
| ( ( sk1 @ y @ x )
!= ( A @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[7,4]) ).
thf(32,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk1 @ y @ y ) ),
inference(pre_uni,[status(thm)],[13:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ y @ B ) ))]]) ).
thf(217,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,72]) ).
thf(219,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( sk6 != y )
| ( sk5 != y ) ),
inference(simp,[status(thm)],[217]) ).
thf(234,plain,
( ( sk5 != y )
| ( sk6 != y )
| ~ ( sk14 @ sk6 @ sk5 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(cnf,[status(esa)],[219]) ).
thf(88,plain,
( ( sk7 @ sk5 @ sk6 )
| ~ ( sk1 @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[81]) ).
thf(31,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk1 @ x @ x ) ),
inference(pre_uni,[status(thm)],[13:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ x ) ))]]) ).
thf(37,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ~ ( sk1 @ x @ x ) ),
inference(pre_uni,[status(thm)],[12:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ x @ B ) ))]]) ).
thf(188,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,37]) ).
thf(189,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(pattern_uni,[status(thm)],[188:[]]) ).
thf(549,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,189]) ).
thf(562,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(7815,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,562]) ).
thf(7903,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[7815]) ).
thf(7800,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,189]) ).
thf(7905,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[7800]) ).
thf(7850,plain,
( ~ ( sk1 @ y @ y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,36]) ).
thf(7869,plain,
( ~ ( sk1 @ y @ y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[7850]) ).
thf(9163,plain,
( ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) )
| ~ ( sk1 @ y @ y ) ),
inference(func_ext,[status(esa)],[7869]) ).
thf(100,plain,
( ~ ( sk1 @ y @ y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,36]) ).
thf(111,plain,
( ~ ( sk1 @ y @ y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(382,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,111]) ).
thf(383,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[382:[]]) ).
thf(736,plain,
( ( ( sk1 @ sk34 @ y )
!= ( sk1 @ sk33 @ sk34 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(func_ext,[status(esa)],[383]) ).
thf(18365,plain,
( ( sk34 != sk33 )
| ( sk34 != y )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(simp,[status(thm)],[736]) ).
thf(83,plain,
( ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,72]) ).
thf(85,plain,
( ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( sk6 != y )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[83]) ).
thf(93,plain,
( ( sk5 != x )
| ( sk6 != y )
| ( cS @ sk8 ) ),
inference(cnf,[status(esa)],[85]) ).
thf(435,plain,
( ( sk5 != x )
| ( sk6 != y )
| ( ( cS @ sk8 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,54]) ).
thf(449,plain,
( ( sk5 != x )
| ( sk6 != y )
| ( sk8
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[435]) ).
thf(369,plain,
( ~ ( sk7 @ sk6 @ sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,87]) ).
thf(379,plain,
( ~ ( sk7 @ sk6 @ sk5 )
| ( sk6 != y )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[369]) ).
thf(218,plain,
( ( sk1 @ y @ y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,32]) ).
thf(223,plain,
( ( sk1 @ y @ y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[218]) ).
thf(612,plain,
! [A: $i > $i > $o] :
( ( sk1
!= ( ^ [B: $i,C: $i] : ( sk1 @ y @ B ) ) )
| ~ ( cS @ A )
| ( A @ y @ x )
| ( ( sk1 @ y @ y )
!= ( A @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,4]) ).
thf(655,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ B ) )
| ( sk1 @ x @ x ) ),
inference(pre_uni,[status(thm)],[612:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ C ) ))]]) ).
thf(186,plain,
( ~ ( sk1 @ x @ x )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,37]) ).
thf(202,plain,
( ~ ( sk1 @ x @ x )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(6987,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[5040,111]) ).
thf(6988,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[6987:[]]) ).
thf(12447,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6988]) ).
thf(12458,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[12447]) ).
thf(160,plain,
! [A: $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ C @ x ) )
| ~ ( cS @ A )
| ( A @ y @ x )
| ( ( sk1 @ x @ x )
!= ( A @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[31,4]) ).
thf(170,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ( sk1 @ y @ y ) ),
inference(pre_uni,[status(thm)],[160:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ B @ B ) ))]]) ).
thf(7799,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,189]) ).
thf(7898,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[7799]) ).
thf(9316,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7898]) ).
thf(9337,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[9316]) ).
thf(550,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[189]) ).
thf(552,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(2007,plain,
( ( ( sk1 @ sk69 @ x )
!= ( sk1 @ x @ sk68 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(func_ext,[status(esa)],[552]) ).
thf(20694,plain,
( ( sk69 != x )
| ( sk68 != x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(simp,[status(thm)],[2007]) ).
thf(55,plain,
( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,54]) ).
thf(57,plain,
( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(68,plain,
( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ sk3 @ sk4 ) ),
inference(func_ext,[status(esa)],[57]) ).
thf(216,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,68]) ).
thf(227,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ( sk1 @ sk3 @ sk4 )
| ( sk4 != y )
| ( sk3 != y ) ),
inference(simp,[status(thm)],[216]) ).
thf(33524,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk4 != y )
| ( sk3 != y )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,227]) ).
thf(33628,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk4 != y )
| ( sk3 != y )
| ( sk3 != y )
| ( sk4 != y ) ),
inference(simp,[status(thm)],[33524]) ).
thf(33663,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk4 != y )
| ( sk3 != y ) ),
inference(simp,[status(thm)],[33628]) ).
thf(7819,plain,
( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7790,5350]) ).
thf(7915,plain,
( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[7819]) ).
thf(7928,plain,
( ( sk2 @ sk140 @ sk141 )
!= ( ~ ( sk1 @ sk140 @ sk141 ) ) ),
inference(func_ext,[status(esa)],[7915]) ).
thf(7954,plain,
( ( sk2 @ sk140 @ sk141 )
| ~ ( sk1 @ sk140 @ sk141 ) ),
inference(bool_ext,[status(thm)],[7928]) ).
thf(7975,plain,
( ~ ( sk1 @ sk140 @ sk141 )
| ( sk2 @ sk140 @ sk141 ) ),
inference(cnf,[status(esa)],[7954]) ).
thf(10122,plain,
( ( sk2 @ sk140 @ sk141 )
| ( ( sk1 @ sk140 @ sk141 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,7975]) ).
thf(10181,plain,
( ( sk2 @ sk140 @ sk141 )
| ( sk140 != y )
| ( sk141 != x ) ),
inference(simp,[status(thm)],[10122]) ).
thf(5039,plain,
( ( sk1 @ x @ x )
| ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ),
inference(pre_uni,[status(thm)],[4934:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ B @ x ) ))]]) ).
thf(192,plain,
( ~ ( sk1 @ x @ x )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,37]) ).
thf(195,plain,
( ~ ( sk1 @ x @ x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(6778,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[5039,195]) ).
thf(6779,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6778:[]]) ).
thf(7824,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,6779]) ).
thf(7873,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[7824]) ).
thf(566,plain,
( ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) )
| ~ ( sk1 @ x @ x ) ),
inference(func_ext,[status(esa)],[195]) ).
thf(16903,plain,
( ( sk24 != x )
| ( sk25 != sk24 )
| ~ ( sk1 @ x @ x ) ),
inference(simp,[status(thm)],[566]) ).
thf(17970,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk24 != x )
| ( sk25 != sk24 )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,16903]) ).
thf(17971,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk24 != x )
| ( sk25 != sk24 ) ),
inference(pattern_uni,[status(thm)],[17970:[]]) ).
thf(19156,plain,
( ( sk24 != x )
| ( sk25 != sk24 )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,17971]) ).
thf(19191,plain,
( ( sk24 != x )
| ( sk25 != sk24 )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[19156]) ).
thf(6101,plain,
( ( ( sk115 @ sk121 @ sk122 )
!= ( sk1 @ sk122 @ sk121 ) )
| ( sk1 @ sk106 @ sk107 ) ),
inference(func_ext,[status(esa)],[6074]) ).
thf(21534,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk115 @ sk121 @ sk122 )
| ( sk1 @ sk122 @ sk121 ) ),
inference(bool_ext,[status(thm)],[6101]) ).
thf(212,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,36]) ).
thf(213,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pattern_uni,[status(thm)],[212:[]]) ).
thf(7826,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,213]) ).
thf(7860,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[7826]) ).
thf(8842,plain,
( ( ( sk2 @ sk161 @ sk162 )
!= ( sk1 @ y @ sk161 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(func_ext,[status(esa)],[7860]) ).
thf(22133,plain,
( ( ( sk2 @ sk161 @ sk162 )
!= ( sk1 @ y @ sk161 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,8842]) ).
thf(22185,plain,
( ( ( sk2 @ sk161 @ sk162 )
!= ( sk1 @ y @ sk161 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[22133]) ).
thf(75,plain,
( ( sk1 @ sk4 @ sk3 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(bool_ext,[status(thm)],[68]) ).
thf(114,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[75,36]) ).
thf(123,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk4 != y )
| ( sk3 != y ) ),
inference(simp,[status(thm)],[114]) ).
thf(13043,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk4 != y )
| ( sk3 != y )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[123,36]) ).
thf(13065,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk4 != y )
| ( sk3 != y )
| ( sk3 != y )
| ( sk4 != y ) ),
inference(simp,[status(thm)],[13043]) ).
thf(13158,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk4 != y )
| ( sk3 != y ) ),
inference(simp,[status(thm)],[13065]) ).
thf(14481,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,13158]) ).
thf(14506,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[14481]) ).
