%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN086+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 08:18:43 AM UTC 2026
% Result : Theorem 169.47s 42.33s
% Output : Refutation 165.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of formulae : 1840 ( 741 unt; 0 typ; 20 def)
% Number of atoms : 5875 (1539 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 20063 (3471 ~;2075 |; 158 &;14359 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 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 : 6170 ( 29 ^;6054 !; 67 ?;6170 :)
% ( 0 !>; 0 ?*; 0 @-; 20 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $o ).
thf(r2_decl,type,
r2: $i > $i > $o ).
thf(r4_decl,type,
r4: $i > $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(12,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
file('/export/starexec/sandbox/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(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox/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(3317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true
| ( A @ sk9 @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[70,90]) ).
thf(3318,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3317]) ).
thf(3319,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[3318:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk11 ))]]) ).
thf(3428,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3319]) ).
thf(6,axiom,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
file('/export/starexec/sandbox/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(45,plain,
! [A: $i] :
( ~ ( sk5 @ ( A @ id ) )
| ( A @ r1 ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(24961,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[3428,45]) ).
thf(24962,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[24961]) ).
thf(24963,plain,
( ( sk5 @ sk11 @ r1 )
| ( sk5 @ sk9 @ ( sk5 @ id ) ) ),
inference(pattern_uni,[status(thm)],[24962:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk11 ))]]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
file('/export/starexec/sandbox/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(3377,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(3378,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3377]) ).
thf(3379,plain,
! [A: $i] : ( A @ sk6 @ ( A @ id ) ),
inference(pattern_uni,[status(thm)],[3378:[bind(A,$thf( D )),bind(B,$thf( D @ sk6 )),bind(C,$thf( D ))]]) ).
thf(3425,plain,
! [A: $i] : ( A @ sk6 @ ( A @ id ) ),
inference(simp,[status(thm)],[3379]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox/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(3852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,54]) ).
thf(3853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[3852]) ).
thf(3854,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk6 @ ( A @ r2 ) )
| ~ ( B @ r1 ) ),
inference(pattern_uni,[status(thm)],[3853:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ sk6 )),bind(D,$thf( E ))]]) ).
thf(3883,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk6 @ ( A @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[3854]) ).
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/sandbox/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(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/sandbox/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(85,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( A @ id ) ),
file('/export/starexec/sandbox/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(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(1038,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)],[85,118]) ).
thf(1039,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)],[1038]) ).
thf(1040,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ r1 ),
inference(pattern_uni,[status(thm)],[1039:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk15 ) )),bind(D,$thf( H @ ( G @ sk18 ) ))]]) ).
thf(1071,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ r1 ),
inference(simp,[status(thm)],[1040]) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,1071]) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) ),
inference(simp,[status(thm)],[1185]) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[1186]) ).
thf(79,plain,
! [A: $i] : ( A @ sk14 @ r1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 ) ),
inference(paramod_ordered,[status(thm)],[88,45]) ).
thf(1638,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 ) ),
inference(simp,[status(thm)],[1637]) ).
thf(1639,plain,
sk5 @ r1,
inference(pattern_uni,[status(thm)],[1638:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 ))]]) ).
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/sandbox/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(34,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk2 ) @ ( A @ ( B @ sk3 ) @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(36,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(1,conjecture,
? [A: $i] :
( ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ( A @ ( B @ ( C @ r4 ) ) )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ r2 ) )
& ( C @ r1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimesoneidzero) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ( A @ ( B @ ( C @ r4 ) ) )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ r2 ) )
& ( C @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ( A @ ( B @ ( C @ r4 ) ) )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ r2 ) )
& ( C @ r1 ) ) ) ),
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 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(cnf,[status(esa)],[21]) ).
thf(147,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( F @ ( B @ id ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
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 @ ( B @ id ) ) )
| ~ ( F @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[147]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[149]) ).
thf(304,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ r2 ) ) )
| ~ ( C @ r1 )
| ~ ( C @ ( D @ ( F @ r4 ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( E @ r1 ) ),
inference(paramod_ordered,[status(thm)],[36,184]) ).
thf(305,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ r2 ) ) )
| ~ ( C @ r1 )
| ~ ( C @ ( D @ ( F @ r4 ) ) )
| ~ ( F @ r1 )
| ~ ( E @ r1 ) ),
inference(simp,[status(thm)],[304]) ).
thf(306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( D @ ( C @ sk3 ) @ ( B @ r4 ) ) )
| ~ ( B @ r1 )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ sk3 ) )),bind(E,$thf( G ))]]) ).
thf(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( D @ ( C @ sk3 ) @ ( B @ r4 ) ) )
| ~ ( B @ r1 )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[306]) ).
thf(38290,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk2 ) @ ( A @ ( B @ sk3 ) @ ( A @ r4 ) ) )
!= ( C @ ( F @ ( E @ sk3 ) @ ( D @ r4 ) ) ) )
| ~ ( C @ r1 )
| ~ $true
| ~ ( D @ r1 )
| ~ ( E @ r1 ) ),
inference(paramod_ordered,[status(thm)],[34,326]) ).
thf(38291,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk2 ) @ ( A @ ( B @ sk3 ) @ ( A @ r4 ) ) )
!= ( C @ ( F @ ( E @ sk3 ) @ ( D @ r4 ) ) ) )
| ~ ( C @ r1 )
| ~ ( D @ r1 )
| ~ ( E @ r1 ) ),
inference(simp,[status(thm)],[38290]) ).
thf(38292,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk2 ) @ r1 )
| ~ ( B @ r1 )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[38291:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk2 ) )),bind(D,$thf( H )),bind(E,$thf( G )),bind(F,$thf( H ))]]) ).
thf(38380,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ sk2 ) @ r1 )
| ~ ( B @ r1 )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[38292]) ).
thf(39017,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( A @ sk2 ) @ r1 )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[1639,38380]) ).
thf(39018,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( A @ sk2 ) @ r1 )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[39017]) ).
thf(39019,plain,
! [A: $i] :
( ~ ( sk5 @ ( A @ sk2 ) @ r1 )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[39018:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(39079,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( sk5 @ ( B @ sk2 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,39019]) ).
thf(39080,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( sk5 @ ( B @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39079]) ).
thf(39081,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk14 @ sk2 ) @ r1 ),
inference(pattern_uni,[status(thm)],[39080:[bind(A,$thf( C )),bind(B,$thf( C @ sk14 ))]]) ).
thf(39098,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk14 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[39081]) ).
thf(78,plain,
! [A: $i] : ( A @ sk14 @ ( A @ sk12 @ id ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(3290,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(3291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3290]) ).
thf(3292,plain,
! [A: $i] : ( A @ sk12 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3291:[bind(A,$thf( E )),bind(B,$thf( E @ sk12 )),bind(C,$thf( E @ sk14 ))]]) ).
thf(3413,plain,
! [A: $i] : ( A @ sk12 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[3292]) ).
