%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN082+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:18:42 AM UTC 2026
% Result : Theorem 106.06s 24.89s
% Output : Refutation 108.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 39
% Syntax : Number of formulae : 1277 ( 557 unt; 0 typ; 20 def)
% Number of atoms : 3947 (1008 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 12595 (2236 ~;1273 |; 155 &;8931 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 3 con; 0-3 aty)
% Number of variables : 4171 ( 29 ^;4055 !; 67 ?;4171 :)
% ( 0 !>; 0 ?*; 0 @-; 20 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r4_decl,type,
r4: $i > $i > $i > $o ).
thf(r1_decl,type,
r1: $i > $o ).
thf(r2_decl,type,
r2: $i > $i > $o ).
thf(id_decl,type,
id: $i > $i > $o ).
thf(r3_decl,type,
r3: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r4 ) ) )
& ( C @ ( B @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( B @ r4 ) ) )
& ( E @ ( A @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ ( B @ r4 ) ) )
& ( D @ ( A @ r2 ) ) )
& ( B @ ( A @ sk1 ) @ ( C @ id ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk2 ) @ ( C @ ( B @ r4 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r4 ) ) )
& ( B @ ( A @ sk1 ) @ ( B @ ( C @ r3 ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk6 @ ( B @ ( A @ r3 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
? [C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( A @ sk10 @ r2 ) )
& ( B @ ( A @ id ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk12 @ ( B @ ( A @ r4 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ r1 )
& ( B @ ( A @ sk12 @ id ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( B @ r3 ) ) )
& ( E @ ( A @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ ( B @ r3 ) ) )
& ( D @ ( A @ r2 ) ) )
& ( B @ ( A @ sk15 ) @ ( C @ id ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk16 ) @ ( C @ ( B @ r3 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r3 ) ) )
& ( B @ ( A @ sk15 ) @ ( C @ r2 ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( A @ ( B @ r4 ) ) ) )
| ( ( D @ ( A @ ( B @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( A @ ( B @ r3 ) ) ) )
| ( ( D @ ( A @ ( B @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ) ) ) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
thf(74,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,plain,
! [A: $i] :
( ( A @ sk14 @ r1 )
& ( A @ sk14 @ ( A @ sk12 @ id ) )
& ( A @ sk12 @ ( A @ sk13 @ ( A @ r4 ) ) )
& ( A @ sk13 @ r1 ) ),
inference(cnf,[status(esa)],[74]) ).
thf(76,plain,
! [A: $i] : ( A @ sk13 @ r1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(6,axiom,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(40,plain,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,plain,
! [A: $i] :
( ( ~ ( sk5 @ ( A @ id ) )
| ( A @ r1 ) )
& ( ~ ( A @ r1 )
| ( A @ r1 ) )
& ( ~ ( sk5 @ ( A @ id ) )
| ( sk5 @ ( A @ id ) ) )
& ( ~ ( A @ r1 )
| ( sk5 @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ~ ( A @ r1 )
| ( sk5 @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[76,42]) ).
thf(1267,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[1266]) ).
thf(1268,plain,
! [A: $i] : ( sk5 @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[1267:[bind(A,$thf( C )),bind(B,$thf( C @ sk13 ))]]) ).
thf(1289,plain,
! [A: $i] : ( sk5 @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[1268]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
thf(53,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( D @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true
| ~ ( C @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[76,54]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( D @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ sk13 @ id ) ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E @ sk13 ))]]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(1372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( C @ ( D @ sk13 @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1289,128]) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( C @ ( D @ sk13 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1372]) ).
thf(1374,plain,
! [A: $i] :
~ ( sk5 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 )),bind(D,$thf( A ))]]) ).
thf(1411,plain,
! [A: $i] :
~ ( sk5 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[1374]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
thf(46,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) )
& ( A @ sk7 @ r1 )
& ( A @ ( A @ sk6 @ id ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ sk6 @ id ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(3146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,90]) ).
thf(3147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3146]) ).
thf(3148,plain,
! [A: $i] : ( A @ sk6 @ ( A @ id ) ),
inference(pattern_uni,[status(thm)],[3147:[bind(A,$thf( D )),bind(B,$thf( D @ sk6 )),bind(C,$thf( D ))]]) ).
thf(3176,plain,
! [A: $i] : ( A @ sk6 @ ( A @ id ) ),
inference(simp,[status(thm)],[3148]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(62,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ~ ( A @ sk8 @ ( B @ id ) )
| ( B @ ( A @ r2 ) ) )
& ( ~ ( B @ ( A @ r2 ) )
| ( B @ ( A @ r2 ) ) )
& ( ~ ( A @ sk8 @ ( B @ id ) )
| ( A @ sk8 @ ( B @ id ) ) )
& ( ~ ( B @ ( A @ r2 ) )
| ( A @ sk8 @ ( B @ id ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk8 @ ( B @ id ) )
| ( B @ ( A @ r2 ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(2805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ~ $true
| ( C @ ( B @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[48,67]) ).
thf(2806,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2805]) ).
thf(2807,plain,
! [A: $i] : ( A @ sk8 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[2806:[bind(A,$thf( E @ sk8 )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk6 ))]]) ).
thf(2836,plain,
! [A: $i] : ( A @ sk8 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[2807]) ).
thf(2968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( D @ sk13 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2836,128]) ).
thf(2969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[2968]) ).
thf(2970,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[2969:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(3019,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[2970]) ).
thf(5508,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,3019]) ).
thf(5509,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[5508]) ).
thf(5538,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 @ sk6 ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[5509]) ).
thf(5561,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[5538]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( A @ id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(87,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(cnf,[status(esa)],[87]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(97,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( A @ ( B @ sk20 ) @ ( C @ id ) )
| ( C @ ( B @ ( A @ r3 ) ) ) )
& ( ~ ( C @ ( B @ ( A @ r3 ) ) )
| ( C @ ( B @ ( A @ r3 ) ) ) )
& ( ~ ( A @ ( B @ sk20 ) @ ( C @ id ) )
| ( A @ ( B @ sk20 ) @ ( C @ id ) ) )
& ( ~ ( C @ ( B @ ( A @ r3 ) ) )
| ( A @ ( B @ sk20 ) @ ( C @ id ) ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ sk20 ) @ ( C @ id ) )
| ( C @ ( B @ ( A @ r3 ) ) ) ),
inference(cnfConj,[status(thm)],[98]) ).
thf(4177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk20 ) @ ( D @ id ) ) )
| ~ $true
| ( D @ ( C @ ( B @ r3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[88,102]) ).
thf(4178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk20 ) @ ( D @ id ) ) )
| ( D @ ( C @ ( B @ r3 ) ) ) ),
inference(simp,[status(thm)],[4177]) ).
thf(4179,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ ( A @ ( B @ r3 ) ) ),
inference(pattern_uni,[status(thm)],[4178:[bind(A,$thf( F @ ( E @ sk20 ) )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk20 ) ))]]) ).
thf(4262,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ ( A @ ( B @ r3 ) ) ),
inference(simp,[status(thm)],[4179]) ).
thf(14,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
thf(80,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk18 ) @ ( B @ ( A @ r3 ) ) )
& ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
& ( A @ ( B @ sk16 ) @ ( A @ ( B @ sk17 ) @ ( A @ r3 ) ) )
& ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
& ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk16 ) @ id ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(83,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ( A @ sk8 @ ( B @ id ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(2524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( C @ sk8 @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[83,64]) ).
thf(2525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( C @ sk8 @ ( D @ id ) ) ),
inference(simp,[status(thm)],[2524]) ).
thf(2526,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[2525:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(2544,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[2526]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
thf(68,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(69,plain,
! [A: $i] :
( ( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
| ( A @ sk9 @ r1 ) )
& ( ( A @ sk11 @ ( A @ id ) )
| ( A @ sk9 @ r1 ) )
& ( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
| ( A @ sk9 @ ( A @ id ) ) )
& ( ( A @ sk11 @ ( A @ id ) )
| ( A @ sk9 @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ id ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(45,plain,
! [A: $i] :
( ~ ( sk5 @ ( A @ id ) )
| ( A @ r1 ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(1558,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[70,45]) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[1558]) ).
thf(1578,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A != B )
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1586,plain,
! [A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[1578]) ).
thf(49,plain,
! [A: $i] : ( A @ sk7 @ r1 ),
inference(cnfConj,[status(thm)],[47]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( D @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true
| ~ ( C @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[49,54]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( D @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ sk7 @ id ) ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E @ sk7 ))]]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(5964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( D @ sk7 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2836,130]) ).
thf(5965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[5964]) ).
thf(5966,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[5965:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(6047,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[5966]) ).
thf(7340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ sk6 @ ( C @ sk7 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,6047]) ).
thf(7341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ sk6 @ ( C @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[7340]) ).
thf(7342,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[7341:[bind(A,$thf( G @ sk8 @ sk6 )),bind(B,$thf( E @ sk7 )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(7373,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[7342]) ).
thf(2776,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ~ $true
| ( C @ ( B @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[88,67]) ).
thf(2777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2778,plain,
! [A: $i] : ( A @ sk8 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[2777:[bind(A,$thf( D @ sk8 )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(2837,plain,
! [A: $i] : ( A @ sk8 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[2778]) ).
thf(5940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( D @ sk7 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2837,130]) ).
thf(5941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[5940]) ).
thf(5942,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[5941:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(6063,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[5942]) ).
thf(17,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(91,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( A @ ( B @ sk19 ) @ ( C @ id ) )
| ( C @ ( B @ ( A @ r4 ) ) ) )
& ( ~ ( C @ ( B @ ( A @ r4 ) ) )
| ( C @ ( B @ ( A @ r4 ) ) ) )
& ( ~ ( A @ ( B @ sk19 ) @ ( C @ id ) )
| ( A @ ( B @ sk19 ) @ ( C @ id ) ) )
& ( ~ ( C @ ( B @ ( A @ r4 ) ) )
| ( A @ ( B @ sk19 ) @ ( C @ id ) ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ sk19 ) @ ( C @ id ) )
| ( C @ ( B @ ( A @ r4 ) ) ) ),
inference(cnfConj,[status(thm)],[92]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( B @ ( C @ ( A @ r4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xtimesoneidzero) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( B @ ( C @ ( A @ r4 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( B @ ( C @ ( A @ r4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ r1 )
| ~ ( E @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(147,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( F @ ( C @ id ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[88,22]) ).