thf(89,plain,
( ( cS @ sk7 )
| ~ ( sk1 @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[81]) ).
thf(131,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,54]) ).
thf(142,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(10261,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,72]) ).
thf(10262,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[10261:[]]) ).
thf(10370,plain,
( ( cS @ sk193 )
| ~ ( sk1 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[10262]) ).
thf(10755,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( ( cS @ sk193 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10370,5350]) ).
thf(10881,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk193
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[10755]) ).
thf(10368,plain,
( ~ ( sk193 @ sk6 @ sk5 )
| ~ ( sk1 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[10262]) ).
thf(19,plain,
! [A: $i > $i > $o] :
( ~ ( A @ x @ y )
| ( A @ y @ x )
| ( ( cS @ A )
!= ( A @ x @ y ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4]) ).
thf(42,plain,
! [A: $i > $i > $o] :
( ( A @ y @ x )
| ~ ( A @ x @ y )
| ( ( cS @ A )
!= ( A @ x @ y ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(6770,plain,
( ( sk1 @ x @ x )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,5039]) ).
thf(6887,plain,
( ( sk1 @ x @ x )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[6770]) ).
thf(20739,plain,
( ( ( sk1 @ sk69 @ x )
!= ( sk1 @ x @ sk68 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,2007]) ).
thf(20803,plain,
( ( sk69 != x )
| ( sk68 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[20739]) ).
thf(609,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,36]) ).
thf(610,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pattern_uni,[status(thm)],[609:[]]) ).
thf(1408,plain,
( ( ( sk1 @ sk63 @ sk64 )
!= ( sk1 @ y @ sk63 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(func_ext,[status(esa)],[610]) ).
thf(18992,plain,
( ( ( sk1 @ sk63 @ sk64 )
!= ( sk1 @ y @ sk63 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,1408]) ).
thf(19069,plain,
( ( ( sk1 @ sk63 @ sk64 )
!= ( sk1 @ y @ sk63 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[18992]) ).
thf(193,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[75,37]) ).
thf(196,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk4 != x )
| ( sk3 != x ) ),
inference(simp,[status(thm)],[193]) ).
thf(25921,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk4 != x )
| ( sk3 != x )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[196,37]) ).
thf(26040,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk4 != x )
| ( sk3 != x )
| ( sk3 != x )
| ( sk4 != x ) ),
inference(simp,[status(thm)],[25921]) ).
thf(26186,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk4 != x )
| ( sk3 != x ) ),
inference(simp,[status(thm)],[26040]) ).
thf(20,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( A @ y @ x )
!= ( ~ ( cS @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4]) ).
thf(29,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( A @ y @ x )
!= ( ~ ( cS @ A ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(255,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ( ( A @ y @ x )
!= ( ~ ( cS @ A ) ) )
| ( ( sk1 @ y @ x )
!= ( A @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[7,29]) ).
thf(301,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( sk1 @ y @ y )
!= ( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[255:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ y @ B ) ))]]) ).
thf(594,plain,
( ( ( sk1 @ sk28 @ sk29 )
!= ( sk1 @ y @ sk28 ) )
| ( sk1 @ y @ y ) ),
inference(func_ext,[status(esa)],[223]) ).
thf(17570,plain,
( ( sk1 @ y @ y )
| ( sk28 != y )
| ( sk29 != sk28 ) ),
inference(simp,[status(thm)],[594]) ).
thf(19293,plain,
( ( sk28 != y )
| ( sk29 != sk28 )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[17570,7869]) ).
thf(19294,plain,
( ( sk28 != y )
| ( sk29 != sk28 )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[19293:[]]) ).
thf(6737,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[5039,37]) ).
thf(6738,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(pattern_uni,[status(thm)],[6737:[]]) ).
thf(7579,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6738]) ).
thf(7592,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[7579]) ).
thf(551,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(16598,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,551]) ).
thf(16626,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[16598]) ).
thf(163,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,72]) ).
thf(179,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( sk6 != x )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[163]) ).
thf(184,plain,
( ( sk5 != x )
| ( sk6 != x )
| ( cS @ sk13 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(164,plain,
( ( sk1 @ x @ x )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,31]) ).
thf(166,plain,
( ( sk1 @ x @ x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(456,plain,
( ( ( sk1 @ sk20 @ x )
!= ( sk1 @ sk19 @ sk20 ) )
| ( sk1 @ x @ x ) ),
inference(func_ext,[status(esa)],[166]) ).
thf(16056,plain,
( ( sk1 @ x @ x )
| ( sk20 != sk19 )
| ( sk20 != x ) ),
inference(simp,[status(thm)],[456]) ).
thf(17365,plain,
( ( sk20 != sk19 )
| ( sk20 != x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[16056,37]) ).
thf(17366,plain,
( ( sk20 != sk19 )
| ( sk20 != x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(pattern_uni,[status(thm)],[17365:[]]) ).
thf(381,plain,
( ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) )
| ~ ( sk1 @ y @ y ) ),
inference(func_ext,[status(esa)],[111]) ).
thf(15838,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,381]) ).
thf(15839,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[15838:[]]) ).
thf(24450,plain,
( ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,15839]) ).
thf(24558,plain,
( ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[24450]) ).
thf(12328,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6976]) ).
thf(12351,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[12328]) ).
thf(138,plain,
( ( sk1 @ sk3 @ sk4 )
| ( cS @ sk7 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[75,89]) ).
thf(139,plain,
( ( sk1 @ sk3 @ sk4 )
| ( cS @ sk7 )
| ( sk6 != sk4 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[138]) ).
thf(10224,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( cS @ sk7 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,89]) ).
thf(10225,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( cS @ sk7 ) ),
inference(pattern_uni,[status(thm)],[10224:[]]) ).
thf(14276,plain,
( ( cS @ sk7 )
| ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[139,10225]) ).
thf(14357,plain,
( ( cS @ sk7 )
| ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( sk5 != sk3 )
| ( sk6 != sk4 ) ),
inference(simp,[status(thm)],[14276]) ).
thf(14457,plain,
( ( cS @ sk7 )
| ( sk6 != sk4 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[14357]) ).
thf(14580,plain,
( ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[14457,54]) ).
thf(14669,plain,
( ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[14580]) ).
thf(28,plain,
! [B: $i > $i > $i,A: $i > $i > $i] :
( ~ ( cS
@ ^ [C: $i,D: $i] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ~ ( sk1 @ ( A @ x @ y ) @ ( B @ x @ y ) )
| ( sk1 @ ( A @ y @ x ) @ ( B @ y @ x ) ) ),
inference(prim_subst,[status(thm)],[4:[bind(A,$thf( ^ [D: $i] : ^ [E: $i] : ( sk1 @ ( B @ D @ E ) @ ( C @ D @ E ) ) ))]]) ).
thf(52,plain,
! [B: $i > $i > $i,A: $i > $i > $i] :
( ~ ( cS
@ ^ [C: $i,D: $i] : ( sk1 @ ( A @ C @ D ) @ ( B @ C @ D ) ) )
| ~ ( sk1 @ ( A @ x @ y ) @ ( B @ x @ y ) )
| ( sk1 @ ( A @ y @ x ) @ ( B @ y @ x ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(718,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[213]) ).
thf(724,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[718]) ).
thf(7820,plain,
( ( sk1 @ x @ x )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,5039]) ).
thf(7862,plain,
( ( sk1 @ x @ x )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[7820]) ).
thf(540,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,189]) ).
thf(559,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[540]) ).
thf(26358,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,26186]) ).
thf(26371,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[26358]) ).
thf(15850,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,381]) ).
thf(15851,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( sk1 @ sk18 @ y )
!= ( sk1 @ sk17 @ sk18 ) ) ),
inference(pattern_uni,[status(thm)],[15850:[]]) ).
thf(18408,plain,
( ( ( sk1 @ sk34 @ y )
!= ( sk1 @ sk33 @ sk34 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,736]) ).
thf(18492,plain,
( ( sk34 != sk33 )
| ( sk34 != y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[18408]) ).
thf(211,plain,
( ( sk1 @ y @ y )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,32]) ).
thf(228,plain,
( ( sk1 @ y @ y )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(787,plain,
( ( ( sk1 @ sk39 @ sk40 )
!= ( sk1 @ x @ sk39 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(func_ext,[status(esa)],[562]) ).
thf(18823,plain,
( ( ( sk1 @ sk39 @ sk40 )
!= ( sk1 @ x @ sk39 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,787]) ).
thf(18959,plain,
( ( sk39 != x )
| ( sk40 != sk39 )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[18823]) ).
thf(8189,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk106 @ sk107 )
| ~ ( A @ sk5 @ sk6 )
| ( A @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk5 )
| ( ( cS @ sk115 )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5864,90]) ).
thf(8190,plain,
( ( sk1 @ sk106 @ sk107 )
| ~ ( sk115 @ sk5 @ sk6 )
| ( sk115 @ sk6 @ sk5 )
| ( sk1 @ sk6 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[8189:[bind(A,$thf( sk115 ))]]) ).
thf(725,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[718]) ).
thf(2037,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) ) ),
inference(simp,[status(thm)],[725]) ).
thf(2090,plain,
( ( sk77 != y )
| ( sk78 != y )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(func_ext,[status(esa)],[2037]) ).
thf(22544,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,9163]) ).
thf(22545,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) ) ),
inference(pattern_uni,[status(thm)],[22544:[]]) ).
thf(33392,plain,
( ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,22545]) ).