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(4438,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)],[3413,129]) ).
thf(4439,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)],[4438]) ).
thf(4440,plain,
! [B: $i,A: $i] :
~ ( B @ sk12 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[4439:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ sk12 )),bind(D,$thf( E ))]]) ).
thf(4513,plain,
! [B: $i,A: $i] :
~ ( B @ sk12 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[4440]) ).
thf(4710,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)],[85,4513]) ).
thf(4711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4710]) ).
thf(4722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk12 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[4711]) ).
thf(4729,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk12 ) ),
inference(simp,[status(thm)],[4722]) ).
thf(317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( E @ r1 )
| ~ ( D @ ( E @ id ) ) ),
inference(paramod_ordered,[status(thm)],[36,54]) ).
thf(318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( E @ r1 )
| ~ ( D @ ( E @ id ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( B @ sk3 ) @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( C @ ( B @ sk3 ) @ ( A @ id ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 ) ),
inference(paramod_ordered,[status(thm)],[48,45]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1664,plain,
sk5 @ sk6 @ r1,
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( A @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,118]) ).
thf(1785,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1784]) ).
thf(1786,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[1785:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B ))]]) ).
thf(1821,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[1786]) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,1821]) ).
thf(1832,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1831]) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( sk5 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[1832]) ).
thf(1840,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1836]) ).
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/sandbox/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(206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[79,184]) ).
thf(207,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk14 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( F )),bind(B,$thf( F @ sk14 ))]]) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk14 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[208]) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ r1 ) )
| ~ ( E @ sk14 @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,218]) ).
thf(335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ r1 ) )
| ~ ( E @ sk14 @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[334]) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ sk14 @ ( A @ ( B @ r4 ) ) )
| ~ ( B @ r1 )
| ~ ( A @ ( D @ sk13 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ sk13 ))]]) ).
thf(358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ sk14 @ ( A @ ( B @ r4 ) ) )
| ~ ( B @ r1 )
| ~ ( A @ ( D @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[336]) ).
thf(375,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( F @ sk13 @ r2 ) ) )
| ~ ( E @ sk14 @ ( C @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,358]) ).
thf(376,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( F @ sk13 @ r2 ) ) )
| ~ ( E @ sk14 @ ( C @ ( D @ r4 ) ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[375]) ).
thf(377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( A @ r4 ) ) )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[376:[bind(A,$thf( I )),bind(B,$thf( J @ sk13 )),bind(C,$thf( I @ ( J @ sk13 @ sk3 ) )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( J ))]]) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( A @ r4 ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[377]) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( A @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,384]) ).
thf(1767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[1766]) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[1767:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ),
inference(simp,[status(thm)],[1768]) ).
thf(4045,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,1817]) ).
thf(4046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[4045]) ).
thf(4047,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ sk6 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[4046:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( I @ ( J @ sk13 @ sk3 ) )),bind(C,$thf( K @ sk14 )),bind(D,$thf( K )),bind(E,$thf( I )),bind(F,$thf( J ))]]) ).
thf(4087,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ sk6 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[4047]) ).
thf(29743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4087]) ).
thf(29744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[29743]) ).
thf(29821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[29744]) ).
thf(29876,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( sk5 @ sk6 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[29821]) ).
thf(71,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(3359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk9 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[71,90]) ).
thf(3360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk9 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[3359]) ).
thf(3361,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ id ) )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[3360:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk9 ))]]) ).
thf(3416,plain,
! [A: $i] :
( ( A @ ( A @ sk9 @ id ) )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[3361]) ).
thf(33484,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[3416,45]) ).
thf(33485,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk9 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[33484]) ).
thf(33486,plain,
( ( sk5 @ sk9 @ r1 )
| ( sk5 @ sk11 @ ( sk5 @ sk10 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[33485:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk9 ))]]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox/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(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ( A @ sk8 @ ( B @ id ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(35027,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk11 @ ( sk5 @ sk10 @ r2 ) )
!= ( B @ ( A @ r2 ) ) )
| ~ $true
| ( A @ sk8 @ ( B @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[33486,64]) ).
thf(35028,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk11 @ ( sk5 @ sk10 @ r2 ) )
!= ( B @ ( A @ r2 ) ) )
| ( A @ sk8 @ ( B @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[35027]) ).
thf(35029,plain,
( ( sk5 @ sk10 @ sk8 @ ( sk5 @ sk11 @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[35028:[bind(A,$thf( sk5 @ sk10 )),bind(B,$thf( sk5 @ sk11 ))]]) ).
thf(983,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)],[36,129]) ).
thf(984,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)],[983]) ).
thf(985,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[984:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(992,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[985]) ).
thf(3392,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)],[90,992]) ).
thf(3393,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)],[3392]) ).
thf(3394,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3393:[bind(A,$thf( H @ ( G @ sk3 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3399,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[3394]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk8 @ ( B @ id ) )
| ( B @ ( A @ r2 ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(3022,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(3023,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3022]) ).
thf(3024,plain,
! [A: $i] : ( A @ sk8 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[3023:[bind(A,$thf( E @ sk8 )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk6 ))]]) ).
thf(3042,plain,
! [A: $i] : ( A @ sk8 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[3024]) ).
thf(49,plain,
! [A: $i] : ( A @ sk7 @ r1 ),
inference(cnfConj,[status(thm)],[47]) ).
thf(372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ r1 ) )
| ~ ( D @ sk14 @ ( B @ ( C @ r4 ) ) )
| ~ $true
| ~ ( B @ ( E @ sk13 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[49,358]) ).
thf(373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ r1 ) )
| ~ ( D @ sk14 @ ( B @ ( C @ r4 ) ) )
| ~ ( B @ ( E @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[372]) ).
thf(374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( A @ ( D @ sk7 @ r4 ) ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[373:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ sk7 ))]]) ).
thf(383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( A @ ( D @ sk7 @ r4 ) ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(3212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk7 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,383]) ).
thf(3213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3212]) ).
thf(3214,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ sk6 @ ( B @ sk7 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3213:[bind(A,$thf( I @ sk13 )),bind(B,$thf( I @ sk13 @ sk8 @ sk6 )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( E ))]]) ).
thf(3234,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ sk6 @ ( B @ sk7 @ r4 ) ) ),
inference(simp,[status(thm)],[3214]) ).
thf(8933,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ sk6 @ ( E @ sk7 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,3234]) ).
thf(8934,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ sk6 @ ( E @ sk7 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[8933]) ).
thf(8935,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[8934:[bind(A,$thf( G @ sk7 )),bind(B,$thf( J @ sk13 @ sk8 @ sk6 )),bind(C,$thf( K @ sk14 )),bind(D,$thf( K )),bind(E,$thf( G )),bind(F,$thf( J ))]]) ).
thf(8945,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[8935]) ).
thf(31569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,8945]) ).
thf(31570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[31569]) ).
thf(31606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[31570]) ).
thf(31656,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[31606]) ).
thf(2992,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(2993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[2992]) ).
thf(2994,plain,
! [A: $i] : ( A @ sk8 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[2993:[bind(A,$thf( D @ sk8 )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(3043,plain,
! [A: $i] : ( A @ sk8 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[2994]) ).
thf(3102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk7 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,383]) ).
thf(3103,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3102]) ).
thf(3104,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ ( B @ sk7 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3103:[bind(A,$thf( H @ sk13 )),bind(B,$thf( H @ sk13 @ sk8 )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(3117,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ ( B @ sk7 @ r4 ) ) ),
inference(simp,[status(thm)],[3104]) ).
thf(4040,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ ( E @ sk7 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,3117]) ).
thf(4041,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ ( E @ sk7 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[4040]) ).