thf(148,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( F @ ( C @ id ) ) )
| ~ ( F @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ $true
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,173]) ).
thf(192,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ sk7 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ sk7 ))]]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ sk7 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( D @ ( E @ sk7 @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,197]) ).
thf(311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( D @ ( E @ sk7 @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ sk7 @ r2 ) )
| ~ ( D @ sk13 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( F )),bind(B,$thf( F @ sk13 ))]]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ sk7 @ r2 ) )
| ~ ( D @ sk13 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(2884,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( E @ sk13 @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2837,327]) ).
thf(2885,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ ( E @ sk13 @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[2884]) ).
thf(2886,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ sk7 @ sk8 @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[2885:[bind(A,$thf( H @ sk7 )),bind(B,$thf( B )),bind(C,$thf( H @ sk7 @ sk8 )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(2900,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ sk7 @ sk8 @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[2886]) ).
thf(3727,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( E @ sk13 @ ( F @ sk7 @ sk8 @ ( D @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,2900]) ).
thf(3728,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( E @ sk13 @ ( F @ sk7 @ sk8 @ ( D @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3727]) ).
thf(3729,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ ( C @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[3728:[bind(A,$thf( A )),bind(B,$thf( H @ sk7 @ sk8 )),bind(C,$thf( I @ sk13 )),bind(D,$thf( A )),bind(E,$thf( I )),bind(F,$thf( H ))]]) ).
thf(3813,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ ( C @ sk13 @ id ) ),
inference(simp,[status(thm)],[3729]) ).
thf(2862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( D @ sk13 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2837,128]) ).
thf(2863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[2862]) ).
thf(2864,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[2863:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(2908,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[2864]) ).
thf(86,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(955,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk13 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[86,128]) ).
thf(956,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[955]) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[956:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk18 ) )),bind(D,$thf( I @ ( H @ sk15 ) )),bind(E,$thf( E ))]]) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[957]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,54]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ sk6 @ r1 ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E @ sk6 ))]]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[145]) ).
thf(2993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[2836,146]) ).
thf(2994,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[2993]) ).
thf(2995,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[2994:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk6 ))]]) ).
thf(3012,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ sk6 @ r1 ),
inference(simp,[status(thm)],[2995]) ).
thf(72,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(1570,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[72,45]) ).
thf(1571,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[1570]) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A != B )
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[1571]) ).
thf(1591,plain,
! [A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[1583]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
thf(30,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
& ( A @ ( B @ sk1 ) @ ( A @ ( A @ ( B @ sk4 ) @ r3 ) ) )
& ( A @ ( B @ sk2 ) @ ( A @ ( B @ sk3 ) @ ( A @ r4 ) ) )
& ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
& ( A @ ( B @ sk1 ) @ ( A @ ( B @ sk2 ) @ id ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(35,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(3595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk13 @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,128]) ).
thf(3596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk13 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3595]) ).
thf(3597,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[3596:[bind(A,$thf( G @ sk13 )),bind(B,$thf( B )),bind(C,$thf( G @ sk13 @ sk6 )),bind(D,$thf( G ))]]) ).
thf(3650,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[3597]) ).
thf(4315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,3650]) ).
thf(4316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4315]) ).
thf(4320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk13 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4316]) ).
thf(4326,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4320]) ).
thf(79,plain,
! [A: $i] : ( A @ sk14 @ r1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( D @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true
| ~ ( C @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[79,54]) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( D @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ sk14 @ id ) ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E @ sk14 ))]]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(2859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( D @ sk14 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2837,129]) ).
thf(2860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[2859]) ).
thf(2861,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[2860:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(2904,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[2861]) ).
thf(3835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk14 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,2904]) ).
thf(3836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk14 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[3835]) ).
thf(3890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ sk8 )
!= sk5 )
| ( A
!= ( B @ sk14 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[3836]) ).
thf(3905,plain,
! [B: $i,A: $i] :
( ( ( B @ sk8 )
!= sk5 )
| ~ ( A @ sk14 @ r1 ) ),
inference(simp,[status(thm)],[3890]) ).
thf(5690,plain,
! [A: $i] :
( ( ( A @ sk8 )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[3905,79]) ).
thf(5691,plain,
! [A: $i] :
( ( A @ sk8 )
!= sk5 ),
inference(simp,[status(thm)],[5690]) ).
thf(188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,173]) ).
thf(189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk14 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( F )),bind(B,$thf( F @ sk14 ))]]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk14 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,54]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[116]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,118]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( D )),bind(B,$thf( D @ sk13 ))]]) ).
thf(140,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[133]) ).
thf(285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,140]) ).
thf(286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk13 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[286]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[300]) ).
thf(1567,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 ) ),
inference(paramod_ordered,[status(thm)],[48,45]) ).
thf(1568,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 ) ),
inference(simp,[status(thm)],[1567]) ).
thf(1569,plain,
sk5 @ sk6 @ r1,
inference(pattern_uni,[status(thm)],[1568:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[86,146]) ).
thf(972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[971]) ).
thf(973,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[972:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk18 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(985,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[973]) ).
thf(1136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,985]) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1136]) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk15 ) @ sk6 ) ),
inference(simp,[status(thm)],[1137]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,118]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 ))]]) ).
thf(142,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[139]) ).
thf(2949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,142]) ).
thf(2950,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2949]) ).
thf(3000,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk7 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2950]) ).
thf(3017,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[3000]) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,1411]) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= sk5 )
| ( B != C ) ),
inference(simp,[status(thm)],[1417]) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= sk5 ),
inference(simp,[status(thm)],[1422]) ).
thf(3695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk19 ) @ ( D @ id ) ) )
| ~ $true
| ( D @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[88,96]) ).
thf(3696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk19 ) @ ( D @ id ) ) )
| ( D @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[3695]) ).
thf(3697,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3696:[bind(A,$thf( F @ ( E @ sk19 ) )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk19 ) ))]]) ).
thf(3826,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) ),
inference(simp,[status(thm)],[3697]) ).
thf(1545,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 ) ),
inference(paramod_ordered,[status(thm)],[88,45]) ).
thf(1546,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 ) ),
inference(simp,[status(thm)],[1545]) ).
thf(1547,plain,
sk5 @ r1,
inference(pattern_uni,[status(thm)],[1546:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
thf(1598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( A @ r1 ) )
| ~ $true
| ~ ( C @ ( D @ sk7 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1547,197]) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( A @ r1 ) )
| ~ ( C @ ( D @ sk7 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[1598]) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ sk7 @ r2 ) )
| ~ ( sk5 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[1599:[bind(A,$thf( sk5 ))]]) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ sk7 @ r2 ) )
| ~ ( sk5 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[1600]) ).
thf(11795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,1647]) ).
thf(11796,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ ( sk5 @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[11795]) ).
thf(11797,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( B @ ( C @ sk7 @ sk3 ) @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[11796:[bind(A,$thf( H )),bind(B,$thf( I @ sk7 )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ sk7 @ sk3 ) )),bind(E,$thf( I ))]]) ).
thf(11816,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( B @ ( C @ sk7 @ sk3 ) @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[11797]) ).
thf(12831,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( sk5 @ ( D @ ( E @ sk7 @ sk3 ) @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3826,11816]) ).
thf(12832,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( sk5 @ ( D @ ( E @ sk7 @ sk3 ) @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[12831]) ).
thf(12909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= sk5 )
| ( A
!= ( D @ ( E @ sk7 @ sk3 ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[12832]) ).
thf(12939,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[12909]) ).
thf(3592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,129]) ).
thf(3593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3592]) ).
thf(3594,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[3593:[bind(A,$thf( G @ sk14 )),bind(B,$thf( B )),bind(C,$thf( G @ sk14 @ sk6 )),bind(D,$thf( G ))]]) ).
thf(3649,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[3594]) ).
thf(4042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,3649]) ).
thf(4043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4042]) ).
thf(4051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk14 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[4043]) ).
thf(4058,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4051]) ).
thf(11778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2836,1647]) ).
thf(11779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ ( sk5 @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[11778]) ).
thf(11780,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ sk7 @ sk8 @ sk6 @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[11779:[bind(A,$thf( H @ sk7 )),bind(B,$thf( B )),bind(C,$thf( H @ sk7 @ sk8 @ sk6 )),bind(D,$thf( H ))]]) ).
thf(11813,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ sk7 @ sk8 @ sk6 @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[11780]) ).
thf(11940,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ sk7 @ sk8 @ sk6 @ ( D @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,11813]) ).
thf(11941,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ sk7 @ sk8 @ sk6 @ ( D @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[11940]) ).
thf(11942,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[11941:[bind(A,$thf( A )),bind(B,$thf( H @ sk7 @ sk8 @ sk6 )),bind(C,$thf( sk5 )),bind(D,$thf( A )),bind(E,$thf( H ))]]) ).
thf(11951,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[11942]) ).
thf(12322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,11951]) ).
thf(12323,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12322]) ).
thf(12417,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[12323]) ).
thf(12421,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[12417]) ).
thf(2887,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[2837,146]) ).
thf(2888,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[2887]) ).
thf(2889,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[2888:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(2901,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ r1 ),
inference(simp,[status(thm)],[2889]) ).
thf(34,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(664,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ ( E @ ( D @ r4 ) ) ) )
| ~ ( C @ r1 )
| ~ ( E @ ( F @ sk7 @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,197]) ).
thf(665,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ ( E @ ( D @ r4 ) ) ) )
| ~ ( C @ r1 )
| ~ ( E @ ( F @ sk7 @ r2 ) ) ),
inference(simp,[status(thm)],[664]) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ sk4 ) @ r1 )
| ~ ( B @ ( A @ sk7 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk4 ) )),bind(D,$thf( H )),bind(E,$thf( G ))]]) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ sk4 ) @ r1 )
| ~ ( B @ ( A @ sk7 @ r2 ) ) ),
inference(simp,[status(thm)],[666]) ).
thf(2974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ sk7 @ r2 ) ) )
| ~ ( D @ ( C @ sk4 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,689]) ).
thf(2975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ sk7 @ r2 ) ) )
| ~ ( D @ ( C @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[2974]) ).
thf(2976,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ),
inference(pattern_uni,[status(thm)],[2975:[bind(A,$thf( H @ sk7 )),bind(B,$thf( H )),bind(C,$thf( H @ sk7 @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(3004,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ),
inference(simp,[status(thm)],[2976]) ).