thf(33440,plain,
( ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[33392]) ).
thf(9557,plain,
( ( ( sk2 @ sk187 @ sk188 )
!= ( sk1 @ x @ sk187 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(func_ext,[status(esa)],[7905]) ).
thf(2038,plain,
( ( ( sk1 @ sk71 @ y )
!= ( sk1 @ y @ sk70 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(func_ext,[status(esa)],[725]) ).
thf(20899,plain,
( ( ( sk1 @ sk71 @ y )
!= ( sk1 @ y @ sk70 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,2038]) ).
thf(21007,plain,
( ( ( sk1 @ sk71 @ y )
!= ( sk1 @ y @ sk70 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[20899]) ).
thf(7821,plain,
( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7790,54]) ).
thf(7899,plain,
( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ),
inference(simp,[status(thm)],[7821]) ).
thf(601,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,111]) ).
thf(602,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[601:[]]) ).
thf(147,plain,
( ( ( sk7 @ sk11 @ sk12 )
!= ( sk1 @ sk12 @ sk11 ) )
| ~ ( sk1 @ sk6 @ sk5 ) ),
inference(func_ext,[status(esa)],[142]) ).
thf(707,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,213]) ).
thf(734,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[707]) ).
thf(5353,plain,
( ( sk5 != x )
| ( sk6 != y )
| ( ( cS @ sk8 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,5350]) ).
thf(5370,plain,
( ( sk5 != x )
| ( sk6 != y )
| ( sk8
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5353]) ).
thf(7811,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,725]) ).
thf(7909,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[7811]) ).
thf(1466,plain,
! [A: $i > $i > $o] :
( ~ ( A @ x @ y )
| ( ( cS @ A )
!= ( A @ x @ y ) )
| ( ( A @ y @ x )
!= ( sk1 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[42,5]) ).
thf(1617,plain,
( ~ ( sk1 @ x @ x )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) ) ),
inference(pre_uni,[status(thm)],[1466:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ x @ B ) ))]]) ).
thf(19871,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,1617]) ).
thf(19872,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) ) ),
inference(pattern_uni,[status(thm)],[19871:[]]) ).
thf(408,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( sk7 @ sk6 @ sk5 )
!= ( sk7 @ sk5 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[88,87]) ).
thf(414,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk6 != sk5 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[408]) ).
thf(422,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[414]) ).
thf(424,plain,
( ( sk6 != sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,422]) ).
thf(428,plain,
( ( sk6 != sk5 )
| ( sk6 != y )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[424]) ).
thf(7668,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6779]) ).
thf(7688,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[7668]) ).
thf(74,plain,
( ~ ( sk1 @ sk4 @ sk3 )
| ~ ( sk1 @ sk3 @ sk4 ) ),
inference(bool_ext,[status(thm)],[68]) ).
thf(5863,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk115 @ sk106 @ sk107 ) ),
inference(cnf,[status(esa)],[5771]) ).
thf(5862,plain,
( ( sk1 @ sk106 @ sk107 )
| ~ ( sk115 @ sk107 @ sk106 ) ),
inference(cnf,[status(esa)],[5771]) ).
thf(6128,plain,
( ( sk1 @ sk106 @ sk107 )
| ( ( sk115 @ sk107 @ sk106 )
!= ( sk115 @ sk106 @ sk107 ) ) ),
inference(paramod_ordered,[status(thm)],[5863,5862]) ).
thf(6144,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk107 != sk106 )
| ( sk107 != sk106 ) ),
inference(simp,[status(thm)],[6128]) ).
thf(6153,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk107 != sk106 ) ),
inference(simp,[status(thm)],[6144]) ).
thf(6187,plain,
( ( sk107 != sk106 )
| ( sk6 != sk5 )
| ( ( sk1 @ sk106 @ sk107 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6153,422]) ).
thf(6210,plain,
( ( sk107 != sk106 )
| ( sk6 != sk5 )
| ( sk106 != sk6 )
| ( sk107 != sk5 ) ),
inference(simp,[status(thm)],[6187]) ).
thf(9311,plain,
( ( ( sk2 @ sk181 @ sk182 )
!= ( sk1 @ sk182 @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(func_ext,[status(esa)],[7898]) ).
thf(23186,plain,
( ( ( sk2 @ sk181 @ sk182 )
!= ( sk1 @ sk182 @ x ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,9311]) ).
thf(23226,plain,
( ( ( sk2 @ sk181 @ sk182 )
!= ( sk1 @ sk182 @ x ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[23186]) ).
thf(460,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,37]) ).
thf(461,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(pattern_uni,[status(thm)],[460:[]]) ).
thf(761,plain,
( ( ( sk1 @ sk36 @ x )
!= ( sk1 @ sk35 @ sk36 ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(func_ext,[status(esa)],[461]) ).
thf(18563,plain,
( ( ( sk1 @ sk36 @ x )
!= ( sk1 @ sk35 @ sk36 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,761]) ).
thf(18639,plain,
( ( ( sk1 @ sk36 @ x )
!= ( sk1 @ sk35 @ sk36 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[18563]) ).
thf(20937,plain,
( ( ( sk1 @ sk71 @ y )
!= ( sk1 @ y @ sk70 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,2038]) ).
thf(20963,plain,
( ( ( sk1 @ sk71 @ y )
!= ( sk1 @ y @ sk70 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[20937]) ).
thf(12342,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6976]) ).
thf(12411,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[12342]) ).
thf(463,plain,
! [A: $i > $i > $o] :
( ( sk1
!= ( ^ [B: $i,C: $i] : ( sk1 @ C @ x ) ) )
| ~ ( cS @ A )
| ( A @ y @ x )
| ( ( sk1 @ x @ x )
!= ( A @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[166,4]) ).
thf(512,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ( sk1 @ y @ y ) ),
inference(pre_uni,[status(thm)],[463:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ B @ B ) ))]]) ).
thf(16058,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk20 @ x )
| ( sk1 @ sk19 @ sk20 ) ),
inference(bool_ext,[status(thm)],[456]) ).
thf(16284,plain,
! [A: $i > $i > $o] :
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ~ ( cS @ A )
| ( A @ x @ y )
| ( sk2 @ x @ y )
| ( ( sk1 @ sk20 @ x )
!= ( A @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[16058,65]) ).
thf(16337,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ~ ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y ) ),
inference(pre_uni,[status(thm)],[16284:[bind(A,$thf( ^ [B: $i] : ( sk1 @ sk20 ) ))]]) ).
thf(17232,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( ( cS @ sk115 )
!= ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5864,16337]) ).
thf(17303,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( sk115
!= ( ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(simp,[status(thm)],[17232]) ).
thf(18811,plain,
( ( ( sk115 @ sk323 @ sk324 )
!= ( sk1 @ sk20 @ sk324 ) )
| ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y ) ),
inference(func_ext,[status(esa)],[17303]) ).
thf(19218,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( sk115 @ sk323 @ sk324 )
| ( sk1 @ sk20 @ sk324 ) ),
inference(bool_ext,[status(thm)],[18811]) ).
thf(214,plain,
! [A: $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ y @ B ) )
| ~ ( cS @ A )
| ( A @ y @ x )
| ( ( sk1 @ y @ y )
!= ( A @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,4]) ).
thf(233,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ B ) )
| ( sk1 @ x @ x ) ),
inference(pre_uni,[status(thm)],[214:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ C ) ))]]) ).
thf(16926,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,566]) ).
thf(16927,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) ) ),
inference(pattern_uni,[status(thm)],[16926:[]]) ).
thf(6973,plain,
( ( sk1 @ y @ y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,5040]) ).
thf(7094,plain,
( ( sk1 @ y @ y )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[6973]) ).
thf(12549,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[7094,7869]) ).
thf(12550,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[12549:[]]) ).
thf(7834,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,6738]) ).
thf(7897,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[7834]) ).
thf(12853,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,7897]) ).
thf(12878,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[12853]) ).
thf(570,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,195]) ).
thf(571,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[570:[]]) ).
thf(1361,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk1 != sk1 )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[571]) ).
thf(1370,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(157,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk1 @ x @ x )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,31]) ).
thf(165,plain,
( ( sk1 @ x @ x )
| ~ ( sk1 @ sk6 @ sk5 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(23984,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,12411]) ).
thf(24012,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[23984]) ).
thf(2006,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) ) ),
inference(simp,[status(thm)],[552]) ).
thf(7813,plain,
( ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,2006]) ).
thf(7870,plain,
( ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[7813]) ).
thf(7835,plain,
( ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,2037]) ).
thf(7881,plain,
( ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[7835]) ).
thf(26339,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,26186]) ).
thf(26378,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[26339]) ).
thf(10369,plain,
( ( sk193 @ sk5 @ sk6 )
| ~ ( sk1 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[10262]) ).
thf(7797,plain,
( ~ ( sk1 @ x @ x )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,37]) ).
thf(7864,plain,
( ~ ( sk1 @ x @ x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[7797]) ).
thf(17405,plain,
( ( sk20 != sk19 )
| ( sk20 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[16056,7864]) ).
thf(17406,plain,
( ( sk20 != sk19 )
| ( sk20 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[17405:[]]) ).
thf(10758,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( ( cS @ sk193 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[10370,54]) ).
thf(10907,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk193
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[10758]) ).
thf(210,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk1 @ y @ y )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,32]) ).
thf(224,plain,
( ( sk1 @ y @ y )
| ~ ( sk1 @ sk6 @ sk5 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(92,plain,
( ( sk5 != x )
| ( sk6 != y )
| ( sk8 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[85]) ).