thf(4042,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[4041:[bind(A,$thf( G @ sk7 )),bind(B,$thf( I @ sk13 @ sk8 )),bind(C,$thf( J @ sk14 )),bind(D,$thf( J )),bind(E,$thf( G )),bind(F,$thf( I ))]]) ).
thf(4085,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[4042]) ).
thf(10415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk7 @ ( D @ sk13 @ sk8 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4085]) ).
thf(10416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk7 @ ( D @ sk13 @ sk8 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[10415]) ).
thf(10417,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[10416:[bind(A,$thf( K @ sk7 @ ( J @ sk13 @ sk8 @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( K )),bind(D,$thf( J )),bind(E,$thf( F ))]]) ).
thf(10452,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[10417]) ).
thf(36420,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk10 @ sk8 @ ( sk5 @ sk11 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ~ $true
| ( sk5 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[35029,90]) ).
thf(36421,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk10 @ sk8 @ ( sk5 @ sk11 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[36420]) ).
thf(36422,plain,
( ( sk5 @ sk11 @ ( sk5 @ sk10 @ sk8 @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[36421:[bind(A,$thf( sk5 @ sk11 )),bind(B,$thf( sk5 @ sk10 @ sk8 ))]]) ).
thf(40037,plain,
! [A: $i] :
( ( ( sk5 @ ( A @ sk14 @ sk2 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,39098]) ).
thf(40038,plain,
! [A: $i] :
( ( sk5 @ ( A @ sk14 @ sk2 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[40037]) ).
thf(40043,plain,
! [A: $i] :
( ( sk5 @ ( A @ sk14 @ sk2 ) )
!= sk5 ),
inference(simp,[status(thm)],[40038]) ).
thf(82,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(490,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)],[82,118]) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[490]) ).
thf(492,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ r1 ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk17 ) )),bind(D,$thf( E ))]]) ).
thf(512,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ r1 ),
inference(simp,[status(thm)],[492]) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,512]) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) ),
inference(simp,[status(thm)],[519]) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[520]) ).
thf(10366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4085]) ).
thf(10367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[10366]) ).
thf(10433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[10367]) ).
thf(10446,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[10433]) ).
thf(1733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( B @ r1 ) )
| ~ ( C @ sk14 @ ( A @ ( B @ r4 ) ) )
| ~ $true
| ~ ( A @ ( D @ sk13 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[1639,358]) ).
thf(1734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( B @ r1 ) )
| ~ ( C @ sk14 @ ( A @ ( B @ r4 ) ) )
| ~ ( A @ ( D @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[1733]) ).
thf(1735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( A @ ( sk5 @ r4 ) ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[1734:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(1748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( A @ ( sk5 @ r4 ) ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[1735]) ).
thf(3206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( sk5 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,1748]) ).
thf(3207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3206]) ).
thf(3208,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk6 @ ( sk5 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3207:[bind(A,$thf( H @ sk13 )),bind(B,$thf( H @ sk13 @ sk8 @ sk6 )),bind(C,$thf( C )),bind(D,$thf( H ))]]) ).
thf(3230,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk6 @ ( sk5 @ r4 ) ) ),
inference(simp,[status(thm)],[3208]) ).
thf(2323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( sk5 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,1748]) ).
thf(2324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[2323]) ).
thf(2325,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[2324:[bind(A,$thf( H )),bind(B,$thf( I @ sk13 )),bind(C,$thf( H @ ( I @ sk13 @ sk17 ) )),bind(D,$thf( D )),bind(E,$thf( I ))]]) ).
thf(2335,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ),
inference(simp,[status(thm)],[2325]) ).
thf(3981,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,2335]) ).
thf(3982,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3981]) ).
thf(3983,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( A @ ( B @ sk13 @ sk17 ) @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3982:[bind(A,$thf( sk5 )),bind(B,$thf( H @ ( I @ sk13 @ sk17 ) )),bind(C,$thf( J @ sk14 )),bind(D,$thf( J )),bind(E,$thf( H )),bind(F,$thf( I ))]]) ).
thf(4086,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( A @ ( B @ sk13 @ sk17 ) @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[3983]) ).
thf(11303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4086]) ).
thf(11304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[11303]) ).
thf(11386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[11304]) ).
thf(11409,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( sk5 @ ( A @ ( B @ sk13 @ sk17 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[11386]) ).
thf(31597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk7 @ ( D @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,8945]) ).
thf(31598,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk7 @ ( D @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[31597]) ).
thf(31599,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[31598:[bind(A,$thf( L @ sk7 @ ( K @ sk13 @ sk8 @ sk6 @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( L )),bind(D,$thf( K )),bind(E,$thf( F ))]]) ).
thf(31654,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[31599]) ).
thf(34649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,31654]) ).
thf(34650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[34649]) ).
thf(34706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[34650]) ).
thf(34729,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[34706]) ).
thf(39074,plain,
! [A: $i] :
( ( ( sk5 @ r1 )
!= ( A @ r1 ) )
| ~ ( sk5 @ ( A @ sk2 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,39019]) ).
thf(39075,plain,
! [A: $i] :
( ( ( sk5 @ r1 )
!= ( A @ r1 ) )
| ~ ( sk5 @ ( A @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39074]) ).
thf(39076,plain,
~ ( sk5 @ ( sk5 @ sk2 ) @ r1 ),
inference(pattern_uni,[status(thm)],[39075:[bind(A,$thf( sk5 ))]]) ).
thf(39473,plain,
! [A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( sk5 @ ( sk5 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,39076]) ).
thf(39474,plain,
! [A: $i] :
( ( A @ sk13 @ r1 )
!= ( sk5 @ ( sk5 @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39473]) ).
thf(39484,plain,
! [A: $i] :
( ( A @ sk13 )
!= ( sk5 @ ( sk5 @ sk2 ) ) ),
inference(simp,[status(thm)],[39474]) ).
thf(32,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk1 ) @ ( A @ ( B @ sk2 ) @ id ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(3332,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(3333,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)],[3332]) ).
thf(3334,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk2 ) @ ( B @ ( A @ sk1 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3333:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk2 ) )),bind(D,$thf( H @ ( G @ sk1 ) ))]]) ).
thf(3402,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk2 ) @ ( B @ ( A @ sk1 ) @ id ) ),
inference(simp,[status(thm)],[3334]) ).
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/sandbox/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(245,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( G @ ( D @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ $true
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[48,27]) ).
thf(246,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( G @ ( D @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(247,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ r4 ) ) )
| ~ ( E @ sk6 @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[246:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ sk6 )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( H ))]]) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ r4 ) ) )
| ~ ( E @ sk6 @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(3166,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)],[3042,129]) ).
thf(3167,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)],[3166]) ).
thf(3168,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3167:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(3226,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[3168]) ).
thf(5553,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,3226]) ).
thf(5554,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[5553]) ).
thf(5604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 @ sk6 ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[5554]) ).
thf(5614,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[5604]) ).