thf(12698,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ ( F @ sk7 @ sk3 ) @ ( D @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,11816]) ).
thf(12699,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ ( F @ sk7 @ sk3 ) @ ( D @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[12698]) ).
thf(12700,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk19 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[12699:[bind(A,$thf( A )),bind(B,$thf( H @ ( I @ sk7 @ sk3 ) )),bind(C,$thf( sk5 )),bind(D,$thf( A )),bind(E,$thf( H )),bind(F,$thf( I ))]]) ).
thf(12714,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk19 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[12700]) ).
thf(322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( D @ ( E @ sk7 @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,197]) ).
thf(323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( D @ ( E @ sk7 @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ sk7 @ r2 ) )
| ~ ( D @ sk7 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( F )),bind(B,$thf( F @ sk7 ))]]) ).
thf(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ sk7 @ r2 ) )
| ~ ( D @ sk7 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(2890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( E @ sk7 @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2837,326]) ).
thf(2891,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ ( E @ sk7 @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[2890]) ).
thf(2892,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ sk7 @ sk8 @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[2891:[bind(A,$thf( H @ sk7 )),bind(B,$thf( B )),bind(C,$thf( H @ sk7 @ sk8 )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(2903,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ sk7 @ sk8 @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[2892]) ).
thf(3995,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( E @ sk7 @ ( F @ sk7 @ sk8 @ ( D @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,2903]) ).
thf(3996,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( E @ sk7 @ ( F @ sk7 @ sk8 @ ( D @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3995]) ).
thf(3997,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ ( C @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[3996:[bind(A,$thf( A )),bind(B,$thf( H @ sk7 @ sk8 )),bind(C,$thf( I @ sk7 )),bind(D,$thf( A )),bind(E,$thf( I )),bind(F,$thf( H ))]]) ).
thf(4011,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ ( C @ sk7 @ id ) ),
inference(simp,[status(thm)],[3997]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ r4 ) ) )
| ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(cnfConj,[status(thm)],[92]) ).
thf(3555,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( E @ ( D @ ( C @ r4 ) ) ) )
| ~ $true
| ( C @ ( D @ sk19 ) @ ( E @ id ) ) ),
inference(paramod_ordered,[status(thm)],[34,93]) ).
thf(3556,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( E @ ( D @ ( C @ r4 ) ) ) )
| ( C @ ( D @ sk19 ) @ ( E @ id ) ) ),
inference(simp,[status(thm)],[3555]) ).
thf(3557,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( B @ ( A @ sk4 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3556:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(3562,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( B @ ( A @ sk4 ) @ id ) ),
inference(simp,[status(thm)],[3557]) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[83,146]) ).
thf(440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[439]) ).
thf(441,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[440:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(463,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[441]) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,463]) ).
thf(1630,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1629]) ).
thf(1640,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[1630]) ).
thf(165,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ $true
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,22]) ).
thf(166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( E @ sk7 @ r2 ) )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ sk7 ))]]) ).
thf(174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( E @ sk7 @ r2 ) )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(3537,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,3004]) ).
thf(3538,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[3537]) ).
thf(3545,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) )
!= sk5 ),
inference(simp,[status(thm)],[3538]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[35,118]) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[293]) ).
thf(295,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ r1 ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk3 ) )),bind(D,$thf( E ))]]) ).
thf(304,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ r1 ),
inference(simp,[status(thm)],[295]) ).
thf(413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,304]) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[413]) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[414]) ).
thf(77,plain,
! [A: $i] : ( A @ sk12 @ ( A @ sk13 @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(3552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ sk13 @ ( A @ r4 ) ) )
!= ( D @ ( C @ ( B @ r4 ) ) ) )
| ~ $true
| ( B @ ( C @ sk19 ) @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[77,93]) ).
thf(3553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ sk13 @ ( A @ r4 ) ) )
!= ( D @ ( C @ ( B @ r4 ) ) ) )
| ( B @ ( C @ sk19 ) @ ( D @ id ) ) ),
inference(simp,[status(thm)],[3552]) ).
thf(3554,plain,
! [A: $i] : ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) ),
inference(pattern_uni,[status(thm)],[3553:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk13 )),bind(D,$thf( F @ sk12 ))]]) ).
thf(3561,plain,
! [A: $i] : ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) ),
inference(simp,[status(thm)],[3554]) ).
thf(8988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3561,90]) ).
thf(8989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[8988]) ).
thf(8990,plain,
! [A: $i] : ( A @ sk12 @ ( A @ ( A @ sk13 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[8989:[bind(A,$thf( F )),bind(B,$thf( F @ sk12 )),bind(C,$thf( F @ ( F @ sk13 @ sk19 ) ))]]) ).
thf(9027,plain,
! [A: $i] : ( A @ sk12 @ ( A @ ( A @ sk13 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[8990]) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ( ( B @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,146]) ).
thf(1634,plain,
! [B: $i,A: $i] :
( ( ( B @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[1633]) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( ( B @ sk6 )
!= sk5 )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[1634]) ).
thf(2990,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( E @ sk13 @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2836,327]) ).
thf(2991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ ( E @ sk13 @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[2990]) ).
thf(2992,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ sk7 @ sk8 @ sk6 @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[2991:[bind(A,$thf( I @ sk7 )),bind(B,$thf( B )),bind(C,$thf( I @ sk7 @ sk8 @ sk6 )),bind(D,$thf( I )),bind(E,$thf( E ))]]) ).
thf(3011,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ sk7 @ sk8 @ sk6 @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[2992]) ).
thf(12847,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3826,3011]) ).
thf(12848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[12847]) ).
thf(12927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( D @ sk13 ) )
| ( A
!= ( E @ sk7 @ sk8 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[12848]) ).
thf(12960,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[12927]) ).
thf(1677,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( A @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,118]) ).
thf(1678,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1677]) ).
thf(1679,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[1678:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B ))]]) ).
thf(1707,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[1679]) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,1707]) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1713]) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( sk5 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1714]) ).
thf(1724,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1720]) ).
thf(5961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk7 @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,130]) ).
thf(5962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk7 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[5961]) ).
thf(5963,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[5962:[bind(A,$thf( G @ sk7 )),bind(B,$thf( B )),bind(C,$thf( G @ sk7 @ sk6 )),bind(D,$thf( G ))]]) ).
thf(6043,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[5963]) ).
thf(6081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,6043]) ).
thf(6082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[6081]) ).
thf(6093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk7 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[6082]) ).
thf(6102,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6093]) ).
thf(11765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2837,1647]) ).
thf(11766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ ( sk5 @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[11765]) ).
thf(11767,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ sk7 @ sk8 @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[11766:[bind(A,$thf( G @ sk7 )),bind(B,$thf( B )),bind(C,$thf( G @ sk7 @ sk8 )),bind(D,$thf( G ))]]) ).
thf(11817,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ sk7 @ sk8 @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[11767]) ).
thf(11916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ sk7 @ sk8 @ ( D @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,11817]) ).
thf(11917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ sk7 @ sk8 @ ( D @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[11916]) ).
thf(11918,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[11917:[bind(A,$thf( A )),bind(B,$thf( G @ sk7 @ sk8 )),bind(C,$thf( sk5 )),bind(D,$thf( A )),bind(E,$thf( G ))]]) ).
thf(11932,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[11918]) ).
thf(12005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,11932]) ).
thf(12006,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12005]) ).
thf(12039,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= sk5 ) ),
inference(simp,[status(thm)],[12006]) ).
thf(12062,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[12039]) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( C @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ $true
| ~ ( B @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[1547,54]) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( C @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[1622]) ).
thf(1624,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( sk5 @ id ) ) ),
inference(pattern_uni,[status(thm)],[1623:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(10214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[83,1624]) ).
thf(10215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10214]) ).
thf(10216,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10215:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(10248,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10216]) ).
thf(642,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( F @ sk13 @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,327]) ).
thf(643,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ ( F @ sk13 @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[642]) ).
thf(644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ ( D @ sk7 @ sk3 ) @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( I )),bind(B,$thf( J @ sk7 )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ sk7 @ sk3 ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ ( D @ sk7 @ sk3 ) @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,985]) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1661]) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[49,42]) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1265,plain,
! [A: $i] : ( sk5 @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[1264:[bind(A,$thf( C )),bind(B,$thf( C @ sk7 ))]]) ).
thf(1287,plain,
! [A: $i] : ( sk5 @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[1265]) ).
thf(2877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( D @ r1 )
| ~ ( C @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2837,54]) ).
thf(2878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( D @ r1 )
| ~ ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[2877]) ).
thf(2879,plain,
! [B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[2878:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(2916,plain,
! [B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[2879]) ).
thf(3421,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,3012]) ).
thf(3422,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3421]) ).
thf(3425,plain,
! [B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ sk8 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[3422]) ).
thf(12889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3826,2903]) ).
thf(12890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[12889]) ).
thf(12913,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( D @ sk7 ) )
| ( A
!= ( E @ sk7 @ sk8 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[12890]) ).
thf(12943,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk19 ) )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[12913]) ).
thf(699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk13 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[35,128]) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[699]) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(719,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[701]) ).
thf(3680,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,2900]) ).
thf(3681,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[3680]) ).
thf(3685,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk13 ) )
| ( B
!= ( E @ sk7 @ sk8 ) )
| ( A != C ) ),
inference(simp,[status(thm)],[3681]) ).
thf(3689,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk4 ) )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[3685]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk14 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[83,129]) ).
thf(907,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk17 ) ))]]) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[908]) ).
thf(3539,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,3004]) ).
thf(3540,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[3539]) ).
thf(3542,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) ) ),
inference(simp,[status(thm)],[3540]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,118]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( D )),bind(B,$thf( D @ sk14 ))]]) ).
thf(141,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[136]) ).
thf(432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,141]) ).
thf(433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk14 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[433]) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[454]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ id ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(84,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk16 ) @ id ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(3065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk16 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[84,90]) ).
thf(3066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk16 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[3065]) ).
thf(3067,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk16 ) @ ( B @ ( A @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3066:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk16 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(3204,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk16 ) @ ( B @ ( A @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[3067]) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[83,118]) ).
thf(446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[445]) ).
thf(447,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ r1 ),
inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk17 ) )),bind(D,$thf( E ))]]) ).
thf(466,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ r1 ),
inference(simp,[status(thm)],[447]) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,466]) ).
thf(1684,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1683]) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1684]) ).
thf(5866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,3813]) ).
thf(5867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[5866]) ).