thf(207,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,142]) ).
thf(229,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( sk6 != y )
| ( sk5 != y ) ),
inference(simp,[status(thm)],[207]) ).
thf(346,plain,
( ~ ( sk1 @ sk4 @ sk3 )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,74]) ).
thf(361,plain,
( ~ ( sk1 @ sk4 @ sk3 )
| ( sk3 != y )
| ( sk4 != x ) ),
inference(simp,[status(thm)],[346]) ).
thf(13281,plain,
( ( sk140 != y )
| ( sk141 != x )
| ( sk1 @ sk140 @ sk141 )
| ( ( sk2 @ sk140 @ sk141 )
!= ( sk2 @ sk140 @ sk141 ) ) ),
inference(paramod_ordered,[status(thm)],[10181,7928]) ).
thf(13282,plain,
( ( sk140 != y )
| ( sk141 != x )
| ( sk1 @ sk140 @ sk141 ) ),
inference(pattern_uni,[status(thm)],[13281:[]]) ).
thf(574,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( sk1
!= ( ^ [B: $i,C: $i] : ( sk1 @ x @ B ) ) )
| ( ( A @ y @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[4,195]) ).
thf(578,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ B ) )
| ~ ( sk1 @ y @ y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pre_uni,[status(thm)],[574:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ C ) ))]]) ).
thf(7848,plain,
( ( sk1 @ y @ y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,5040]) ).
thf(7917,plain,
( ( sk1 @ y @ y )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[7848]) ).
thf(15815,plain,
( ( sk18 != sk17 )
| ( sk18 != y )
| ~ ( sk1 @ y @ y ) ),
inference(simp,[status(thm)],[381]) ).
thf(16162,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk18 != sk17 )
| ( sk18 != y )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,15815]) ).
thf(16163,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk18 != sk17 )
| ( sk18 != y ) ),
inference(pattern_uni,[status(thm)],[16162:[]]) ).
thf(7569,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,6738]) ).
thf(7610,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[7569]) ).
thf(21583,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,7592]) ).
thf(21616,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[21583]) ).
thf(32331,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[21616]) ).
thf(32332,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[32331]) ).
thf(16948,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,566]) ).
thf(16949,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) ) ),
inference(pattern_uni,[status(thm)],[16948:[]]) ).
thf(98,plain,
( ~ ( sk1 @ y @ y )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,36]) ).
thf(109,plain,
( ~ ( sk1 @ y @ y )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(19070,plain,
( ( sk63 != y )
| ( sk64 != sk63 )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[18992]) ).
thf(4947,plain,
! [A: $i > $i > $o] :
( ~ ( A @ y @ x )
| ( A @ x @ y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [B: $i,C: $i] :
~ ( A @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,51]) ).
thf(5031,plain,
! [A: $i > $i > $o] :
( ( A @ x @ y )
| ~ ( A @ y @ x )
| ( sk1
!= ( ^ [B: $i,C: $i] :
~ ( A @ B @ C ) ) ) ),
inference(simp,[status(thm)],[4947]) ).
thf(17717,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,724]) ).
thf(17883,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[17717]) ).
thf(8894,plain,
( ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) )
| ~ ( sk1 @ x @ x ) ),
inference(func_ext,[status(esa)],[7864]) ).
thf(22273,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,8894]) ).
thf(22274,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) ) ),
inference(pattern_uni,[status(thm)],[22273:[]]) ).
thf(7794,plain,
! [A: $i > $i > $o] :
( ( A @ y @ x )
| ~ ( A @ x @ y )
| ( ( cS @ sk2 )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7790,42]) ).
thf(7795,plain,
( ( sk2 @ y @ x )
| ~ ( sk2 @ x @ y ) ),
inference(pattern_uni,[status(thm)],[7794:[bind(A,$thf( sk2 ))]]) ).
thf(17208,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ~ ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) )
| ( sk1 @ sk20 @ y )
| ( sk2 @ y @ x )
| ( ( sk2 @ x @ y )
!= ( sk2 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[16337,7795]) ).
thf(17209,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ~ ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) )
| ( sk1 @ sk20 @ y )
| ( sk2 @ y @ x ) ),
inference(pattern_uni,[status(thm)],[17208:[]]) ).
thf(26455,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ y @ x )
| ( ( cS @ sk115 )
!= ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5864,17209]) ).
thf(26539,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ y @ x )
| ( sk115
!= ( ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(simp,[status(thm)],[26455]) ).
thf(27177,plain,
( ( ( sk115 @ sk420 @ sk421 )
!= ( sk1 @ sk20 @ sk421 ) )
| ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ y @ x ) ),
inference(func_ext,[status(esa)],[26539]) ).
thf(27874,plain,
( ( sk1 @ sk106 @ sk107 )
| ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ y @ x )
| ( sk115 @ sk420 @ sk421 )
| ( sk1 @ sk20 @ sk421 ) ),
inference(bool_ext,[status(thm)],[27177]) ).
thf(7927,plain,
( ( sk2 @ sk138 @ sk139 )
!= ( sk1 @ sk139 @ sk138 ) ),
inference(func_ext,[status(esa)],[7899]) ).
thf(7930,plain,
( ( sk2 @ sk138 @ sk139 )
| ( sk1 @ sk139 @ sk138 ) ),
inference(bool_ext,[status(thm)],[7927]) ).
thf(7814,plain,
( ( sk1 @ y @ y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,32]) ).
thf(7895,plain,
( ( sk1 @ y @ y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[7814]) ).
thf(84,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ! [B: $i > $i > $o] :
( ( ( cS @ B )
& ( B @ sk5 @ sk6 ) )
=> ( B @ sk6 @ sk5 ) )
| ( ( A @ y @ x )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4,72]) ).
thf(86,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ sk6 @ sk5 ) )
| ~ ( sk1 @ sk6 @ sk5 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[84:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ sk6 @ sk5 ) ))]]) ).
thf(96,plain,
( ( cS @ sk9 )
| ~ ( sk1 @ sk6 @ sk5 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ sk6 @ sk5 ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(22162,plain,
( ( ( sk2 @ sk161 @ sk162 )
!= ( sk1 @ y @ sk161 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,8842]) ).
thf(22181,plain,
( ( ( sk2 @ sk161 @ sk162 )
!= ( sk1 @ y @ sk161 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[22162]) ).
thf(18860,plain,
( ( ( sk1 @ sk39 @ sk40 )
!= ( sk1 @ x @ sk39 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,787]) ).
thf(18917,plain,
( ( ( sk1 @ sk39 @ sk40 )
!= ( sk1 @ x @ sk39 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[18860]) ).
thf(12298,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,6976]) ).
thf(12408,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[12298]) ).
thf(7825,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,552]) ).
thf(7878,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[7825]) ).
thf(161,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( sk1 @ x @ x )
| ( ( A @ y @ x )
!= ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ C @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,31]) ).
thf(173,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
( cS
@ ^ [C: $i,D: $i] : ( sk1 @ D @ B ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk1 @ x @ x ) ),
inference(pre_uni,[status(thm)],[161:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( cS @ ^ [D: $i] : ^ [E: $i] : ( sk1 @ E @ C ) ) ))]]) ).
thf(10206,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,142]) ).
thf(10207,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[10206:[]]) ).
thf(1384,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk1 != sk1 )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[602]) ).
thf(1393,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(162,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,68]) ).
thf(176,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( sk1 @ sk3 @ sk4 )
| ( sk4 != x )
| ( sk3 != x ) ),
inference(simp,[status(thm)],[162]) ).
thf(22886,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk4 != x )
| ( sk3 != x )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,176]) ).
thf(22981,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk4 != x )
| ( sk3 != x )
| ( sk3 != x )
| ( sk4 != x ) ),
inference(simp,[status(thm)],[22886]) ).
thf(23000,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk4 != x )
| ( sk3 != x ) ),
inference(simp,[status(thm)],[22981]) ).
thf(24048,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,23000]) ).
thf(24084,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[24048]) ).
thf(20964,plain,
( ( sk71 != y )
| ( sk70 != y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[20937]) ).
thf(18640,plain,
( ( sk36 != sk35 )
| ( sk36 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[18563]) ).
thf(118,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[75,72]) ).
thf(121,plain,
( ( sk1 @ sk3 @ sk4 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk5 @ sk6 ) )
=> ( A @ sk6 @ sk5 ) )
| ( sk6 != sk4 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[118]) ).
thf(128,plain,
( ( sk5 != sk3 )
| ( sk6 != sk4 )
| ( cS @ sk10 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[121]) ).
thf(18958,plain,
( ( ( sk1 @ sk39 @ sk40 )
!= ( sk1 @ x @ sk39 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[18823]) ).
thf(19331,plain,
( ( sk28 != y )
| ( sk29 != sk28 )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[17570,111]) ).
thf(19332,plain,
( ( sk28 != y )
| ( sk29 != sk28 )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[19331:[]]) ).
thf(2043,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,725]) ).
thf(2057,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[2043]) ).
thf(1616,plain,
( ~ ( sk1 @ y @ y )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) ) ),
inference(pre_uni,[status(thm)],[1466:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ y ) ))]]) ).
thf(33936,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,33663]) ).
thf(33952,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[33936]) ).
thf(17425,plain,
( ( sk20 != sk19 )
| ( sk20 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[16056,195]) ).
thf(17426,plain,
( ( sk20 != sk19 )
| ( sk20 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[17425:[]]) ).