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(1051,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)],[85,146]) ).
thf(1052,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)],[1051]) ).
thf(1053,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[1052:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk18 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(1074,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[1053]) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,1074]) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1200,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk15 ) @ sk6 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ r1 ) )
| ~ ( D @ sk14 @ ( B @ ( C @ r4 ) ) )
| ~ $true
| ~ ( B @ ( E @ sk13 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[76,358]) ).
thf(367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ r1 ) )
| ~ ( D @ sk14 @ ( B @ ( C @ r4 ) ) )
| ~ ( B @ ( E @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[366]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( A @ ( D @ sk13 @ r4 ) ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[367:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ sk13 ))]]) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( A @ ( D @ sk13 @ r4 ) ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(3180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk13 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,381]) ).
thf(3181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3180]) ).
thf(3182,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ sk6 @ ( B @ sk13 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3181:[bind(A,$thf( I @ sk13 )),bind(B,$thf( I @ sk13 @ sk8 @ sk6 )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( E ))]]) ).
thf(3233,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ sk6 @ ( B @ sk13 @ r4 ) ) ),
inference(simp,[status(thm)],[3182]) ).
thf(8909,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ sk6 @ ( E @ sk13 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,3233]) ).
thf(8910,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ sk6 @ ( E @ sk13 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[8909]) ).
thf(8911,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[8910:[bind(A,$thf( G @ sk13 )),bind(B,$thf( J @ sk13 @ sk8 @ sk6 )),bind(C,$thf( K @ sk14 )),bind(D,$thf( K )),bind(E,$thf( G )),bind(F,$thf( J ))]]) ).
thf(8925,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[8911]) ).
thf(31442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk13 @ ( D @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,8925]) ).
thf(31443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk13 @ ( D @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[31442]) ).
thf(31444,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[31443:[bind(A,$thf( L @ sk13 @ ( K @ sk13 @ sk8 @ sk6 @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( L )),bind(D,$thf( K )),bind(E,$thf( F ))]]) ).
thf(31490,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[31444]) ).
thf(33176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,31490]) ).
thf(33177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[33176]) ).
thf(33270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[33177]) ).
thf(33309,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[33270]) ).
thf(3951,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( sk5 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,3230]) ).
thf(3952,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( sk5 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3951]) ).
thf(3953,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( B @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3952:[bind(A,$thf( sk5 )),bind(B,$thf( H @ sk13 @ sk8 @ sk6 )),bind(C,$thf( I @ sk14 )),bind(D,$thf( I )),bind(E,$thf( H ))]]) ).
thf(4116,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( B @ sk14 @ id ) ),
inference(simp,[status(thm)],[3953]) ).
thf(6012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4116]) ).
thf(6013,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[6012]) ).
thf(6047,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[6013]) ).
thf(6057,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[6047]) ).
thf(22623,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ sk6 @ ( A @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,3883]) ).
thf(22624,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ sk6 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[22623]) ).
thf(22625,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[22624:[bind(A,$thf( A )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(22694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,22625]) ).
thf(22695,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[22694]) ).
thf(22703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( sk5 @ sk6 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[22695]) ).
thf(22717,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( sk5 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[22703]) ).
thf(320,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)],[36,146]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[320]) ).
thf(322,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(327,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[322]) ).
thf(1792,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,327]) ).
thf(1793,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1792]) ).
thf(1808,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1793]) ).
thf(33,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(2644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,2335]) ).
thf(2645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[2644]) ).
thf(2654,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ ( E @ sk13 @ sk17 ) ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[2645]) ).
thf(2659,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[2654]) ).
thf(84,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk16 ) @ id ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(3296,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(3297,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)],[3296]) ).
thf(3298,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk16 ) @ ( B @ ( A @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3297:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk16 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(3417,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk16 ) @ ( B @ ( A @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[3298]) ).
thf(3929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,3117]) ).
thf(3930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3929]) ).
thf(3938,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ sk13 @ sk8 ) )
| ( A
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[3930]) ).
thf(3942,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[3938]) ).
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(8929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,3234]) ).
thf(8930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[8929]) ).
thf(8941,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ sk13 @ sk8 @ sk6 ) )
| ( A
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[8930]) ).
thf(8947,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[8941]) ).
thf(3092,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,1821]) ).
thf(3093,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3092]) ).
thf(3111,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( sk5 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3093]) ).
thf(3121,plain,
! [A: $i] :
( ( A @ sk8 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[3111]) ).
thf(42,plain,
! [A: $i] :
( ~ ( A @ r1 )
| ( sk5 @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[79,42]) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[1346]) ).
thf(1348,plain,
! [A: $i] : ( sk5 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[1347:[bind(A,$thf( C )),bind(B,$thf( C @ sk14 ))]]) ).
thf(1354,plain,
! [A: $i] : ( sk5 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[1348]) ).
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(3824,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)],[3425,128]) ).
thf(3825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk13 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3824]) ).
thf(3826,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[3825:[bind(A,$thf( G @ sk13 )),bind(B,$thf( B )),bind(C,$thf( G @ sk13 @ sk6 )),bind(D,$thf( G ))]]) ).
thf(3902,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[3826]) ).
thf(4746,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)],[36,3902]) ).
thf(4747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4746]) ).
thf(4750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk13 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4747]) ).
thf(4762,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4750]) ).
thf(3070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk13 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,381]) ).
thf(3071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( E @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3070]) ).
thf(3072,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ ( B @ sk13 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3071:[bind(A,$thf( H @ sk13 )),bind(B,$thf( H @ sk13 @ sk8 )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( E ))]]) ).
thf(3116,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ sk8 @ ( B @ sk13 @ r4 ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(3969,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ ( E @ sk13 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,3116]) ).
thf(3970,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ sk13 @ sk8 @ ( E @ sk13 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3969]) ).
thf(3971,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3970:[bind(A,$thf( G @ sk13 )),bind(B,$thf( I @ sk13 @ sk8 )),bind(C,$thf( J @ sk14 )),bind(D,$thf( J )),bind(E,$thf( G )),bind(F,$thf( I ))]]) ).
thf(4083,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[3971]) ).
thf(9395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4083]) ).
thf(9396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[9395]) ).
thf(9463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[9396]) ).
thf(9481,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[9463]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ r4 ) ) )
| ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(cnfConj,[status(thm)],[92]) ).
thf(3782,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)],[33,93]) ).
thf(3783,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)],[3782]) ).
thf(3784,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( B @ ( A @ sk4 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3783:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(3794,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( B @ ( A @ sk4 ) @ id ) ),
inference(simp,[status(thm)],[3784]) ).
thf(3821,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)],[3425,129]) ).
thf(3822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3821]) ).
thf(3823,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[3822:[bind(A,$thf( G @ sk14 )),bind(B,$thf( B )),bind(C,$thf( G @ sk14 @ sk6 )),bind(D,$thf( G ))]]) ).
thf(3901,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[3823]) ).
thf(4381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,3901]) ).
thf(4382,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4381]) ).
thf(4401,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk14 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4382]) ).
thf(4403,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4401]) ).
thf(25051,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ~ $true
| ( C @ ( B @ r2 ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[3428,67]) ).
thf(25052,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[25051]) ).
thf(25053,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
| ( A @ sk8 @ sk9 @ ( A @ sk8 @ id ) ) ),
inference(pattern_uni,[status(thm)],[25052:[bind(A,$thf( E @ sk8 )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk11 ))]]) ).
thf(25259,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
| ( A @ sk8 @ sk9 @ ( A @ sk8 @ id ) ) ),
inference(simp,[status(thm)],[25053]) ).
thf(37528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk9 @ ( A @ sk8 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[25259,90]) ).