thf(5906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[5867]) ).
thf(5925,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk13 @ sk6 )
!= ( A @ ( B @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[5906]) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,304]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[411]) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(2874,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ $true
| ~ ( B @ r1 ) ),
inference(paramod_ordered,[status(thm)],[2837,118]) ).
thf(2875,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[2874]) ).
thf(2876,plain,
! [A: $i] :
~ ( A @ sk8 @ r1 ),
inference(pattern_uni,[status(thm)],[2875:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(2914,plain,
! [A: $i] :
~ ( A @ sk8 @ r1 ),
inference(simp,[status(thm)],[2876]) ).
thf(2925,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,2914]) ).
thf(2926,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ r1 ) ),
inference(simp,[status(thm)],[2925]) ).
thf(2929,plain,
! [B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[2926]) ).
thf(2996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( E @ sk7 @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2836,326]) ).
thf(2997,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( D @ sk7 @ r2 ) ) )
| ~ ( E @ sk7 @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[2996]) ).
thf(2998,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ sk7 @ sk8 @ sk6 @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[2997:[bind(A,$thf( I @ sk7 )),bind(B,$thf( B )),bind(C,$thf( I @ sk7 @ sk8 @ sk6 )),bind(D,$thf( I )),bind(E,$thf( E ))]]) ).
thf(3014,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ sk7 @ sk8 @ sk6 @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[2998]) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,466]) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1625]) ).
thf(1641,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) )
!= sk5 ),
inference(simp,[status(thm)],[1626]) ).
thf(78,plain,
! [A: $i] : ( A @ sk14 @ ( A @ sk12 @ id ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(3998,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,2903]) ).
thf(3999,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[3998]) ).
thf(4004,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk7 ) )
| ( B
!= ( E @ sk7 @ sk8 ) )
| ( A != C ) ),
inference(simp,[status(thm)],[3999]) ).
thf(4008,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk4 ) )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[4004]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,466]) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) ),
inference(simp,[status(thm)],[471]) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[472]) ).
thf(3928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,2908]) ).
thf(3929,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[3928]) ).
thf(3961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[3929]) ).
thf(3983,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[3961]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(23,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) ) )
| ~ ( E @ ( B @ id ) ) )
| ~ ( D @ ( A @ id ) ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(27,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( F @ ( C @ id ) )
!= ( D @ ( A @ id ) ) )
| ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ r4 ) ) )
| ~ ( B @ ( A @ ( B @ r4 ) ) )
| ~ ( C @ ( A @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F ))]]) ).
thf(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ r4 ) ) )
| ~ ( B @ ( A @ ( B @ r4 ) ) )
| ~ ( C @ ( A @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(12368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,11951]) ).
thf(12369,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12368]) ).
thf(12412,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) )
| ( ( A @ sk6 )
!= sk5 ) ),
inference(simp,[status(thm)],[12369]) ).
thf(12436,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[12412]) ).
thf(6497,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ ( E @ sk7 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4011]) ).
thf(6498,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ ( E @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[6497]) ).
thf(6499,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[6498:[bind(A,$thf( H @ ( J @ sk7 @ sk8 @ sk19 ) )),bind(B,$thf( F @ sk7 )),bind(C,$thf( H )),bind(D,$thf( J )),bind(E,$thf( F ))]]) ).
thf(6524,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[6499]) ).
thf(8447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,6524]) ).
thf(8448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[8447]) ).
thf(8515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk7 ) )
| ( A
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[8448]) ).
thf(8532,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ sk7 @ sk8 @ sk19 ) )
!= ( A @ sk7 ) ),
inference(simp,[status(thm)],[8515]) ).
thf(4046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,3649]) ).
thf(4047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4046]) ).
thf(4048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk14 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4047]) ).
thf(4055,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4048]) ).
thf(2868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ sk7 @ r2 ) ) )
| ~ ( D @ ( C @ sk4 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,689]) ).
thf(2869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ sk7 @ r2 ) ) )
| ~ ( D @ ( C @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[2868]) ).
thf(2870,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk4 ) @ r1 ),
inference(pattern_uni,[status(thm)],[2869:[bind(A,$thf( G @ sk7 )),bind(B,$thf( G )),bind(C,$thf( G @ sk7 @ sk8 )),bind(D,$thf( D ))]]) ).
thf(2912,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ sk7 @ sk8 @ sk4 ) @ r1 ),
inference(simp,[status(thm)],[2870]) ).
thf(3023,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk7 @ sk8 @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,2912]) ).
thf(3024,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3023]) ).
thf(3036,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk4 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[3024]) ).
thf(209,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( G @ ( D @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ $true
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[88,27]) ).
thf(210,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( G @ ( D @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ r4 ) ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( A ))]]) ).
thf(243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ r4 ) ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(1008,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ sk7 @ r2 ) ) )
| ~ ( E @ ( D @ sk4 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,689]) ).
thf(1009,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ sk7 @ r2 ) ) )
| ~ ( E @ ( D @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) @ r1 ),
inference(pattern_uni,[status(thm)],[1009:[bind(A,$thf( H )),bind(B,$thf( I @ sk7 )),bind(C,$thf( I )),bind(D,$thf( H @ ( I @ sk7 @ sk17 ) )),bind(E,$thf( E ))]]) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) @ r1 ),
inference(simp,[status(thm)],[1010]) ).
thf(1659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,1016]) ).
thf(1660,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1659]) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1660]) ).
thf(6086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,6043]) ).
thf(6087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[6086]) ).
thf(6094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk7 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[6087]) ).
thf(6103,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6094]) ).
thf(3053,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk7 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1287,90]) ).
thf(3054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk7 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3053]) ).
thf(3055,plain,
! [A: $i] : ( A @ sk7 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[3054:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 )),bind(C,$thf( sk5 ))]]) ).
thf(3196,plain,
! [A: $i] : ( A @ sk7 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[3055]) ).
thf(12386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,11951]) ).
thf(12387,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12386]) ).
thf(12399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12387]) ).
thf(12430,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[12399]) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,1016]) ).
thf(1210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1209]) ).
thf(1215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[1210]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[35,146]) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(302,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[289]) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,302]) ).
thf(1655,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1654]) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1655]) ).
thf(3158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1289,90]) ).
thf(3159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3158]) ).
thf(3160,plain,
! [A: $i] : ( A @ sk13 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[3159:[bind(A,$thf( D )),bind(B,$thf( D @ sk13 )),bind(C,$thf( sk5 ))]]) ).
thf(3184,plain,
! [A: $i] : ( A @ sk13 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[3160]) ).
thf(3850,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,2904]) ).
thf(3851,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3850]) ).
thf(3881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3851]) ).
thf(3899,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[3881]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(55,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(56,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) ) )
| ~ ( E @ ( B @ id ) ) )
| ~ ( D @ ( A @ id ) ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
| ~ ( F @ ( E @ ( D @ r3 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( F @ ( E @ ( D @ r3 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( F @ ( E @ ( D @ r3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(60,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( F @ ( E @ ( D @ r3 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(2880,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,1707]) ).
thf(2881,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2880]) ).
thf(2897,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( sk5 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2881]) ).
thf(2910,plain,
! [A: $i] :
( ( A @ sk8 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[2897]) ).
thf(3155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[72,90]) ).
thf(3156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[3155]) ).
thf(3157,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[3156:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk11 ))]]) ).
thf(3182,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[3157]) ).
thf(7002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ~ $true
| ( C @ ( B @ r2 ) )
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[3182,67]) ).
thf(7003,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7002]) ).
thf(7004,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[7003:[bind(A,$thf( E @ sk8 )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk11 ))]]) ).
thf(7082,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7004]) ).
thf(12112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ( B @ sk8 @ ( C @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[7082,64]) ).
thf(12113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ( B @ sk8 @ ( C @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[12112]) ).
thf(12114,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[12113:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk11 ))]]) ).
thf(12203,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[12114]) ).
thf(15276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[12203,90]) ).
thf(15277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[15276]) ).
thf(15278,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ sk8 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[15277:[bind(A,$thf( F )),bind(B,$thf( F @ sk8 @ sk11 )),bind(C,$thf( F @ sk8 ))]]) ).
thf(15345,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ sk8 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[15278]) ).
thf(6950,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[3182,45]) ).
thf(6951,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[6950]) ).
thf(6952,plain,
( ( sk5 @ sk11 @ r1 )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[6951:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk11 ))]]) ).
thf(7391,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ r1 )
!= ( A @ r1 ) )
| ~ $true
| ( sk5 @ ( A @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[6952,42]) ).
thf(7392,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ r1 )
!= ( A @ r1 ) )
| ( sk5 @ ( A @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7391]) ).
thf(7393,plain,
( ( sk5 @ ( sk5 @ sk11 @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[7392:[bind(A,$thf( sk5 @ sk11 ))]]) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk14 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[35,129]) ).
thf(899,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[898]) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(914,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[900]) ).
thf(3161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk3 ) @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,914]) ).
thf(3162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk3 ) @ ( C @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3161]) ).
thf(3163,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3162:[bind(A,$thf( H @ ( G @ sk3 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3186,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[3163]) ).
thf(11801,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[83,1647]) ).
thf(11802,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ ( sk5 @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[11801]) ).
thf(11803,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( B @ ( C @ sk7 @ sk17 ) @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[11802:[bind(A,$thf( H )),bind(B,$thf( I @ sk7 )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ sk7 @ sk17 ) )),bind(E,$thf( I ))]]) ).
thf(11820,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( B @ ( C @ sk7 @ sk17 ) @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[11803]) ).
thf(50,plain,
! [A: $i] : ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ r3 ) ) )
| ( A @ ( B @ sk20 ) @ ( C @ id ) ) ),
inference(cnfConj,[status(thm)],[98]) ).
thf(4021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) )
!= ( D @ ( C @ ( B @ r3 ) ) ) )
| ~ $true
| ( B @ ( C @ sk20 ) @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[50,99]) ).
thf(4022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) )
!= ( D @ ( C @ ( B @ r3 ) ) ) )
| ( B @ ( C @ sk20 ) @ ( D @ id ) ) ),
inference(simp,[status(thm)],[4021]) ).
thf(4023,plain,
! [A: $i] : ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[4022:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk7 )),bind(D,$thf( F @ sk6 ))]]) ).
thf(4031,plain,
! [A: $i] : ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) ),
inference(simp,[status(thm)],[4023]) ).
thf(3029,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk7 @ sk8 @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,2912]) ).