thf(19510,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,1616]) ).
thf(19511,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) ) ),
inference(pattern_uni,[status(thm)],[19510:[]]) ).
thf(23413,plain,
( ( ( sk2 @ sk187 @ sk188 )
!= ( sk1 @ x @ sk187 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,9557]) ).
thf(23489,plain,
( ( ( sk2 @ sk187 @ sk188 )
!= ( sk1 @ x @ sk187 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[23413]) ).
thf(22554,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,9163]) ).
thf(22555,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( sk2 @ sk165 @ sk166 )
!= ( sk1 @ sk166 @ y ) ) ),
inference(pattern_uni,[status(thm)],[22554:[]]) ).
thf(11836,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[6887,7864]) ).
thf(11837,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[11836:[]]) ).
thf(7792,plain,
( ( sk1 @ x @ x )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,31]) ).
thf(7884,plain,
( ( sk1 @ x @ x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[7792]) ).
thf(9254,plain,
( ( ( sk2 @ sk167 @ sk168 )
!= ( sk1 @ sk168 @ x ) )
| ( sk1 @ x @ x ) ),
inference(func_ext,[status(esa)],[7884]) ).
thf(22686,plain,
( ( sk1 @ x @ x )
| ( sk2 @ sk167 @ sk168 )
| ( sk1 @ sk168 @ x ) ),
inference(bool_ext,[status(thm)],[9254]) ).
thf(76,plain,
( ~ ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,68]) ).
thf(79,plain,
( ~ ( sk1 @ sk3 @ sk4 )
| ( sk4 != y )
| ( sk3 != x ) ),
inference(simp,[status(thm)],[76]) ).
thf(1731,plain,
( ( sk4 != y )
| ( sk3 != x )
| ( ( sk1 @ sk3 @ sk4 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,79]) ).
thf(1747,plain,
( ( sk4 != y )
| ( sk3 != x )
| ( sk3 != y )
| ( sk4 != x ) ),
inference(simp,[status(thm)],[1731]) ).
thf(9180,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[5040,7869]) ).
thf(9181,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pattern_uni,[status(thm)],[9180:[]]) ).
thf(2012,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,552]) ).
thf(2028,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[2012]) ).
thf(17,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( B @ x @ y )
| ( B @ y @ x )
| ( ( A @ y @ x )
!= ( cS @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4,4]) ).
thf(34,plain,
! [A: $i > $i > $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] : ( cS @ ( A @ B @ C ) ) )
| ~ ( cS @ ( A @ x @ y ) )
| ~ ( A @ y @ x @ x @ y )
| ( A @ y @ x @ y @ x ) ),
inference(pre_uni,[status(thm)],[17:[bind(A,$thf( ^ [D: $i] : ^ [E: $i] : ( cS @ ( C @ D @ E ) ) )),bind(B,$thf( C @ y @ x ))]]) ).
thf(44,plain,
! [A: $i > $i > $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] : ( cS @ ( A @ B @ C ) ) )
| ~ ( cS @ ( A @ x @ y ) )
| ~ ( A @ y @ x @ x @ y )
| ( A @ y @ x @ y @ x ) ),
inference(simp,[status(thm)],[34]) ).
thf(6161,plain,
( ( sk107 != sk106 )
| ( ( sk1 @ sk106 @ sk107 )
!= ( sk1 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[6153,5]) ).
thf(6229,plain,
( ( sk107 != sk106 )
| ( sk106 != x )
| ( sk107 != y ) ),
inference(simp,[status(thm)],[6161]) ).
thf(190,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( sk1 @ x @ x )
| ( ( A @ y @ x )
!= ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ x @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,37]) ).
thf(204,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
( cS
@ ^ [C: $i,D: $i] : ( sk1 @ B @ C ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ~ ( sk1 @ x @ x ) ),
inference(pre_uni,[status(thm)],[190:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( cS @ ^ [D: $i] : ^ [E: $i] : ( sk1 @ C @ D ) ) ))]]) ).
thf(9310,plain,
( ( ( sk2 @ sk179 @ sk180 )
!= ( sk1 @ y @ sk179 ) )
| ( sk1 @ y @ y ) ),
inference(func_ext,[status(esa)],[7895]) ).
thf(23110,plain,
( ( sk1 @ y @ y )
| ( sk2 @ sk179 @ sk180 )
| ( sk1 @ y @ sk179 ) ),
inference(bool_ext,[status(thm)],[9310]) ).
thf(17197,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,16337]) ).
thf(17241,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( sk2
!= ( ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(simp,[status(thm)],[17197]) ).
thf(133,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ( sk1 @ y @ y )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,36]) ).
thf(144,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ( sk1 @ y @ y )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(19029,plain,
( ( ( sk1 @ sk63 @ sk64 )
!= ( sk1 @ y @ sk63 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,1408]) ).
thf(19112,plain,
( ( sk63 != y )
| ( sk64 != sk63 )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[19029]) ).
thf(24,plain,
! [A: $i > $i > $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] : ( cS @ ( A @ B @ C ) ) )
| ~ ( cS @ ( A @ x @ y ) )
| ( cS @ ( A @ y @ x ) ) ),
inference(prim_subst,[status(thm)],[4:[bind(A,$thf( ^ [C: $i] : ^ [D: $i] : ( cS @ ( B @ C @ D ) ) ))]]) ).
thf(49,plain,
! [A: $i > $i > $i > $i > $o] :
( ~ ( cS
@ ^ [B: $i,C: $i] : ( cS @ ( A @ B @ C ) ) )
| ~ ( cS @ ( A @ x @ y ) )
| ( cS @ ( A @ y @ x ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(5906,plain,
( ( cS @ sk115 )
| ( ( sk1 @ sk106 @ sk107 )
!= ( sk1 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[5864,5]) ).
thf(5997,plain,
( ( cS @ sk115 )
| ( sk106 != x )
| ( sk107 != y ) ),
inference(simp,[status(thm)],[5906]) ).
thf(10211,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[8673,5]) ).
thf(10348,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk6 != x )
| ( sk5 != y ) ),
inference(simp,[status(thm)],[10211]) ).
thf(13356,plain,
( ( sk6 != x )
| ( sk5 != y )
| ( ( sk1 @ sk5 @ sk6 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,10348]) ).
thf(13377,plain,
( ( sk6 != x )
| ( sk5 != y )
| ( sk5 != y )
| ( sk6 != x ) ),
inference(simp,[status(thm)],[13356]) ).
thf(13407,plain,
( ( sk6 != x )
| ( sk5 != y ) ),
inference(simp,[status(thm)],[13377]) ).
thf(18373,plain,
( ( ( sk1 @ sk34 @ y )
!= ( sk1 @ sk33 @ sk34 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,736]) ).
thf(18516,plain,
( ( sk34 != sk33 )
| ( sk34 != y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[18373]) ).
thf(18817,plain,
( ( sk39 != x )
| ( sk40 != sk39 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(simp,[status(thm)],[787]) ).
thf(6156,plain,
( ( sk107 != sk106 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( ( sk1 @ sk106 @ sk107 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[6153,142]) ).
thf(6196,plain,
( ( sk107 != sk106 )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( sk106 != sk6 )
| ( sk107 != sk5 ) ),
inference(simp,[status(thm)],[6156]) ).
thf(23444,plain,
( ( ( sk2 @ sk187 @ sk188 )
!= ( sk1 @ x @ sk187 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,9557]) ).
thf(23477,plain,
( ( ( sk2 @ sk187 @ sk188 )
!= ( sk1 @ x @ sk187 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[23444]) ).
thf(6268,plain,
( ( sk106 != x )
| ( sk107 != y )
| ( ( cS @ sk115 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5997,5350]) ).
thf(6308,plain,
( ( sk106 != x )
| ( sk107 != y )
| ( sk115
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[6268]) ).
thf(4139,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk7 @ sk11 @ sk12 )
| ( sk1 @ sk12 @ sk11 ) ),
inference(bool_ext,[status(thm)],[147]) ).
thf(737,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,383]) ).
thf(758,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[737]) ).
thf(91,plain,
( ( sk5 != x )
| ( sk6 != y )
| ~ ( sk8 @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[85]) ).
thf(17765,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,724]) ).
thf(17914,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[17765]) ).
thf(762,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,461]) ).
thf(769,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[762]) ).
thf(10380,plain,
( ( ( sk7 @ sk194 @ sk195 )
!= ( sk1 @ sk195 @ sk194 ) )
| ~ ( sk1 @ sk5 @ sk6 ) ),
inference(func_ext,[status(esa)],[10207]) ).
thf(102,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ C @ y ) )
| ( ( A @ y @ x )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[4,36]) ).
thf(108,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( sk1 @ x @ x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pre_uni,[status(thm)],[102:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ B @ B ) ))]]) ).
thf(7833,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,6738]) ).
thf(7901,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[7833]) ).
thf(17956,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk24 != x )
| ( sk25 != sk24 )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,16903]) ).
thf(17957,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk24 != x )
| ( sk25 != sk24 ) ),
inference(pattern_uni,[status(thm)],[17956:[]]) ).
thf(20892,plain,
( ( sk71 != y )
| ( sk70 != y )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(simp,[status(thm)],[2038]) ).
thf(22252,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,8894]) ).
thf(22253,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) ) ),
inference(pattern_uni,[status(thm)],[22252:[]]) ).
thf(66,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ y @ x )
| ( A @ x @ y )
| ~ ( sk2 @ y @ x ) ),
inference(cnf,[status(esa)],[61]) ).