thf(37529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk9 @ ( A @ sk8 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[37528]) ).
thf(37530,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk9 @ id ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[37529:[bind(A,$thf( F )),bind(B,$thf( F @ sk8 )),bind(C,$thf( F @ sk8 @ sk9 ))]]) ).
thf(37658,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk9 @ id ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[37530]) ).
thf(38020,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ sk8 @ sk9 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ~ $true
| ( C @ ( B @ r2 ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[37658,67]) ).
thf(38021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ sk8 @ sk9 @ id ) )
!= ( B @ sk8 @ ( C @ id ) ) )
| ( C @ ( B @ r2 ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[38020]) ).
thf(38022,plain,
! [A: $i] :
( ( A @ sk8 @ sk9 @ ( A @ r2 ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[38021:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk9 ))]]) ).
thf(38209,plain,
! [A: $i] :
( ( A @ sk8 @ sk9 @ ( A @ r2 ) )
| ( A @ sk8 @ sk11 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[38022]) ).
thf(3077,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)],[3043,128]) ).
thf(3078,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3079,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[3078:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(3120,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[3079]) ).
thf(72,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(3383,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(3384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[3383]) ).
thf(3385,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[3384:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk11 ))]]) ).
thf(3429,plain,
! [A: $i] :
( ( A @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[3385]) ).
thf(11316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4086]) ).
thf(11317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[11316]) ).
thf(11396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[11317]) ).
thf(11399,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( sk5 @ ( A @ ( B @ sk13 @ sk17 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[11396]) ).
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(6497,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)],[82,130]) ).
thf(6498,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)],[6497]) ).
thf(6499,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[6498:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk17 ) ))]]) ).
thf(6537,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[6499]) ).
thf(13523,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)],[3425,6537]) ).
thf(13524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[13523]) ).
thf(13610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk17 ) ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[13524]) ).
thf(13623,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[13610]) ).
thf(16752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,10452]) ).
thf(16753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[16752]) ).
thf(16797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[16753]) ).
thf(16817,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[16797]) ).
thf(466,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,327]) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[466]) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk3 ) @ sk6 ) ),
inference(simp,[status(thm)],[467]) ).
thf(1023,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)],[85,129]) ).
thf(1024,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)],[1023]) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[1024:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk18 ) )),bind(D,$thf( I @ ( H @ sk15 ) )),bind(E,$thf( E ))]]) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[1025]) ).
thf(3089,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)],[3043,54]) ).
thf(3090,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)],[3089]) ).
thf(3091,plain,
! [B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[3090:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(3130,plain,
! [B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[3091]) ).
thf(16203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ id ) ) )
| ~ ( C @ r1 )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,3130]) ).
thf(16204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ id ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[16203]) ).
thf(16205,plain,
! [B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ sk8 @ id ) ) ),
inference(pattern_uni,[status(thm)],[16204:[bind(A,$thf( E @ sk8 )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E ))]]) ).
thf(16236,plain,
! [B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ sk8 @ id ) ) ),
inference(simp,[status(thm)],[16205]) ).
thf(4035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk19 ) @ ( D @ id ) ) )
| ~ $true
| ( D @ ( C @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,96]) ).
thf(4036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk19 ) @ ( D @ id ) ) )
| ( D @ ( C @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[4035]) ).
thf(4037,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[4036:[bind(A,$thf( G @ ( F @ sk19 ) )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk19 ) @ sk6 ))]]) ).
thf(4084,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) ),
inference(simp,[status(thm)],[4037]) ).
thf(19025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,3116]) ).
thf(19026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[19025]) ).
thf(19133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 ) )
| ( B
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[19026]) ).
thf(19191,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[19133]) ).
thf(3867,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)],[3425,992]) ).
thf(3868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3867]) ).
thf(3876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk3 ) ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3868]) ).
thf(3895,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[3876]) ).
thf(3108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,358]) ).
thf(3109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[3108]) ).
thf(3110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( C @ sk13 @ sk8 @ ( A @ r4 ) ) )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[3109:[bind(A,$thf( H @ sk13 )),bind(B,$thf( H @ sk13 @ sk8 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H ))]]) ).
thf(3119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ sk14 @ ( C @ sk13 @ sk8 @ ( A @ r4 ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[3110]) ).
thf(23129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( B @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,3119]) ).
thf(23130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[23129]) ).
thf(23131,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ ( C @ sk14 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[23130:[bind(A,$thf( E )),bind(B,$thf( E @ sk14 ))]]) ).
thf(23152,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ ( C @ sk14 @ r4 ) ) ),
inference(simp,[status(thm)],[23131]) ).
thf(25284,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ ( F @ sk14 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,23152]) ).
thf(25285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ ( F @ sk14 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[25284]) ).
thf(25286,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[25285:[bind(A,$thf( G @ sk14 )),bind(B,$thf( I @ sk13 @ sk8 )),bind(C,$thf( J @ sk14 )),bind(D,$thf( J )),bind(E,$thf( I )),bind(F,$thf( G ))]]) ).
thf(25316,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[25286]) ).
thf(26060,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,25316]) ).
thf(26061,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[26060]) ).
thf(26062,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[26061:[bind(A,$thf( K @ sk14 @ ( J @ sk13 @ sk8 @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( K )),bind(D,$thf( J )),bind(E,$thf( F ))]]) ).
thf(26106,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[26062]) ).
thf(28683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,26106]) ).
thf(28684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[28683]) ).
thf(28723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( D @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[28684]) ).
thf(28769,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[28723]) ).
thf(23081,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk14 @ ( C @ sk13 @ sk8 @ ( A @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,3119]) ).
thf(23082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk14 @ ( C @ sk13 @ sk8 @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[23081]) ).
thf(23083,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[23082:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(23144,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ),
inference(simp,[status(thm)],[23083]) ).
thf(165,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ $true
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[79,22]) ).
thf(166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( E @ sk14 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ sk14 ))]]) ).
thf(185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( E @ sk14 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[167]) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( C @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ $true
| ~ ( B @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[1639,54]) ).
thf(1719,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( C @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1720,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ ( sk5 @ id ) ) ),
inference(pattern_uni,[status(thm)],[1719:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(10895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ ( sk5 @ id ) ) )
| ~ ( D @ ( C @ r2 ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,1720]) ).
thf(10896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ ( sk5 @ id ) ) )
| ~ ( D @ ( C @ r2 ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[10895]) ).
thf(10897,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( sk5 @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[10896:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(10923,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( sk5 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[10897]) ).
thf(1369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk14 @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1354,129]) ).
thf(1370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk14 @ id ) )
!= ( C @ ( D @ sk14 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[1369]) ).
thf(1371,plain,
! [A: $i] :
~ ( sk5 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[1370:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk5 )),bind(D,$thf( A ))]]) ).
thf(1423,plain,
! [A: $i] :
~ ( sk5 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,1423]) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1432]) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= sk5 )
| ( B != C ) ),
inference(simp,[status(thm)],[1433]) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= sk5 ),
inference(simp,[status(thm)],[1437]) ).
thf(3762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ sk6 @ ( sk5 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,3230]) ).
thf(3763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ sk6 @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3762]) ).
thf(3772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ sk13 @ sk8 @ sk6 ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[3763]) ).
thf(3777,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[3772]) ).
thf(275,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( E @ ( B @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( F @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,27]) ).