thf(3030,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[3029]) ).
thf(3037,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk4 ) )
!= sk5 ),
inference(simp,[status(thm)],[3030]) ).
thf(6449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4011]) ).
thf(6450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6449]) ).
thf(6512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[6450]) ).
thf(6529,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk7 )
!= ( A @ ( B @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[6512]) ).
thf(85,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk18 ) @ ( B @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ $true
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,173]) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ sk14 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ sk14 ))]]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ sk14 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(4036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,3649]) ).
thf(4037,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4036]) ).
thf(4052,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk14 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4037]) ).
thf(4059,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4052]) ).
thf(2843,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,142]) ).
thf(2844,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2843]) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk7 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2844]) ).
thf(2905,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[2893]) ).
thf(707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk13 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[83,128]) ).
thf(708,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk17 ) ))]]) ).
thf(714,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[709]) ).
thf(28,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(1213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,1016]) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1213]) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[1214]) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,302]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[418]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk3 ) @ sk6 ) ),
inference(simp,[status(thm)],[419]) ).
thf(3568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,719]) ).
thf(3569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[3568]) ).
thf(3639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk3 ) ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[3569]) ).
thf(3664,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[3639]) ).
thf(33,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk2 ) @ ( A @ ( B @ sk3 ) @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(7307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,6047]) ).
thf(7308,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[7307]) ).
thf(7356,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 @ sk6 ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[7308]) ).
thf(7378,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[7356]) ).
thf(3056,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk3 ) @ ( C @ sk13 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,719]) ).
thf(3057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk3 ) @ ( C @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3056]) ).
thf(3058,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3057:[bind(A,$thf( H @ ( G @ sk3 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3198,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[3058]) ).
thf(10149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2836,1624]) ).
thf(10150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10149]) ).
thf(10151,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10150:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk6 ))]]) ).
thf(10247,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10151]) ).
thf(427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,142]) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk7 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[428]) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[455]) ).
thf(952,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk14 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[86,129]) ).
thf(953,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[952]) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[953:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk18 ) )),bind(D,$thf( I @ ( H @ sk15 ) )),bind(E,$thf( E ))]]) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[954]) ).
thf(3630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,993]) ).
thf(3631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3630]) ).
thf(3641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk15 ) ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3631]) ).
thf(3667,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[3641]) ).
thf(3027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,2912]) ).
thf(3028,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[3027]) ).
thf(3033,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) ) ),
inference(simp,[status(thm)],[3028]) ).
thf(32,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk1 ) @ ( A @ ( B @ sk2 ) @ id ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(3104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk1 ) @ ( A @ ( B @ sk2 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,90]) ).
thf(3105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk1 ) @ ( A @ ( B @ sk2 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[3104]) ).
thf(3106,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk2 ) @ ( B @ ( A @ sk1 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3105:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk2 ) )),bind(D,$thf( H @ ( G @ sk1 ) ))]]) ).
thf(3191,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk2 ) @ ( B @ ( A @ sk1 ) @ id ) ),
inference(simp,[status(thm)],[3106]) ).
thf(480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,463]) ).
thf(481,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[480]) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk17 ) @ sk6 ) ),
inference(simp,[status(thm)],[481]) ).
thf(4307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,3650]) ).
thf(4308,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4307]) ).
thf(4321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk13 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4308]) ).
thf(4327,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4321]) ).
thf(1138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,985]) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1138]) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk15 ) @ sk6 ) ),
inference(simp,[status(thm)],[1139]) ).
thf(6076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,6043]) ).
thf(6077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[6076]) ).
thf(6092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk7 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[6077]) ).
thf(6101,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6092]) ).
thf(2938,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,2901]) ).
thf(2939,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[2938]) ).
thf(2946,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[2939]) ).
thf(11984,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,11932]) ).
thf(11985,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[11984]) ).
thf(12044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[11985]) ).
thf(12063,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk19 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[12044]) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,1411]) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1414]) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= sk5 )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= sk5 ),
inference(simp,[status(thm)],[1421]) ).
thf(943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,142]) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[943]) ).
thf(979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk7 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[944]) ).
thf(989,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[979]) ).
thf(3062,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,90]) ).
thf(3063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3062]) ).
thf(3064,plain,
! [A: $i] : ( A @ sk12 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3063:[bind(A,$thf( E )),bind(B,$thf( E @ sk12 )),bind(C,$thf( E @ sk14 ))]]) ).
thf(3202,plain,
! [A: $i] : ( A @ sk12 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[3064]) ).
thf(4093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ sk14 @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3202,129]) ).
thf(4094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk12 @ ( A @ sk14 @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4093]) ).
thf(4095,plain,
! [B: $i,A: $i] :
~ ( B @ sk12 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[4094:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ sk12 )),bind(D,$thf( E ))]]) ).
thf(4174,plain,
! [B: $i,A: $i] :
~ ( B @ sk12 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[4095]) ).
thf(4287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,4174]) ).
thf(4288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4287]) ).
thf(4294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk12 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4288]) ).
thf(4301,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk12 ) ),
inference(simp,[status(thm)],[4294]) ).
thf(451,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( F @ sk7 @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[83,326]) ).
thf(452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ ( F @ sk7 @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[451]) ).
thf(453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ ( D @ sk7 @ sk17 ) @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( I )),bind(B,$thf( J @ sk7 )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ sk7 @ sk17 ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ ( D @ sk7 @ sk17 ) @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[453]) ).
thf(659,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ ( F @ sk7 @ sk17 ) @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,459]) ).
thf(660,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ ( F @ sk7 @ sk17 ) @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(679,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk7 ) )
| ( B
!= ( E @ ( F @ sk7 @ sk17 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[660]) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[679]) ).
thf(1687,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,463]) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1687]) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1688]) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,1016]) ).
thf(1602,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1601]) ).
thf(1644,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk4 ) )
!= sk5 ),
inference(simp,[status(thm)],[1602]) ).
thf(3581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,714]) ).
thf(3582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[3581]) ).
thf(3644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk17 ) ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[3582]) ).
thf(3671,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[3644]) ).
thf(12845,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( sk5 @ ( D @ ( E @ sk7 @ sk17 ) @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3826,11820]) ).
thf(12846,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( sk5 @ ( D @ ( E @ sk7 @ sk17 ) @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[12845]) ).
thf(12922,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= sk5 )
| ( A
!= ( D @ ( E @ sk7 @ sk17 ) ) )
| ( B != C ) ),
inference(simp,[status(thm)],[12846]) ).
thf(12955,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[12922]) ).
thf(6070,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,6043]) ).
thf(6071,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[6070]) ).
thf(6088,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk7 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[6071]) ).
thf(6097,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6088]) ).
thf(3533,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,3004]) ).
thf(3534,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[3533]) ).
thf(3541,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) ) ),
inference(simp,[status(thm)],[3534]) ).
thf(71,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ( ( A @ sk9 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[71,45]) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ( ( A @ sk9 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[1562]) ).
thf(1580,plain,
! [B: $i,A: $i] :
( ( ( A @ sk9 )
!= sk5 )
| ( A != B )
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[1563]) ).
thf(1588,plain,
! [A: $i] :
( ( ( A @ sk9 )
!= sk5 )
| ( A @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[1580]) ).
thf(3077,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk17 ) @ ( C @ sk13 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,714]) ).
thf(3078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk17 ) @ ( C @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3079,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3078:[bind(A,$thf( H @ ( G @ sk17 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[3079]) ).
thf(2854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,141]) ).
thf(2855,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2854]) ).
thf(2896,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk14 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2855]) ).
thf(2909,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[2896]) ).
thf(73,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
| ( A @ sk9 @ r1 ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(16811,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ $true
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[1569,2916]) ).
thf(16812,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[16811]) ).
thf(16813,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[16812:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B ))]]) ).
thf(16970,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ sk6 @ id ) ),
inference(simp,[status(thm)],[16813]) ).
thf(17829,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk8 @ ( sk5 @ sk6 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,16970]) ).
thf(17830,plain,
! [B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk8 @ ( sk5 @ sk6 @ id ) ) ),
inference(simp,[status(thm)],[17829]) ).
thf(17889,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk8 ) )
| ( A
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[17830]) ).
thf(17915,plain,
! [A: $i] :
( ( A @ sk8 )
!= ( sk5 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[17889]) ).
thf(227,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
!= ( I @ ( H @ ( G @ r4 ) ) ) )
| ( L @ ( K @ ( J @ r4 ) ) )
| ~ $true
| ~ ( L @ ( I @ id ) )
| ~ ( K @ ( H @ id ) )
| ~ ( J @ ( G @ id ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[27,27]) ).
thf(228,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
!= ( I @ ( H @ ( G @ r4 ) ) ) )
| ( L @ ( K @ ( J @ r4 ) ) )
| ~ ( L @ ( I @ id ) )
| ~ ( K @ ( H @ id ) )
| ~ ( J @ ( G @ id ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(229,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( G @ r4 ) ) )
| ~ ( I @ ( F @ id ) )
| ~ ( H @ ( E @ id ) )
| ~ ( G @ ( D @ id ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( D )),bind(H,$thf( E )),bind(I,$thf( F ))]]) ).
thf(237,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( G @ r4 ) ) )
| ~ ( I @ ( F @ id ) )
| ~ ( H @ ( E @ id ) )
| ~ ( G @ ( D @ id ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[86,118]) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[961]) ).
thf(963,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ r1 ),
inference(pattern_uni,[status(thm)],[962:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk15 ) )),bind(D,$thf( H @ ( G @ sk18 ) ))]]) ).
thf(983,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ r1 ),
inference(simp,[status(thm)],[963]) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,983]) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[1132]) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,302]) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[420]) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk3 ) @ sk6 ) ),
inference(simp,[status(thm)],[421]) ).
thf(1003,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ sk7 @ r2 ) ) )
| ~ ( E @ ( D @ sk4 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,689]) ).
thf(1004,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ sk7 @ r2 ) ) )
| ~ ( E @ ( D @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1003]) ).
thf(1005,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) @ r1 ),
inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( H )),bind(B,$thf( I @ sk7 )),bind(C,$thf( I )),bind(D,$thf( H @ ( I @ sk7 @ sk3 ) )),bind(E,$thf( E ))]]) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) @ r1 ),
inference(simp,[status(thm)],[1005]) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,1019]) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1694]) ).
thf(1698,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1695]) ).
thf(2478,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ( B @ sk8 @ ( C @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[73,64]) ).