thf(16550,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,551]) ).
thf(16731,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[16550]) ).
thf(5354,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,5350]) ).
thf(5377,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ( sk7
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5354]) ).
thf(10274,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk6 != sk5 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,422]) ).
thf(10275,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk6 != sk5 ) ),
inference(pattern_uni,[status(thm)],[10274:[]]) ).
thf(386,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( sk1
!= ( ^ [B: $i,C: $i] : ( sk1 @ C @ y ) ) )
| ( ( A @ y @ x )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[4,111]) ).
thf(394,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( sk1 @ x @ x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(pre_uni,[status(thm)],[386:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ B @ B ) ))]]) ).
thf(134,plain,
! [A: $i > $i > $o] :
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ( A @ x @ y )
| ( A @ y @ x )
| ( ( cS @ sk7 )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[89,4]) ).
thf(135,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ( sk7 @ x @ y )
| ( sk7 @ y @ x ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( sk7 ))]]) ).
thf(10930,plain,
( ( ( sk193 @ sk200 @ sk201 )
!= ( sk1 @ sk201 @ sk200 ) )
| ~ ( sk1 @ sk5 @ sk6 ) ),
inference(func_ext,[status(esa)],[10907]) ).
thf(9313,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,7898]) ).
thf(9345,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[9313]) ).
thf(12432,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,6988]) ).
thf(12482,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[12432]) ).
thf(7791,plain,
( ( sk77 != y )
| ( sk78 != y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,2090]) ).
thf(7916,plain,
( ( sk77 != y )
| ( sk78 != y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[7791]) ).
thf(73,plain,
( ( sk4 != sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[68]) ).
thf(80,plain,
sk4 != sk3,
inference(simp,[status(thm)],[73]) ).
thf(18598,plain,
( ( ( sk1 @ sk36 @ x )
!= ( sk1 @ sk35 @ sk36 ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,761]) ).
thf(18715,plain,
( ( ( sk1 @ sk36 @ x )
!= ( sk1 @ sk35 @ sk36 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[18598]) ).
thf(16169,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk18 != sk17 )
| ( sk18 != y )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,15815]) ).
thf(16170,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk18 != sk17 )
| ( sk18 != y ) ),
inference(pattern_uni,[status(thm)],[16169:[]]) ).
thf(132,plain,
( ( cS @ sk7 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,89]) ).
thf(143,plain,
( ( cS @ sk7 )
| ( sk6 != y )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[132]) ).
thf(5359,plain,
( ( sk6 != y )
| ( sk5 != x )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[143,5350]) ).
thf(5372,plain,
( ( sk6 != y )
| ( sk5 != x )
| ( sk7
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[5359]) ).
thf(7827,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,213]) ).
thf(7896,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[7827]) ).
thf(9264,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7896]) ).
thf(9294,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[9264]) ).
thf(7929,plain,
( ~ ( sk2 @ sk138 @ sk139 )
| ~ ( sk1 @ sk139 @ sk138 ) ),
inference(bool_ext,[status(thm)],[7927]) ).
thf(20701,plain,
( ( ( sk1 @ sk69 @ x )
!= ( sk1 @ x @ sk68 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,2007]) ).
thf(20815,plain,
( ( sk69 != x )
| ( sk68 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[20701]) ).
thf(215,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( sk1 @ y @ y )
| ( ( A @ y @ x )
!= ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,32]) ).
thf(226,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
( cS
@ ^ [C: $i,D: $i] : ( sk1 @ A @ C ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( sk1 @ y @ y ) ),
inference(pre_uni,[status(thm)],[215:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( cS @ ^ [D: $i] : ^ [E: $i] : ( sk1 @ B @ D ) ) ))]]) ).
thf(2039,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,725]) ).
thf(2054,plain,
( ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[2039]) ).
thf(18918,plain,
( ( sk39 != x )
| ( sk40 != sk39 )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[18860]) ).
thf(9259,plain,
( ( ( sk2 @ sk177 @ sk178 )
!= ( sk1 @ sk178 @ y ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(func_ext,[status(esa)],[7896]) ).
thf(14496,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,13158]) ).
thf(14530,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[14496]) ).
thf(8847,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7860]) ).
thf(8885,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[8847]) ).
thf(2070,plain,
( ( sk73 != x )
| ( sk74 != x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(func_ext,[status(esa)],[2006]) ).
thf(4318,plain,
( ( sk73 != x )
| ( sk74 != x )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,2070]) ).
thf(4336,plain,
( ( sk73 != x )
| ( sk74 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[4318]) ).
thf(185,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ( sk1 @ x @ x )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,37]) ).
thf(194,plain,
( ~ ( sk1 @ sk6 @ sk5 )
| ~ ( sk1 @ x @ x )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(2098,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( ^ [B: $i,C: $i] : C )
!= ( ^ [B: $i,C: $i] : y ) )
| ( ( ^ [B: $i,C: $i] : y )
!= ( ^ [B: $i,C: $i] : B ) )
| ( ( A @ y @ x )
!= ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,2037]) ).
thf(2107,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
( cS
@ ^ [C: $i,D: $i] : ( sk1 @ A @ C ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
| ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) ) ),
inference(pre_uni,[status(thm)],[2098:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( cS @ ^ [D: $i] : ^ [E: $i] : ( sk1 @ B @ D ) ) ))]]) ).
thf(6416,plain,
! [A: $i > $i > $o] :
( ( sk1 @ sk106 @ sk107 )
| ~ ( A @ y @ x )
| ( A @ x @ y )
| ( sk2 @ x @ y )
| ( ( cS @ sk115 )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5864,65]) ).
thf(6417,plain,
( ( sk1 @ sk106 @ sk107 )
| ~ ( sk115 @ y @ x )
| ( sk115 @ x @ y )
| ( sk2 @ x @ y ) ),
inference(pattern_uni,[status(thm)],[6416:[bind(A,$thf( sk115 ))]]) ).
thf(14578,plain,
( ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( ( cS @ sk7 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[14457,5350]) ).
thf(14703,plain,
( ( sk6 != sk4 )
| ( sk5 != sk3 )
| ( sk7
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(simp,[status(thm)],[14578]) ).
thf(4706,plain,
( ~ ( sk1 @ x @ x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,108]) ).
thf(4813,plain,
( ~ ( sk1 @ x @ x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ A @ A ) ) ) ),
inference(simp,[status(thm)],[4706]) ).
thf(10222,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( ( sk7 @ sk11 @ sk12 )
!= ( sk1 @ sk12 @ sk11 ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,147]) ).
thf(10223,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( ( sk7 @ sk11 @ sk12 )
!= ( sk1 @ sk12 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[10222:[]]) ).
thf(10248,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk7
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,5377]) ).
thf(10249,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk7
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[10248:[]]) ).
thf(1409,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,610]) ).
thf(1420,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(27001,plain,
( ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,16949]) ).
thf(27072,plain,
( ( ( sk1 @ sk24 @ sk25 )
!= ( sk1 @ x @ sk24 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[27001]) ).
thf(22,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( cS
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
| ~ ( ( A @ x @ y )
| ( B @ x @ y ) )
| ( A @ y @ x )
| ( B @ y @ x ) ),
inference(prim_subst,[status(thm)],[4:[bind(A,$thf( ^ [D: $i] : ^ [E: $i] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).
thf(46,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ y @ x )
| ( B @ y @ x )
| ~ ( B @ x @ y )
| ~ ( cS
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(48,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ y @ x )
| ( B @ y @ x )
| ~ ( B @ x @ y )
| ~ ( cS
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(541,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,189]) ).
thf(557,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(13272,plain,
( ( sk140 != y )
| ( sk141 != x )
| ( sk2 @ x @ y )
| ( ( sk2 @ sk140 @ sk141 )
!= ( sk2 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[10181,7922]) ).
thf(13304,plain,
( ( sk2 @ x @ y )
| ( sk140 != y )
| ( sk141 != x )
| ( sk140 != y )
| ( sk141 != x ) ),
inference(simp,[status(thm)],[13272]) ).
thf(13320,plain,
( ( sk2 @ x @ y )
| ( sk140 != y )
| ( sk141 != x ) ),
inference(simp,[status(thm)],[13304]) ).
thf(15550,plain,
( ( sk140 != y )
| ( sk141 != x )
| ( sk2 @ y @ x )
| ( ( sk2 @ x @ y )
!= ( sk2 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[13320,7795]) ).
thf(15551,plain,
( ( sk140 != y )
| ( sk141 != x )
| ( sk2 @ y @ x ) ),
inference(pattern_uni,[status(thm)],[15550:[]]) ).
thf(18986,plain,
( ( sk63 != y )
| ( sk64 != sk63 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(simp,[status(thm)],[1408]) ).
thf(95,plain,
( ( sk9 @ sk5 @ sk6 )
| ~ ( sk1 @ sk6 @ sk5 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ sk6 @ sk5 ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(19319,plain,
( ( sk28 != y )
| ( sk29 != sk28 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[17570,36]) ).
thf(19320,plain,
( ( sk28 != y )
| ( sk29 != sk28 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pattern_uni,[status(thm)],[19319:[]]) ).
thf(19837,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,1617]) ).
thf(19838,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) ) ),
inference(pattern_uni,[status(thm)],[19837:[]]) ).
thf(19530,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) )
| ( ( sk1 @ y @ y )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[223,1616]) ).
thf(19531,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) ) ),
inference(pattern_uni,[status(thm)],[19530:[]]) ).