thf(276,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( E @ ( B @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( F @ ( C @ id ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ sk14 @ r4 ) ) )
| ~ ( B @ ( A @ ( E @ sk12 @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( I )),bind(B,$thf( I @ sk12 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I @ sk14 )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ sk14 @ r4 ) ) )
| ~ ( B @ ( A @ ( E @ sk12 @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(3948,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(3949,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)],[3948]) ).
thf(3950,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3949:[bind(A,$thf( F @ ( E @ sk19 ) )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk19 ) ))]]) ).
thf(4111,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) ),
inference(simp,[status(thm)],[3950]) ).
thf(536,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk13 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,381]) ).
thf(537,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk17 ) @ ( B @ sk13 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( I )),bind(B,$thf( J @ sk13 )),bind(C,$thf( I @ ( J @ sk13 @ sk17 ) )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk17 ) @ ( B @ sk13 @ r4 ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(14405,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,547]) ).
thf(14406,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14405]) ).
thf(14472,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ ( F @ sk13 @ sk17 ) ) )
| ( B
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[14406]) ).
thf(14488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14472]) ).
thf(7400,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ~ $true
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[3429,45]) ).
thf(7401,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk11 @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7400]) ).
thf(7402,plain,
( ( sk5 @ sk11 @ r1 )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[7401:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk11 ))]]) ).
thf(7775,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ r1 )
!= ( A @ r1 ) )
| ~ $true
| ( sk5 @ ( A @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[7402,42]) ).
thf(7776,plain,
! [A: $i] :
( ( ( sk5 @ sk11 @ r1 )
!= ( A @ r1 ) )
| ( sk5 @ ( A @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7775]) ).
thf(7777,plain,
( ( sk5 @ ( sk5 @ sk11 @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[7776:[bind(A,$thf( sk5 @ sk11 ))]]) ).
thf(8328,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk11 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ~ $true
| ( sk5 @ sk9 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[7777,90]) ).
thf(8329,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk11 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[8328]) ).
thf(8330,plain,
( ( sk5 @ sk11 @ ( sk5 @ id ) )
| ( sk5 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[8329:[bind(A,$thf( sk5 @ sk11 )),bind(B,$thf( sk5 ))]]) ).
thf(23172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,23144]) ).
thf(23173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[23172]) ).
thf(23174,plain,
! [B: $i,A: $i] :
~ ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) @ ( B @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[23173:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( H @ sk13 @ sk8 )),bind(C,$thf( I @ sk14 )),bind(D,$thf( I )),bind(E,$thf( H ))]]) ).
thf(23200,plain,
! [B: $i,A: $i] :
~ ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) @ ( B @ sk14 @ id ) ),
inference(simp,[status(thm)],[23174]) ).
thf(24629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,23200]) ).
thf(24630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[24629]) ).
thf(24631,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[24630:[bind(A,$thf( sk5 @ sk6 @ ( I @ sk13 @ sk8 @ sk19 ) )),bind(B,$thf( E @ sk14 )),bind(C,$thf( I )),bind(D,$thf( E ))]]) ).
thf(24683,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[24631]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox/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(5590,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)],[90,3226]) ).
thf(5591,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)],[5590]) ).
thf(5592,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[5591:[bind(A,$thf( G @ sk8 @ sk6 )),bind(B,$thf( E @ sk14 )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(5621,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[5592]) ).
thf(4736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,3902]) ).
thf(4737,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4736]) ).
thf(4755,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk13 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4737]) ).
thf(4760,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4755]) ).
thf(6467,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)],[3042,130]) ).
thf(6468,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)],[6467]) ).
thf(6469,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[6468:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(6529,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[6469]) ).
thf(7727,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)],[90,6529]) ).
thf(7728,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)],[7727]) ).
thf(7729,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[7728:[bind(A,$thf( G @ sk8 @ sk6 )),bind(B,$thf( E @ sk7 )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(7761,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[7729]) ).
thf(3798,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)],[3425,1063]) ).
thf(3799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3798]) ).
thf(3873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk15 ) ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3799]) ).
thf(3891,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[3873]) ).
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/sandbox/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(3096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( sk5 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,1748]) ).
thf(3097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( D @ sk13 @ r2 ) ) )
| ~ ( C @ sk14 @ ( B @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3096]) ).
thf(3098,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ ( sk5 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[3097:[bind(A,$thf( G @ sk13 )),bind(B,$thf( G @ sk13 @ sk8 )),bind(C,$thf( C )),bind(D,$thf( G ))]]) ).
thf(3133,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk13 @ sk8 @ ( sk5 @ r4 ) ) ),
inference(simp,[status(thm)],[3098]) ).
thf(3249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,3133]) ).
thf(3250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3249]) ).
thf(3258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ sk13 @ sk8 ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[3250]) ).
thf(3263,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( B @ sk13 @ sk8 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[3258]) ).
thf(4029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ ( sk5 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,3133]) ).
thf(4030,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ sk13 @ sk8 @ ( sk5 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[4029]) ).
thf(4031,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) @ ( B @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[4030:[bind(A,$thf( sk5 )),bind(B,$thf( G @ sk13 @ sk8 )),bind(C,$thf( H @ sk14 )),bind(D,$thf( H )),bind(E,$thf( G ))]]) ).
thf(4123,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) @ ( B @ sk14 @ id ) ),
inference(simp,[status(thm)],[4031]) ).
thf(4325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4123]) ).
thf(4326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[4325]) ).
thf(4327,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[4326:[bind(A,$thf( sk5 @ ( I @ sk13 @ sk8 @ sk19 ) )),bind(B,$thf( E @ sk14 )),bind(C,$thf( I )),bind(D,$thf( E ))]]) ).
thf(4348,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[4327]) ).
thf(24698,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,24683]) ).
thf(24699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[24698]) ).
thf(24801,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ sk14 )
!= sk5 )
| ( A
!= ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[24699]) ).
thf(24826,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 )
!= sk5 )
| ~ ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ r1 ) ),
inference(simp,[status(thm)],[24801]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox/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(25280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( E @ sk14 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,23152]) ).
thf(25281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( E @ sk14 @ r4 ) ) ) ),
inference(simp,[status(thm)],[25280]) ).
thf(25308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ sk13 @ sk8 ) )
| ( A
!= ( E @ sk14 ) ) ),
inference(simp,[status(thm)],[25281]) ).
thf(25324,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ ( B @ sk13 @ sk8 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[25308]) ).