thf(2479,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ( B @ sk8 @ ( C @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[2478]) ).
thf(2480,plain,
! [A: $i] :
( ( A @ sk10 @ sk8 @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[2479:[bind(A,$thf( E )),bind(B,$thf( E @ sk10 )),bind(C,$thf( E @ sk11 ))]]) ).
thf(2554,plain,
! [A: $i] :
( ( A @ sk10 @ sk8 @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[2480]) ).
thf(11679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ sk8 @ ( A @ sk11 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[2554,90]) ).
thf(11680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk10 @ sk8 @ ( A @ sk11 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[11679]) ).
thf(11681,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ sk8 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[11680:[bind(A,$thf( F )),bind(B,$thf( F @ sk11 )),bind(C,$thf( F @ sk10 @ sk8 ))]]) ).
thf(11737,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ sk8 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[11681]) ).
thf(168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( F @ r1 ) )
| ~ $true
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,22]) ).
thf(169,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( F @ r1 ) )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk7 @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ sk7 ))]]) ).
thf(176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk7 @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(4313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,3650]) ).
thf(4314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4313]) ).
thf(4322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk13 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[4314]) ).
thf(4328,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4322]) ).
thf(5306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( B @ ( A @ sk17 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2544,90]) ).
thf(5307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( B @ ( A @ sk17 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[5306]) ).
thf(5308,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[5307:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ sk17 ) )),bind(D,$thf( G @ sk8 ))]]) ).
thf(5350,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[5308]) ).
thf(1222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,1019]) ).
thf(1223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1222]) ).
thf(1226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[1223]) ).
thf(59,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ r3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(8487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk7 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,6524]) ).
thf(8488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk7 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[8487]) ).
thf(8517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk7 ) )
| ( ( A @ sk6 )
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[8488]) ).
thf(8534,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[8517]) ).
thf(11959,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,11932]) ).
thf(11960,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[11959]) ).
thf(12052,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[11960]) ).
thf(12067,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[12052]) ).
thf(4044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,3649]) ).
thf(4045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4044]) ).
thf(4053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk14 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4045]) ).
thf(4060,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4053]) ).
thf(224,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
!= ( H @ ( I @ ( G @ r4 ) ) ) )
| ~ ( K @ r1 )
| ~ ( K @ ( H @ id ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( J @ r1 )
| ~ $true
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[27,22]) ).
thf(225,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
!= ( H @ ( I @ ( G @ r4 ) ) ) )
| ~ ( K @ r1 )
| ~ ( K @ ( H @ id ) )
| ~ ( I @ ( J @ r2 ) )
| ~ ( J @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ r1 )
| ~ ( H @ ( F @ id ) )
| ~ ( E @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( D )),bind(H,$thf( F )),bind(I,$thf( E ))]]) ).
thf(236,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ r1 )
| ~ ( H @ ( F @ id ) )
| ~ ( E @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(645,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( F @ sk13 @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[83,327]) ).
thf(646,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ ( F @ sk13 @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ ( D @ sk7 @ sk17 ) @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[646:[bind(A,$thf( I )),bind(B,$thf( J @ sk7 )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ sk7 @ sk17 ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk13 @ ( C @ ( D @ sk7 @ sk17 ) @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[647]) ).
thf(795,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ ( F @ sk7 @ sk17 ) @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,652]) ).
thf(796,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ ( F @ sk7 @ sk17 ) @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[795]) ).
thf(801,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk13 ) )
| ( B
!= ( E @ ( F @ sk7 @ sk17 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[796]) ).
thf(804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[801]) ).
thf(9617,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4031,90]) ).
thf(9618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[9617]) ).
thf(9619,plain,
! [A: $i] : ( A @ sk6 @ ( A @ ( A @ sk7 @ sk20 ) @ id ) ),
inference(pattern_uni,[status(thm)],[9618:[bind(A,$thf( F )),bind(B,$thf( F @ sk6 )),bind(C,$thf( F @ ( F @ sk7 @ sk20 ) ))]]) ).
thf(9659,plain,
! [A: $i] : ( A @ sk6 @ ( A @ ( A @ sk7 @ sk20 ) @ id ) ),
inference(simp,[status(thm)],[9619]) ).
thf(8768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,994]) ).
thf(8769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[8768]) ).
thf(8822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk15 ) ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[8769]) ).
thf(8841,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[8822]) ).
thf(775,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ ( F @ sk7 @ sk3 ) @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,651]) ).
thf(776,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ ( F @ sk7 @ sk3 ) @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(782,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk13 ) )
| ( B
!= ( E @ ( F @ sk7 @ sk3 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[776]) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[782]) ).
thf(6466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,4011]) ).
thf(6467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6466]) ).
thf(6518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[6467]) ).
thf(6532,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk7 @ sk6 )
!= ( A @ ( B @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[6518]) ).
thf(2965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( D @ sk14 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2836,129]) ).
thf(2966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[2965]) ).
thf(2967,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[2966:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(3015,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[2967]) ).
thf(5175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ sk6 @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,3015]) ).
thf(5176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ sk6 @ ( C @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[5175]) ).
thf(5177,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[5176:[bind(A,$thf( G @ sk8 @ sk6 )),bind(B,$thf( E @ sk14 )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(5207,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[5177]) ).
thf(1631,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,304]) ).
thf(1632,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1631]) ).
thf(1638,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) )
!= sk5 ),
inference(simp,[status(thm)],[1632]) ).
thf(1218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,1019]) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1218]) ).
thf(1224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[1219]) ).
thf(6481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4011]) ).
thf(6482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6481]) ).
thf(6501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[6482]) ).
thf(6525,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ sk6 )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[6501]) ).
thf(7993,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk11 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ~ $true
| ( sk5 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[7393,90]) ).
thf(7994,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk11 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7993]) ).
thf(7995,plain,
( ( sk5 @ sk11 @ ( sk5 @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[7994:[bind(A,$thf( sk5 @ sk11 )),bind(B,$thf( sk5 ))]]) ).
thf(5992,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk7 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[35,130]) ).
thf(5993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[5992]) ).
thf(5994,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[5993:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(6059,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[5994]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( B @ r1 )
| ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
& ( ( A @ r1 )
| ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
& ( ( B @ r1 )
| ~ ( A @ r1 )
| ~ ( B @ ( A @ id ) ) )
& ( ( A @ r1 )
| ~ ( A @ r1 )
| ~ ( B @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[110]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( B @ r1 )
| ~ ( A @ r1 )
| ~ ( B @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[111]) ).
thf(6155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk7 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,6063]) ).
thf(6156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[6155]) ).
thf(6157,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[6156:[bind(A,$thf( F @ sk8 )),bind(B,$thf( E @ sk7 )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(6179,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[6157]) ).
thf(2882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,140]) ).
thf(2883,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2882]) ).
thf(2894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk13 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2883]) ).
thf(2906,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[2894]) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,140]) ).
thf(968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[967]) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk13 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[968]) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[980]) ).
thf(1140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,985]) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1140]) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk15 ) @ sk6 ) ),
inference(simp,[status(thm)],[1141]) ).
thf(38,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(miniscope,[status(thm)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(4279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,4174]) ).
thf(4280,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4279]) ).
thf(4293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk12 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4280]) ).
thf(4300,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk12 ) ),
inference(simp,[status(thm)],[4293]) ).
thf(162,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( F @ r1 ) )
| ~ $true
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,22]) ).
thf(163,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( F @ r1 ) )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk14 @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ sk14 ))]]) ).
thf(172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk14 @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(10184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[35,1624]) ).
thf(10185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10184]) ).
thf(10186,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10185:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(10236,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10186]) ).
thf(2936,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,2901]) ).
thf(2937,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[2936]) ).
thf(2943,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[2937]) ).
thf(2934,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,2901]) ).
thf(2935,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[2934]) ).
thf(2945,plain,
! [B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[2935]) ).
thf(5148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,3015]) ).
thf(5149,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[5148]) ).
thf(5190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 @ sk6 ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[5149]) ).
thf(5202,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[5190]) ).
thf(5895,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ ( E @ sk13 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,3813]) ).
thf(5896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ ( E @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[5895]) ).
thf(5897,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[5896:[bind(A,$thf( H @ ( J @ sk7 @ sk8 @ sk19 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( H )),bind(D,$thf( J )),bind(E,$thf( F ))]]) ).
thf(5920,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[5897]) ).
thf(3570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,917]) ).
thf(3571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3570]) ).
thf(3642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk17 ) ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3571]) ).
thf(3668,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[3642]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(103,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,463]) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[478]) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk17 ) @ sk6 ) ),
inference(simp,[status(thm)],[479]) ).
thf(2519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( C @ sk8 @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[35,64]) ).
thf(2520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( C @ sk8 @ ( D @ id ) ) ),
inference(simp,[status(thm)],[2519]) ).
thf(2521,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[2520:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(2542,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[2521]) ).
thf(104,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) ) )
| ~ ( C @ ( A @ id ) ) ),
inference(miniscope,[status(thm)],[103]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ r2 ) )
| ~ ( D @ ( C @ r2 ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) )
& ( ( B @ ( A @ r2 ) )
| ~ ( D @ ( C @ r2 ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) )
& ( ( D @ ( C @ r2 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) )
& ( ( B @ ( A @ r2 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[104]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ r2 ) )
| ~ ( D @ ( C @ r2 ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,140]) ).
thf(438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[437]) ).
thf(456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk13 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[438]) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[456]) ).
thf(3031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,2912]) ).
thf(3032,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[3031]) ).
thf(3034,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) ) ),
inference(simp,[status(thm)],[3032]) ).
thf(230,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( E @ ( B @ id ) )
!= ( D @ ( A @ id ) ) )
| ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ r4 ) ) )
| ~ ( B @ ( A @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ r4 ) ) )
| ~ ( B @ ( A @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(2921,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,2914]) ).
thf(2922,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ r1 ) ),
inference(simp,[status(thm)],[2921]) ).
thf(2928,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[2922]) ).
thf(194,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,173]) ).
thf(195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk7 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( F )),bind(B,$thf( F @ sk7 ))]]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk7 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,304]) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1689]) ).
thf(1699,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1690]) ).
thf(5362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,3014]) ).
thf(5363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[5362]) ).
thf(5367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk7 ) )
| ( B
!= ( E @ sk7 @ sk8 @ sk6 ) )
| ( A != C ) ),
inference(simp,[status(thm)],[5363]) ).