thf(13182,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,9181]) ).
thf(13229,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[13182]) ).
thf(23037,plain,
( ( ( sk2 @ sk177 @ sk178 )
!= ( sk1 @ sk178 @ y ) )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,9259]) ).
thf(23052,plain,
( ( ( sk2 @ sk177 @ sk178 )
!= ( sk1 @ sk178 @ y ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[23037]) ).
thf(9626,plain,
( ~ ( sk2 @ sk138 @ sk139 )
| ( ( sk1 @ sk139 @ sk138 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,7929]) ).
thf(9664,plain,
( ~ ( sk2 @ sk138 @ sk139 )
| ( sk139 != y )
| ( sk138 != x ) ),
inference(simp,[status(thm)],[9626]) ).
thf(13245,plain,
( ( sk1 @ sk139 @ sk138 )
| ( sk139 != y )
| ( sk138 != x )
| ( ( sk2 @ sk138 @ sk139 )
!= ( sk2 @ sk138 @ sk139 ) ) ),
inference(paramod_ordered,[status(thm)],[7930,9664]) ).
thf(13246,plain,
( ( sk1 @ sk139 @ sk138 )
| ( sk139 != y )
| ( sk138 != x ) ),
inference(pattern_uni,[status(thm)],[13245:[]]) ).
thf(182,plain,
( ( sk5 != x )
| ( sk6 != x )
| ~ ( sk13 @ sk6 @ sk5 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(8844,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,7860]) ).
thf(8873,plain,
( ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[8844]) ).
thf(127,plain,
( ( sk5 != sk3 )
| ( sk6 != sk4 )
| ( sk10 @ sk5 @ sk6 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[121]) ).
thf(7856,plain,
( ( sk73 != x )
| ( sk74 != x )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,2070]) ).
thf(7876,plain,
( ( sk73 != x )
| ( sk74 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[7856]) ).
thf(7812,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,610]) ).
thf(7919,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[7812]) ).
thf(9,plain,
( ( sk1 @ y @ x )
!= ( sk1 @ x @ y ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(10,plain,
( ( y != x )
| ( y != x ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
y != x,
inference(simp,[status(thm)],[10]) ).
thf(155,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,142]) ).
thf(175,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( sk6 != x )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[155]) ).
thf(1372,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(21,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( A @ y @ x )
!= ( ~ ( A @ x @ y ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4]) ).
thf(43,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( A @ y @ x )
!= ( ~ ( A @ x @ y ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(2078,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ( ( ^ [B: $i,C: $i] : x )
!= ( ^ [B: $i,C: $i] : C ) )
| ( ( ^ [B: $i,C: $i] : B )
!= ( ^ [B: $i,C: $i] : x ) )
| ( ( A @ y @ x )
!= ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ C @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,2006]) ).
thf(2088,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
( cS
@ ^ [C: $i,D: $i] : ( sk1 @ D @ B ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) ) ),
inference(pre_uni,[status(thm)],[2078:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( cS @ ^ [D: $i] : ^ [E: $i] : ( sk1 @ E @ C ) ) ))]]) ).
thf(17132,plain,
( ( sk18 != sk17 )
| ( sk18 != y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,16163]) ).
thf(17155,plain,
( ( sk18 != sk17 )
| ( sk18 != y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[17132]) ).
thf(7807,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,461]) ).
thf(7889,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[7807]) ).
thf(101,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( sk1 @ y @ y )
| ( ( A @ y @ x )
!= ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ C @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,36]) ).
thf(104,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
( cS
@ ^ [C: $i,D: $i] : ( sk1 @ D @ A ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( sk1 @ y @ y ) ),
inference(pre_uni,[status(thm)],[101:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( cS @ ^ [D: $i] : ^ [E: $i] : ( sk1 @ E @ B ) ) ))]]) ).
thf(20814,plain,
( ( ( sk1 @ sk69 @ x )
!= ( sk1 @ x @ sk68 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[20701]) ).
thf(7953,plain,
( ~ ( sk2 @ sk140 @ sk141 )
| ~ ~ ( sk1 @ sk140 @ sk141 ) ),
inference(bool_ext,[status(thm)],[7928]) ).
thf(7974,plain,
( ( sk1 @ sk140 @ sk141 )
| ~ ( sk2 @ sk140 @ sk141 ) ),
inference(cnf,[status(esa)],[7953]) ).
thf(19111,plain,
( ( ( sk1 @ sk63 @ sk64 )
!= ( sk1 @ y @ sk63 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[19029]) ).
thf(4677,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,108]) ).
thf(4678,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pattern_uni,[status(thm)],[4677:[]]) ).
thf(17231,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,16337]) ).
thf(17316,plain,
( ( sk1 @ x @ x )
| ( sk1 @ sk19 @ sk20 )
| ( sk1 @ sk20 @ y )
| ( sk2 @ x @ y )
| ( sk1
!= ( ^ [A: $i] : ( sk1 @ sk20 ) ) ) ),
inference(simp,[status(thm)],[17231]) ).
thf(23007,plain,
( ( ( sk2 @ sk177 @ sk178 )
!= ( sk1 @ sk178 @ y ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,9259]) ).
thf(23089,plain,
( ( ( sk2 @ sk177 @ sk178 )
!= ( sk1 @ sk178 @ y ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[23007]) ).
thf(18,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( cS @ B )
| ( B @ y @ x )
| ( ( A @ y @ x )
!= ( B @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[4,4]) ).
thf(39,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( cS @ B )
| ( B @ y @ x )
| ( ( A @ y @ x )
!= ( B @ x @ y ) ) ),
inference(pre_uni,[status(thm)],[18:[]]) ).
thf(40,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( B @ y @ x )
| ~ ( cS @ B )
| ~ ( A @ x @ y )
| ~ ( cS @ A )
| ( ( A @ y @ x )
!= ( B @ x @ y ) ) ),
inference(pre_uni,[status(thm)],[39:[]]) ).
thf(8036,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ sk5 @ sk6 )
| ( sk1 @ sk6 @ sk5 )
| ~ ! [B: $i > $i > $o] :
( ( ( cS @ B )
& ( B @ sk106 @ sk107 ) )
=> ( B @ sk107 @ sk106 ) )
| ( ( A @ sk6 @ sk5 )
!= ( ~ ( sk1 @ sk106 @ sk107 ) ) ) ),
inference(paramod_ordered,[status(thm)],[90,5383]) ).
thf(8425,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ sk106 @ sk107 ) )
| ~ ~ ( sk1 @ sk106 @ sk107 )
| ( sk1 @ sk6 @ sk5 )
| ~ ! [A: $i > $i > $o] :
( ( ( cS @ A )
& ( A @ sk106 @ sk107 ) )
=> ( A @ sk107 @ sk106 ) ) ),
inference(pre_uni,[status(thm)],[8036:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ~ ( sk1 @ sk106 @ sk107 ) ))]]) ).
thf(8634,plain,
( ( cS @ sk154 )
| ( sk1 @ sk6 @ sk5 )
| ( sk1 @ sk106 @ sk107 )
| ~ ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ sk106 @ sk107 ) ) ),
inference(cnf,[status(esa)],[8425]) ).
thf(156,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( cS @ sk7 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[31,89]) ).
thf(171,plain,
( ( cS @ sk7 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( sk6 != x )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[156]) ).
thf(406,plain,
( ( sk7 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,88]) ).
thf(418,plain,
( ( sk7 @ sk5 @ sk6 )
| ( sk6 != y )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[406]) ).
thf(20802,plain,
( ( ( sk1 @ sk69 @ x )
!= ( sk1 @ x @ sk68 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[20739]) ).
thf(10209,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk7 @ sk5 @ sk6 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ sk6 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[8673,88]) ).
thf(10210,plain,
( ~ ( sk1 @ sk5 @ sk6 )
| ( sk7 @ sk5 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[10209:[]]) ).
thf(21565,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,7592]) ).
thf(21618,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ A @ x ) ) ) ),
inference(simp,[status(thm)],[21565]) ).
thf(235,plain,
( ( sk5 != y )
| ( sk6 != y )
| ( sk14 @ sk5 @ sk6 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ),
inference(cnf,[status(esa)],[219]) ).
thf(33917,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,33663]) ).
thf(33943,plain,
( ( sk4 != y )
| ( sk3 != y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[33917]) ).
thf(18515,plain,
( ( ( sk1 @ sk34 @ y )
!= ( sk1 @ sk33 @ sk34 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[18373]) ).
thf(2008,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,552]) ).
thf(2036,plain,
( ( ( ^ [A: $i,B: $i] : x )
!= ( ^ [A: $i,B: $i] : B ) )
| ( ( ^ [A: $i,B: $i] : A )
!= ( ^ [A: $i,B: $i] : x ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[2008]) ).
thf(788,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,562]) ).
thf(800,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[788]) ).
thf(18491,plain,
( ( ( sk1 @ sk34 @ y )
!= ( sk1 @ sk33 @ sk34 ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[18408]) ).
thf(148,plain,
( ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7,142]) ).
thf(151,plain,
( ( sk7
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) )
| ( sk6 != y )
| ( sk5 != x ) ),
inference(simp,[status(thm)],[148]) ).
thf(4686,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[166,108]) ).
thf(4687,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ),
inference(pattern_uni,[status(thm)],[4686:[]]) ).
thf(18555,plain,
( ( sk36 != sk35 )
| ( sk36 != x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(simp,[status(thm)],[761]) ).
thf(30302,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,19511]) ).