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(3075,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,141]) ).
thf(3076,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3075]) ).
thf(3114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk14 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3076]) ).
thf(3125,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[3114]) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( B @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,384]) ).
thf(1284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[1283]) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ ( D @ sk14 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[1284:[bind(A,$thf( F )),bind(B,$thf( F @ sk14 ))]]) ).
thf(1291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ ( D @ sk14 @ r4 ) ) ),
inference(simp,[status(thm)],[1285]) ).
thf(14398,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( F @ sk14 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,1291]) ).
thf(14399,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( F @ sk14 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14398]) ).
thf(14463,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( B
!= ( F @ sk14 ) ) ),
inference(simp,[status(thm)],[14399]) ).
thf(14515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14463]) ).
thf(1187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,1071]) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) ),
inference(simp,[status(thm)],[1187]) ).
thf(1191,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[1188]) ).
thf(22684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,22625]) ).
thf(22685,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[22684]) ).
thf(22704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( sk5 @ sk6 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[22685]) ).
thf(22710,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( sk5 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[22704]) ).
thf(4744,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)],[82,3902]) ).
thf(4745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4744]) ).
thf(4756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk13 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4745]) ).
thf(4761,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4756]) ).
thf(3086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ $true
| ~ ( B @ r1 ) ),
inference(paramod_ordered,[status(thm)],[3043,118]) ).
thf(3087,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[3086]) ).
thf(3088,plain,
! [A: $i] :
~ ( A @ sk8 @ r1 ),
inference(pattern_uni,[status(thm)],[3087:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(3128,plain,
! [A: $i] :
~ ( A @ sk8 @ r1 ),
inference(simp,[status(thm)],[3088]) ).
thf(3144,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,3128]) ).
thf(3145,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ r1 ) ),
inference(simp,[status(thm)],[3144]) ).
thf(3148,plain,
! [B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[3145]) ).
thf(3215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[3042,146]) ).
thf(3216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3215]) ).
thf(3217,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[3216:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk6 ))]]) ).
thf(3235,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ sk6 @ r1 ),
inference(simp,[status(thm)],[3217]) ).
thf(3649,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,3235]) ).
thf(3650,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3649]) ).
thf(3653,plain,
! [B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ sk8 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[3650]) ).
thf(2677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( C @ sk8 @ ( D @ id ) ) ),
inference(paramod_ordered,[status(thm)],[85,64]) ).
thf(2678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( C @ sk8 @ ( D @ id ) ) ),
inference(simp,[status(thm)],[2677]) ).
thf(2679,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk18 ) @ sk8 @ ( B @ ( A @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[2678:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk18 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(2768,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk18 ) @ sk8 @ ( B @ ( A @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[2679]) ).
thf(22961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk18 ) @ sk8 @ ( B @ ( A @ sk15 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2768,90]) ).
thf(22962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk18 ) @ sk8 @ ( B @ ( A @ sk15 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[22961]) ).
thf(22963,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk15 ) @ ( B @ ( A @ sk18 ) @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[22962:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ sk15 ) )),bind(D,$thf( I @ ( H @ sk18 ) @ sk8 ))]]) ).
thf(23057,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk15 ) @ ( B @ ( A @ sk18 ) @ sk8 @ id ) ),
inference(simp,[status(thm)],[22963]) ).
thf(14378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,3116]) ).
thf(14379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14378]) ).
thf(14471,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 ) )
| ( B
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[14379]) ).
thf(14487,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14471]) ).
thf(5976,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4116]) ).
thf(5977,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[5976]) ).
thf(6028,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( A
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[5977]) ).
thf(6049,plain,
! [B: $i,A: $i] :
( ( B @ sk14 )
!= ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[6028]) ).
thf(171,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( D @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,22]) ).
thf(172,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( D @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( E @ sk7 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ sk7 ))]]) ).
thf(189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( E @ sk7 @ r2 ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(39059,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( sk5 @ ( A @ sk2 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,39019]) ).
thf(39060,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( sk5 @ ( A @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39059]) ).
thf(39061,plain,
~ ( sk5 @ ( sk5 @ sk6 @ sk2 ) @ r1 ),
inference(pattern_uni,[status(thm)],[39060:[bind(A,$thf( sk5 @ sk6 ))]]) ).
thf(26157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[85,10923]) ).
thf(26158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( sk5 @ ( C @ id ) ) ),
inference(simp,[status(thm)],[26157]) ).
thf(26159,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ ( A @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[26158:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk15 ) )),bind(D,$thf( H @ ( G @ sk18 ) ))]]) ).
thf(26326,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ ( A @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[26159]) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,1071]) ).
thf(1705,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1704]) ).
thf(1741,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) )
!= sk5 ),
inference(simp,[status(thm)],[1705]) ).
thf(6024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4116]) ).
thf(6025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[6024]) ).
thf(6026,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[6025:[bind(A,$thf( sk5 @ ( J @ sk13 @ sk8 @ sk6 @ sk19 ) )),bind(B,$thf( E @ sk14 )),bind(C,$thf( J )),bind(D,$thf( E ))]]) ).
thf(6048,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[6026]) ).
thf(6967,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,6048]) ).
thf(6968,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[6967]) ).
thf(7032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ sk14 )
!= sk5 )
| ( A
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[6968]) ).
thf(7047,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 )
!= sk5 )
| ~ ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ r1 ) ),
inference(simp,[status(thm)],[7032]) ).
thf(5548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,3226]) ).
thf(5549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk14 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[5548]) ).
thf(5611,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ sk8 @ sk6 )
!= sk5 )
| ( A
!= ( B @ sk14 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[5549]) ).
thf(5619,plain,
! [B: $i,A: $i] :
( ( ( B @ sk8 @ sk6 )
!= sk5 )
| ~ ( A @ sk14 @ r1 ) ),
inference(simp,[status(thm)],[5611]) ).
thf(8702,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[5619,79]) ).
thf(8703,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[8702]) ).
thf(278,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( F @ ( C @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ $true
| ~ ( E @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[78,27]) ).
thf(279,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( F @ ( C @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ sk14 @ ( C @ r4 ) ) )
| ~ ( B @ ( E @ sk12 @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ sk12 )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( I @ sk14 )),bind(G,$thf( G ))]]) ).
thf(289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ sk14 @ ( C @ r4 ) ) )
| ~ ( B @ ( E @ sk12 @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(11349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4086]) ).
thf(11350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[11349]) ).
thf(11378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[11350]) ).
thf(11404,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( A @ ( B @ sk13 @ sk17 ) @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[11378]) ).
thf(255,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(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ r4 ) ) )
| ~ ( B @ ( A @ ( B @ r4 ) ) )
| ~ ( C @ ( A @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F ))]]) ).
thf(261,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)],[258]) ).
thf(4534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4348]) ).
thf(4535,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[4534]) ).
thf(4577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[4535]) ).
thf(4595,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[4577]) ).
thf(1333,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[76,42]) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[1333]) ).
thf(1335,plain,
! [A: $i] : ( sk5 @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[1334:[bind(A,$thf( C )),bind(B,$thf( C @ sk13 ))]]) ).
thf(1365,plain,
! [A: $i] : ( sk5 @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[1335]) ).
thf(3320,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1365,90]) ).
thf(3321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3320]) ).
thf(3322,plain,
! [A: $i] : ( A @ sk13 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[3321:[bind(A,$thf( D )),bind(B,$thf( D @ sk13 )),bind(C,$thf( sk5 ))]]) ).
thf(3430,plain,
! [A: $i] : ( A @ sk13 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[3322]) ).
thf(4321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ ( sk5 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3430,4123]) ).
thf(4322,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ ( sk5 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[4321]) ).
thf(4329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( ( C @ sk14 )
!= sk5 ) ),
inference(simp,[status(thm)],[4322]) ).
thf(1773,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,1071]) ).
thf(1774,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1773]) ).
thf(1811,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1774]) ).
thf(4529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,4348]) ).
thf(4530,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[4529]) ).
thf(4589,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ sk14 )
!= sk5 )
| ( A
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[4530]) ).
thf(4600,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 )
!= sk5 )
| ~ ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ r1 ) ),
inference(simp,[status(thm)],[4589]) ).