thf(5372,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[5367]) ).
thf(3413,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,3012]) ).
thf(3414,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3413]) ).
thf(3423,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[3414]) ).
thf(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,142]) ).
thf(279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk7 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[279]) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[299]) ).
thf(2988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,140]) ).
thf(2989,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2988]) ).
thf(2999,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk13 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2989]) ).
thf(3016,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[2999]) ).
thf(4285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,4174]) ).
thf(4286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4285]) ).
thf(4297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk12 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[4286]) ).
thf(4304,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk12 ) ),
inference(simp,[status(thm)],[4297]) ).
thf(3149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk15 ) @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,993]) ).
thf(3150,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk15 ) @ ( C @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3149]) ).
thf(3151,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3150:[bind(A,$thf( H @ ( G @ sk15 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3178,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[3151]) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[79,42]) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[1275]) ).
thf(1277,plain,
! [A: $i] : ( sk5 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( C )),bind(B,$thf( C @ sk14 ))]]) ).
thf(1294,plain,
! [A: $i] : ( sk5 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[1277]) ).
thf(3164,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk14 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1294,90]) ).
thf(3165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk14 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3164]) ).
thf(3166,plain,
! [A: $i] : ( A @ sk14 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[3165:[bind(A,$thf( D )),bind(B,$thf( D @ sk14 )),bind(C,$thf( sk5 ))]]) ).
thf(3188,plain,
! [A: $i] : ( A @ sk14 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[3166]) ).
thf(12015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3188,11932]) ).
thf(12016,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12015]) ).
thf(12034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12016]) ).
thf(12060,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[12034]) ).
thf(1635,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,1019]) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1635]) ).
thf(1643,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ sk7 @ sk3 ) @ sk4 ) )
!= sk5 ),
inference(simp,[status(thm)],[1636]) ).
thf(1717,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,1707]) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1717]) ).
thf(1722,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( sk5 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1722]) ).
thf(7497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,5920]) ).
thf(7498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[7497]) ).
thf(7555,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk13 ) )
| ( A
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[7498]) ).
thf(7558,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk13 ) ),
inference(simp,[status(thm)],[7555]) ).
thf(203,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( E @ ( B @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( F @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,27]) ).
thf(204,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( E @ ( B @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( F @ ( C @ id ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,466]) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) ),
inference(simp,[status(thm)],[467]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(4317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,3650]) ).
thf(4318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4317]) ).
thf(4325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk13 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4318]) ).
thf(4331,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4325]) ).
thf(3419,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,3012]) ).
thf(3420,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[3419]) ).
thf(3427,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[3420]) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,302]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[422]) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk3 ) @ sk6 ) ),
inference(simp,[status(thm)],[423]) ).
thf(10168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[86,1624]) ).
thf(10169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10168]) ).
thf(10170,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10169:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk18 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(10269,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10170]) ).
thf(3634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,914]) ).
thf(3635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3634]) ).
thf(3645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk3 ) ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3635]) ).
thf(3672,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[3645]) ).
thf(3954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk13 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,2908]) ).
thf(3955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3954]) ).
thf(3956,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[3955:[bind(A,$thf( F @ sk8 )),bind(B,$thf( E @ sk13 )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(3981,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[3956]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,983]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[1130]) ).
thf(5981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk7 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[86,130]) ).
thf(5982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[5981]) ).
thf(5983,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[5982:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk18 ) )),bind(D,$thf( I @ ( H @ sk15 ) )),bind(E,$thf( E ))]]) ).
thf(6056,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[5983]) ).
thf(12339,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3184,11951]) ).
thf(12340,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12339]) ).
thf(12407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12340]) ).
thf(12434,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[12407]) ).
thf(2932,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,2901]) ).
thf(2933,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[2932]) ).
thf(2942,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[2933]) ).
thf(330,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ $true
| ~ ( F @ sk7 @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,326]) ).
thf(331,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ sk7 @ r2 ) ) )
| ~ ( F @ sk7 @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ ( D @ sk7 @ sk3 ) @ ( A @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( I )),bind(B,$thf( J @ sk7 )),bind(C,$thf( C )),bind(D,$thf( I @ ( J @ sk7 @ sk3 ) )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ sk7 @ ( C @ ( D @ sk7 @ sk3 ) @ ( A @ r4 ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(675,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ ( F @ sk7 @ sk3 ) @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,336]) ).
thf(676,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk7 @ ( E @ ( F @ sk7 @ sk3 ) @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[675]) ).
thf(682,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk7 ) )
| ( B
!= ( E @ ( F @ sk7 @ sk3 ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[676]) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[682]) ).
thf(5879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,3813]) ).
thf(5880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[5879]) ).
thf(5913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[5880]) ).
thf(5927,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk19 ) @ sk6 )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[5913]) ).
thf(1220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,1019]) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1220]) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ ( C @ ( D @ sk7 @ sk3 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[1221]) ).
thf(179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ $true
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,173]) ).
thf(180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ sk13 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ sk13 ))]]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( D @ sk13 @ r2 ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(1627,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,983]) ).
thf(1628,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1627]) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) )
!= sk5 ),
inference(simp,[status(thm)],[1628]) ).
thf(153,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( F @ r1 ) )
| ~ $true
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,22]) ).
thf(154,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( F @ r1 ) )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk13 @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ sk13 ))]]) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk13 @ ( B @ id ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(7480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,5920]) ).
thf(7481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[7480]) ).
thf(7549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk13 ) )
| ( A
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[7481]) ).
thf(7568,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ sk7 @ sk8 @ sk19 ) )
!= ( A @ sk13 ) ),
inference(simp,[status(thm)],[7549]) ).
thf(12722,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ ( F @ sk7 @ sk17 ) @ ( D @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,11820]) ).
thf(12723,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( sk5 @ ( E @ ( F @ sk7 @ sk17 ) @ ( D @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[12722]) ).
thf(12724,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk19 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[12723:[bind(A,$thf( A )),bind(B,$thf( H @ ( I @ sk7 @ sk17 ) )),bind(C,$thf( sk5 )),bind(D,$thf( A )),bind(E,$thf( H )),bind(F,$thf( I ))]]) ).
thf(12733,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ sk7 @ sk17 ) @ sk19 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[12724]) ).
thf(3531,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,3004]) ).
thf(3532,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3531]) ).
thf(3544,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk4 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[3532]) ).
thf(3143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( B @ ( A @ sk3 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2542,90]) ).
thf(3144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( B @ ( A @ sk3 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[3143]) ).
thf(3145,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[3144:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ sk3 ) )),bind(D,$thf( G @ sk8 ))]]) ).
thf(3174,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[3145]) ).
thf(5535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ sk6 @ ( C @ sk13 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,3019]) ).
thf(5536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ sk6 @ ( C @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[5535]) ).
thf(5537,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[5536:[bind(A,$thf( G @ sk8 @ sk6 )),bind(B,$thf( E @ sk13 )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(5560,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[5537]) ).
thf(5133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,3015]) ).
thf(5134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[5133]) ).
thf(5191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ sk8 @ sk6 )
!= sk5 )
| ( A
!= ( B @ sk14 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[5134]) ).
thf(5203,plain,
! [B: $i,A: $i] :
( ( ( B @ sk8 @ sk6 )
!= sk5 )
| ~ ( A @ sk14 @ r1 ) ),
inference(simp,[status(thm)],[5191]) ).
thf(8247,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[5203,79]) ).
thf(8248,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[8247]) ).
thf(12378,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3188,11951]) ).
thf(12379,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ ( sk5 @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12378]) ).
thf(12391,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12379]) ).
thf(12424,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[12391]) ).
thf(6125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,6063]) ).
thf(6126,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6125]) ).
thf(6178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[6126]) ).
thf(6188,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[6178]) ).
thf(1685,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1569,983]) ).
thf(1686,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1685]) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1686]) ).
thf(1418,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,1411]) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1418]) ).
thf(1423,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= sk5 )
| ( B != C ) ),
inference(simp,[status(thm)],[1419]) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= sk5 ),
inference(simp,[status(thm)],[1423]) ).
thf(150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ $true
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,22]) ).
thf(151,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( E @ sk13 @ r2 ) )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ sk13 ))]]) ).
thf(175,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( E @ sk13 @ r2 ) )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,141]) ).
thf(946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[945]) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk14 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[946]) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[981]) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,463]) ).
thf(477,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[476]) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk17 ) @ sk6 ) ),
inference(simp,[status(thm)],[477]) ).
thf(1211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,1016]) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[1211]) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ ( C @ ( D @ sk7 @ sk17 ) @ sk4 ) ) ),
inference(simp,[status(thm)],[1212]) ).
thf(8468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,6524]) ).
thf(8469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[8468]) ).
thf(8516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk7 ) )
| ( A
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[8469]) ).
thf(8533,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk7 ) ),
inference(simp,[status(thm)],[8516]) ).
thf(4034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,3649]) ).
thf(4035,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4034]) ).
thf(4054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk14 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4035]) ).
thf(4061,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4054]) ).
thf(2841,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,1411]) ).
thf(2842,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2841]) ).
thf(2895,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 )
!= sk5 )
| ( A != B ) ),
inference(simp,[status(thm)],[2842]) ).
thf(2907,plain,
! [A: $i] :
( ( A @ sk8 )
!= sk5 ),
inference(simp,[status(thm)],[2895]) ).
thf(1596,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,302]) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1596]) ).
thf(1646,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[1597]) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true
| ~ ( B @ ( A @ sk7 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[1547,689]) ).
thf(1612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sk4 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ ( B @ ( A @ sk7 @ r2 ) ) ),
inference(simp,[status(thm)],[1611]) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ sk4 ) )
!= sk5 )
| ~ ( B @ ( A @ sk7 @ r2 ) ) ),
inference(simp,[status(thm)],[1612]) ).
thf(5849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,3813]) ).
thf(5850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) @ ( D @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[5849]) ).
thf(5901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[5850]) ).
thf(5922,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk13 )
!= ( A @ ( B @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[5901]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A @ r1 )
| ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[111]) ).
thf(159,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ $true
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,22]) ).
thf(160,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( C @ id ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( E @ sk14 @ r2 ) )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ sk14 ))]]) ).
thf(171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( E @ sk14 @ r2 ) )
| ~ ( B @ ( C @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(2940,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,2901]) ).
thf(2941,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[2940]) ).
thf(2944,plain,
! [B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[2941]) ).