thf(30445,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( sk1 @ y @ y ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[30302]) ).
thf(183,plain,
( ( sk5 != x )
| ( sk6 != x )
| ( sk13 @ sk5 @ sk6 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(23156,plain,
( ( ( sk2 @ sk181 @ sk182 )
!= ( sk1 @ sk182 @ x ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,9311]) ).
thf(23247,plain,
( ( ( sk2 @ sk181 @ sk182 )
!= ( sk1 @ sk182 @ x ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[23156]) ).
thf(34443,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[24012]) ).
thf(34444,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) ) ),
inference(simp,[status(thm)],[34443]) ).
thf(300,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) )
| ( ( sk1 @ x @ x )
!= ( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ) ),
inference(pre_uni,[status(thm)],[255:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ x ) ))]]) ).
thf(31174,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,19872]) ).
thf(31399,plain,
( ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) )
!= ( sk1 @ x @ x ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[31174]) ).
thf(1395,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) )
| ( ( ^ [A: $i,B: $i] : B )
!= ( ^ [A: $i,B: $i] : y ) )
| ( ( ^ [A: $i,B: $i] : y )
!= ( ^ [A: $i,B: $i] : A ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(33278,plain,
( ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,22274]) ).
thf(33347,plain,
( ( ( sk2 @ sk163 @ sk164 )
!= ( sk1 @ x @ sk163 ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[33278]) ).
thf(126,plain,
( ( sk5 != sk3 )
| ( sk6 != sk4 )
| ~ ( sk10 @ sk6 @ sk5 )
| ( sk1 @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[121]) ).
thf(94,plain,
( ~ ( sk9 @ sk6 @ sk5 )
| ~ ( sk1 @ sk6 @ sk5 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ sk6 @ sk5 ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(23966,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,12411]) ).
thf(23997,plain,
( ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] :
~ ( sk1 @ y @ B ) ) ) ),
inference(simp,[status(thm)],[23966]) ).
thf(6269,plain,
( ( sk106 != x )
| ( sk107 != y )
| ( ( cS @ sk115 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[5997,54]) ).
thf(6351,plain,
( ( sk106 != x )
| ( sk107 != y )
| ( sk115
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ A ) ) ) ),
inference(simp,[status(thm)],[6269]) ).
thf(21008,plain,
( ( sk71 != y )
| ( sk70 != y )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[20899]) ).
thf(4357,plain,
( ( sk77 != y )
| ( sk78 != y )
| ( ( cS @ sk1 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,2090]) ).
thf(4382,plain,
( ( sk77 != y )
| ( sk78 != y )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[4357]) ).
thf(17572,plain,
( ( sk1 @ y @ y )
| ( sk1 @ sk28 @ sk29 )
| ( sk1 @ y @ sk28 ) ),
inference(bool_ext,[status(thm)],[594]) ).
thf(18716,plain,
( ( sk36 != sk35 )
| ( sk36 != x )
| ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(simp,[status(thm)],[18598]) ).
thf(706,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,213]) ).
thf(723,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[706]) ).
thf(24030,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,23000]) ).
thf(24067,plain,
( ( sk4 != x )
| ( sk3 != x )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[24030]) ).
thf(45,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ y @ x )
| ( B @ y @ x )
| ~ ( A @ x @ y )
| ~ ( cS
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(47,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ y @ x )
| ( B @ y @ x )
| ~ ( A @ x @ y )
| ~ ( cS
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(191,plain,
! [A: $i > $i > $o] :
( ~ ( cS @ A )
| ~ ( A @ x @ y )
| ~ ( cS
@ ^ [B: $i,C: $i] : ( sk1 @ x @ B ) )
| ( ( A @ y @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[4,37]) ).
thf(200,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ B ) )
| ~ ( sk1 @ y @ y )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ),
inference(pre_uni,[status(thm)],[191:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 @ C @ C ) ))]]) ).
thf(158,plain,
( ( sk1 @ x @ x )
| ( ( cS
@ ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,31]) ).
thf(178,plain,
( ( sk1 @ x @ x )
| ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(8917,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) )
| ( ( sk1 @ x @ x )
!= ( sk1 @ x @ x ) ) ),
inference(paramod_ordered,[status(thm)],[178,7864]) ).
thf(8918,plain,
( ( ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ( ( cS @ C )
& ( C @ A @ B ) )
=> ( C @ B @ A ) ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ x ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[8917:[]]) ).
thf(113,plain,
( ( sk1 @ sk3 @ sk4 )
| ( ( sk1 @ sk4 @ sk3 )
!= ( sk1 @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[75,5]) ).
thf(122,plain,
( ( sk1 @ sk3 @ sk4 )
| ( sk4 != x )
| ( sk3 != y ) ),
inference(simp,[status(thm)],[113]) ).
thf(7831,plain,
( ~ ( sk1 @ x @ x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,108]) ).
thf(7861,plain,
( ~ ( sk1 @ x @ x )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ A @ A ) ) ) ),
inference(simp,[status(thm)],[7831]) ).
thf(4721,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( sk1 @ x @ x )
| ( ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[108]) ).
thf(4752,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ A @ A ) )
| ~ ( sk1 @ x @ x )
| ( ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) )
!= ( ^ [A: $i,B: $i] : ( sk1 @ A @ A ) ) ) ),
inference(simp,[status(thm)],[4721]) ).
thf(209,plain,
( ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( cS @ sk7 )
| ( ( sk1 @ sk6 @ sk5 )
!= ( sk1 @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,89]) ).
thf(222,plain,
( ( cS @ sk7 )
| ~ ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) )
| ( sk6 != y )
| ( sk5 != y ) ),
inference(simp,[status(thm)],[209]) ).
thf(7849,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( ( cS @ sk2 )
!= ( cS
@ ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7790,383]) ).
thf(7893,plain,
( ( sk1
!= ( ^ [A: $i,B: $i] : ( sk1 @ B @ y ) ) )
| ( sk2
!= ( ^ [A: $i,B: $i] : ( sk1 @ y @ A ) ) ) ),
inference(simp,[status(thm)],[7849]) ).
thf(39146,plain,
$false,
inference(e,[status(thm)],[6976,10267,7922,6042,6074,234,88,7903,7905,9163,18365,449,379,655,5383,202,12458,170,5,9337,20694,33663,10181,7873,19191,21534,22185,14506,142,10881,10368,42,6887,20803,19069,26186,301,19294,37,7592,7790,16626,184,17366,24558,12351,14669,52,724,7862,559,26371,189,93,15851,18492,228,18959,57,29,2007,8190,2090,33440,9557,21007,7899,602,147,734,5370,7909,19872,428,7688,74,6210,23226,89,18639,20963,12411,512,761,381,8842,19218,233,6,5862,16927,12550,12878,1370,165,24012,7870,17303,7881,26378,10369,17406,461,551,10907,456,224,92,13158,229,566,361,65,13282,578,6101,7917,16163,725,7610,32332,610,16949,6153,109,19070,5031,17883,22274,27874,7930,2038,7895,96,7898,22181,16903,18917,8673,7927,12408,7878,173,10207,16058,6988,1393,24084,2006,20964,18640,128,18958,19332,2057,1616,33952,17426,19511,15815,23489,22555,11837,22686,166,32,1747,9181,2028,7860,562,22545,44,8894,6229,5350,204,23110,17241,7795,5039,54,787,144,19112,17209,7094,49,5997,13407,18516,10370,17971,736,18817,6196,23477,1408,6308,6779,7,4139,758,552,16056,213,91,17914,7869,769,10380,108,7901,17957,20892,22253,27177,5863,594,7928,66,16731,5377,10275,223,394,135,10930,9345,12482,7916,80,7884,18715,16170,5372,9294,7929,6738,20815,226,3,2054,18918,9259,2037,7897,14530,21616,8885,4336,194,7896,2107,6417,14703,4813,7975,10223,10249,1420,27072,7864,48,557,15551,63,18986,95,19320,19838,19531,13229,23052,13246,182,8873,127,13320,31,7876,17570,7919,15839,11,72,175,571,1372,1617,143,43,2088,9664,87,18811,17155,7889,104,20814,7974,19111,4678,17316,23089,40,10225,8634,171,418,20802,14457,16337,8,75,10210,21618,235,5040,33943,18515,383,2036,9311,5864,800,18491,151,4687,36,18555,30445,183,422,23247,34444,300,31399,1395,51,33347,4,126,79,195,2070,23000,94,23997,6351,21008,4382,7915,17572,18716,723,24067,47,200,68,178,5376,8918,26539,122,9310,7861,4752,90,111,222,9254,7893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV116^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:11:55 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (99ms).
% 1.24/0.97 % [INFO] Running in sequential loop mode.
% 1.61/1.17 % [INFO] eprover registered as external prover.
% 1.61/1.18 % [INFO] Scanning for conjecture ...
% 1.73/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.84/1.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.84/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.25 % [INFO] Type checking passed.
% 1.84/1.25 % [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 ...
% 79.66/17.93 % External prover 'e' found a proof!
% 79.66/17.93 % [INFO] Killing All external provers ...
% 79.66/17.93 % Time passed: 17399ms (effective reasoning time: 16951ms)
% 79.66/17.93 % 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)>
% 79.66/17.93 % Axioms used in derivation (0):
% 79.66/17.93 % No. of inferences in proof: 692
% 79.66/17.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17399 ms resp. 16951 ms w/o parsing
% 80.68/18.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 80.68/18.11 % [INFO] Killing All external provers ...
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