thf(82,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk16 ) @ ( A @ ( B @ sk17 ) @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,1707]) ).
thf(1716,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1715]) ).
thf(1721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( sk5 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[1716]) ).
thf(1725,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1721]) ).
thf(36,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk1 ) @ ( A @ ( A @ ( B @ sk4 ) @ r3 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(2919,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,2914]) ).
thf(2920,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ r1 ) ),
inference(simp,[status(thm)],[2919]) ).
thf(2930,plain,
! [B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[2920]) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,983]) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) ),
inference(simp,[status(thm)],[1127]) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[1128]) ).
thf(1603,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1547,985]) ).
thf(1604,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1603]) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[1604]) ).
thf(4806,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,3011]) ).
thf(4807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[4806]) ).
thf(4811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk13 ) )
| ( B
!= ( E @ sk7 @ sk8 @ sk6 ) )
| ( A != C ) ),
inference(simp,[status(thm)],[4807]) ).
thf(4816,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[4811]) ).
thf(7514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk13 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,5920]) ).
thf(7515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk13 @ ( C @ ( D @ sk7 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[7514]) ).
thf(7554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk13 ) )
| ( ( A @ sk6 )
!= ( C @ ( D @ sk7 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[7515]) ).
thf(7557,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( B @ ( C @ sk7 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[7554]) ).
thf(6018,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ ( E @ sk7 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[83,130]) ).
thf(6019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( E @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6018]) ).
thf(6020,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[6019:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk17 ) ))]]) ).
thf(6035,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[6020]) ).
thf(13681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,6035]) ).
thf(13682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[13681]) ).
thf(13746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk17 ) ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[13682]) ).
thf(13765,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[13746]) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,466]) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) ),
inference(simp,[status(thm)],[469]) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[470]) ).
thf(3417,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,3012]) ).
thf(3418,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3417]) ).
thf(3424,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ sk8 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[3418]) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,304]) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[409]) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ r2 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(8803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk15 ) @ ( C @ sk13 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,994]) ).
thf(8804,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk15 ) @ ( C @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[8803]) ).
thf(8805,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[8804:[bind(A,$thf( H @ ( G @ sk15 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(8833,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[8805]) ).
thf(232,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( F @ ( C @ id ) )
!= ( E @ ( B @ id ) ) )
| ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ r4 ) ) )
| ~ ( B @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( A )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ r4 ) ) )
| ~ ( B @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(206,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( F @ ( C @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ $true
| ~ ( E @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[88,27]) ).
thf(207,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( F @ ( C @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( D @ r4 ) ) )
| ~ ( C @ ( A @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( D @ r4 ) ) )
| ~ ( C @ ( A @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(4277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,4174]) ).
thf(4278,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4277]) ).
thf(4296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk12 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4278]) ).
thf(4303,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk12 ) ),
inference(simp,[status(thm)],[4296]) ).
thf(3876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,2904]) ).
thf(3877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3876]) ).
thf(3878,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[3877:[bind(A,$thf( F @ sk8 )),bind(B,$thf( E @ sk14 )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(3897,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[3878]) ).
thf(3415,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,3012]) ).
thf(3416,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3415]) ).
thf(3426,plain,
! [B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ sk8 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[3416]) ).
thf(10121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[2837,1624]) ).
thf(10122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10121]) ).
thf(10123,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10122:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(10237,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10123]) ).
thf(12347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3176,11951]) ).
thf(12348,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[12347]) ).
thf(12400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[12348]) ).
thf(12431,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk7 @ sk8 @ sk6 @ sk19 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[12400]) ).
thf(12860,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3826,2900]) ).
thf(12861,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk13 @ ( E @ sk7 @ sk8 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[12860]) ).
thf(12914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( D @ sk13 ) )
| ( A
!= ( E @ sk7 @ sk8 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[12861]) ).
thf(12944,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk19 ) )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[12914]) ).
thf(13842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk15 ) @ ( C @ sk7 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,6056]) ).
thf(13843,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk15 ) @ ( C @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[13842]) ).
thf(13844,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[13843:[bind(A,$thf( H @ ( G @ sk15 ) )),bind(B,$thf( F @ sk7 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(13877,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[13844]) ).
thf(2960,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2836,141]) ).
thf(2961,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2960]) ).
thf(3002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk14 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2961]) ).
thf(3020,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[3002]) ).
thf(182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,173]) ).
thf(183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk13 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( F )),bind(B,$thf( F @ sk13 ))]]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk13 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(156,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( F @ ( C @ id ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,22]) ).
thf(157,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( F @ ( C @ id ) ) )
| ~ ( F @ r1 )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk6 @ ( B @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ sk6 )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( D @ sk6 @ ( B @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(6068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,6043]) ).
thf(6069,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[6068]) ).
thf(6090,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk7 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[6069]) ).
thf(6099,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6090]) ).
thf(3535,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,3004]) ).
thf(3536,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[3535]) ).
thf(3543,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ ( C @ sk7 @ sk8 @ sk6 @ sk4 ) ) ),
inference(simp,[status(thm)],[3536]) ).
thf(4305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2837,3650]) ).
thf(4306,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4305]) ).
thf(4324,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk13 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4306]) ).
thf(4330,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4324]) ).
thf(12843,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3826,3014]) ).
thf(12844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( D @ sk7 @ ( E @ sk7 @ sk8 @ sk6 @ ( C @ r4 ) ) ) ),
inference(simp,[status(thm)],[12843]) ).
thf(12917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( D @ sk7 ) )
| ( A
!= ( E @ sk7 @ sk8 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[12844]) ).
thf(12948,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ sk7 @ sk8 @ sk6 @ sk19 ) )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[12917]) ).
thf(13724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk17 ) @ ( C @ sk7 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,6035]) ).
thf(13725,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk17 ) @ ( C @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[13724]) ).
thf(13726,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[13725:[bind(A,$thf( H @ ( G @ sk17 ) )),bind(B,$thf( F @ sk7 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(13760,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[13726]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,141]) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk14 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[281]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[301]) ).
thf(3025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,2912]) ).
thf(3026,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) @ r1 ) ),
inference(simp,[status(thm)],[3025]) ).
thf(3035,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ ( C @ sk7 @ sk8 @ sk4 ) ) ),
inference(simp,[status(thm)],[3026]) ).
thf(4289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,4174]) ).
thf(4290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4289]) ).
thf(4291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk12 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4290]) ).
thf(4298,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk12 ) ),
inference(simp,[status(thm)],[4291]) ).
thf(3059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk17 ) @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,917]) ).
thf(3060,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk17 ) @ ( C @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3059]) ).
thf(3061,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3060:[bind(A,$thf( H @ ( G @ sk17 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3200,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[3061]) ).
thf(39358,plain,
$false,
inference(e,[status(thm)],[1411,5561,4262,2544,88,1586,7373,6063,3813,2908,994,3012,1591,4326,5691,202,308,1569,2837,1142,3017,1426,12939,142,4058,3826,12421,2901,11816,3004,12714,4011,3649,3562,1640,174,3545,42,417,9027,1645,12960,1724,6102,12062,10248,651,37,1703,1287,2916,3425,12943,719,3689,11817,110,917,3542,460,52,3204,1704,46,93,5925,416,2929,3014,1641,78,4008,475,3983,238,12436,84,8532,4055,3036,89,243,1697,6103,74,12430,1215,1696,3184,3899,60,2910,15345,7393,6047,3186,11820,102,4031,3037,3011,6529,85,201,4059,2905,714,302,28,1217,70,424,21,3664,33,7378,197,3198,97,10247,461,3667,3033,3191,484,11813,6043,4327,1624,1143,6101,2946,12063,1425,53,989,3176,3650,141,4301,77,686,1700,1644,96,1016,3671,12955,6097,3541,2836,2900,173,129,1588,985,3173,2909,73,17915,128,237,6524,1135,425,2904,1698,11737,45,64,689,32,34,176,22,4328,5350,1226,27,59,118,71,8534,54,12067,11951,466,4060,236,804,1707,9659,8841,787,6532,49,5207,1638,1224,86,6525,7995,6059,113,6179,11932,2906,990,76,1144,39,4300,3182,172,10236,2943,2945,5202,5920,3668,103,140,91,483,2542,108,462,3034,240,2928,198,983,130,1699,5372,3423,306,3016,4304,3178,35,12060,16970,1643,1726,7558,241,80,473,4331,2914,3427,426,10269,3672,3981,1134,6056,12434,2942,1547,48,690,5927,1225,327,1647,993,67,199,1637,177,7568,3202,12733,3544,3174,3019,50,463,5560,8248,2903,12424,6188,336,1702,1427,72,175,991,99,87,482,1216,1289,3188,8533,4061,2907,1646,1639,40,652,23,5922,2554,304,55,7082,114,3561,171,2944,914,2912,1294,82,1725,36,146,30,51,2930,1133,1642,4816,3015,7557,79,13765,474,3424,6952,415,326,107,8833,239,242,4303,3897,3196,3426,10237,12431,12944,13877,1019,459,3020,200,178,6099,3543,4330,68,12948,62,90,12203,83,13760,309,4174,3035,4298,6035,3200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN082+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n015.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 04:34:58 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.27/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.80/1.57 % [INFO] Parsing done (306ms).
% 1.80/1.59 % [INFO] Running in sequential loop mode.
% 2.99/2.18 % [INFO] eprover registered as external prover.
% 2.99/2.19 % [INFO] Scanning for conjecture ...
% 3.29/2.33 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.45/2.42 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.71/2.50 % [INFO] Problem is first-order (TPTP FOF).
% 3.71/2.51 % [INFO] Type checking passed.
% 3.71/2.52 % [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 ...
% 106.06/24.89 % External prover 'e' found a proof!
% 106.06/24.89 % [INFO] Killing All external provers ...
% 106.06/24.89 % Time passed: 24209ms (effective reasoning time: 23289ms)
% 106.06/24.89 % 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)>
% 106.06/24.89 % Axioms used in derivation (18): axiom_7, axiom_10, axiom_1a, axiom_4a, axiom_2, axiom_6, axiom_3, axiom_7a, axiom_8, axiom_6a, axiom_5, axiom_3a, axiom_11, axiom_9, axiom_4, axiom_1, axiom_2a, axiom_5a
% 106.06/24.89 % No. of inferences in proof: 1257
% 106.06/24.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24209 ms resp. 23289 ms w/o parsing
% 108.56/25.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 108.56/25.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------