thf(31369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,8925]) ).
thf(31370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[31369]) ).
thf(31474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[31370]) ).
thf(31500,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[31474]) ).
thf(4714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,4513]) ).
thf(4715,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4714]) ).
thf(4726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk12 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4715]) ).
thf(4733,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk12 ) ),
inference(simp,[status(thm)],[4726]) ).
thf(3105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[3043,146]) ).
thf(3106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3105]) ).
thf(3107,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[3106:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(3118,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ r1 ),
inference(simp,[status(thm)],[3107]) ).
thf(3157,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,3118]) ).
thf(3158,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[3157]) ).
thf(3163,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[3158]) ).
thf(10816,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[3043,1720]) ).
thf(10817,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10816]) ).
thf(10818,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10817:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk8 ))]]) ).
thf(10918,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10818]) ).
thf(1650,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(1651,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[1650]) ).
thf(1670,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A != B )
| ( B @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[1651]) ).
thf(1677,plain,
! [A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A @ r1 )
| ( A @ sk9 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[1670]) ).
thf(5980,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,4116]) ).
thf(5981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[5980]) ).
thf(6046,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= sk5 )
| ( A
!= ( C @ sk14 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[5981]) ).
thf(6056,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= sk5 )
| ~ ( B @ sk14 @ r1 ) ),
inference(simp,[status(thm)],[6046]) ).
thf(12980,plain,
! [A: $i] :
( ( ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[6056,79]) ).
thf(12981,plain,
! [A: $i] :
( ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[12980]) ).
thf(980,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)],[82,129]) ).
thf(981,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)],[980]) ).
thf(982,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[981:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk17 ) ))]]) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[982]) ).
thf(3386,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)],[90,991]) ).
thf(3387,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)],[3386]) ).
thf(3388,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3387:[bind(A,$thf( H @ ( G @ sk17 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3431,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[3388]) ).
thf(50,plain,
! [A: $i] : ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
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/sandbox/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(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ r3 ) ) )
| ( A @ ( B @ sk20 ) @ ( C @ id ) ) ),
inference(cnfConj,[status(thm)],[98]) ).
thf(4371,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(4372,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)],[4371]) ).
thf(4373,plain,
! [A: $i] : ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[4372:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk7 )),bind(D,$thf( F @ sk6 ))]]) ).
thf(4378,plain,
! [A: $i] : ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) ),
inference(simp,[status(thm)],[4373]) ).
thf(10278,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)],[4378,90]) ).
thf(10279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk7 @ sk20 ) @ ( A @ sk6 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[10278]) ).
thf(10280,plain,
! [A: $i] : ( A @ sk6 @ ( A @ ( A @ sk7 @ sk20 ) @ id ) ),
inference(pattern_uni,[status(thm)],[10279:[bind(A,$thf( F )),bind(B,$thf( F @ sk6 )),bind(C,$thf( F @ ( F @ sk7 @ sk20 ) ))]]) ).
thf(10324,plain,
! [A: $i] : ( A @ sk6 @ ( A @ ( A @ sk7 @ sk20 ) @ id ) ),
inference(simp,[status(thm)],[10280]) ).
thf(29816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ sk6 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4087]) ).
thf(29817,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ sk6 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[29816]) ).
thf(29818,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[29817:[bind(A,$thf( sk5 @ sk6 @ ( J @ ( K @ sk13 @ sk3 ) @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( F ))]]) ).
thf(29875,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[29818]) ).
thf(644,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk7 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,383]) ).
thf(645,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( B @ sk7 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( I )),bind(B,$thf( J @ sk13 )),bind(C,$thf( I @ ( J @ sk13 @ sk3 ) )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( B @ sk7 @ r4 ) ) ),
inference(simp,[status(thm)],[646]) ).
thf(744,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,650]) ).
thf(745,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[744]) ).
thf(751,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ ( F @ sk13 @ sk3 ) ) )
| ( A
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[745]) ).
thf(756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ ( D @ sk13 @ sk3 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[751]) ).
thf(6437,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)],[3425,130]) ).
thf(6438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ ( D @ sk7 @ id ) ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[6437]) ).
thf(6439,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ sk6 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[6438:[bind(A,$thf( G @ sk7 )),bind(B,$thf( B )),bind(C,$thf( G @ sk7 @ sk6 )),bind(D,$thf( G ))]]) ).
thf(6540,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ sk6 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[6439]) ).
thf(6564,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)],[85,6540]) ).
thf(6565,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)],[6564]) ).
thf(6583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk7 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[6565]) ).
thf(6591,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6583]) ).
thf(19071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,3234]) ).
thf(19072,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[19071]) ).
thf(19148,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 @ sk6 ) )
| ( B
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[19072]) ).
thf(19165,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[19148]) ).
thf(23168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,23144]) ).
thf(23169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) ),
inference(simp,[status(thm)],[23168]) ).
thf(23195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ sk13 @ sk8 ) )
| ( A
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[23169]) ).
thf(23208,plain,
! [B: $i,A: $i] :
( ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[23195]) ).
thf(3169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,142]) ).
thf(3170,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3169]) ).
thf(3225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk7 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3170]) ).
thf(3243,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[3225]) ).
thf(29788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4087]) ).
thf(29789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[29788]) ).
thf(29837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[29789]) ).
thf(29865,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ sk6 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[29837]) ).
thf(233,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(234,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)],[233]) ).
thf(235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ r4 ) ) )
| ~ ( A @ ( C @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$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(265,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)],[235]) ).
thf(9442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk13 @ ( D @ sk13 @ sk8 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4083]) ).
thf(9443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( C @ sk13 @ ( D @ sk13 @ sk8 @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[9442]) ).
thf(9444,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[9443:[bind(A,$thf( K @ sk13 @ ( J @ sk13 @ sk8 @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( K )),bind(D,$thf( J )),bind(E,$thf( F ))]]) ).
thf(9473,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[9444]) ).
thf(15065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,9473]) ).
thf(15066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[15065]) ).
thf(15138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[15066]) ).
thf(15165,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[15138]) ).
thf(7684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,6529]) ).
thf(7685,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[7684]) ).
thf(7751,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 @ sk6 ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[7685]) ).
thf(7758,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[7751]) ).
thf(1697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( A @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,384]) ).
thf(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[1697]) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[1698:[bind(A,$thf( sk5 ))]]) ).
thf(1747,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ),
inference(simp,[status(thm)],[1699]) ).
thf(4005,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,1747]) ).
thf(4006,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[4005]) ).
thf(4007,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[4006:[bind(A,$thf( sk5 )),bind(B,$thf( H @ ( I @ sk13 @ sk3 ) )),bind(C,$thf( J @ sk14 )),bind(D,$thf( J )),bind(E,$thf( H )),bind(F,$thf( I ))]]) ).
thf(4103,plain,
! [C: $i,B: $i,A: $i] :
~ ( sk5 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) @ ( C @ sk14 @ id ) ),
inference(simp,[status(thm)],[4007]) ).
thf(12423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4103]) ).
thf(12424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[12423]) ).
thf(12425,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[12424:[bind(A,$thf( sk5 @ ( J @ ( K @ sk13 @ sk3 ) @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( F ))]]) ).
thf(12456,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[12425]) ).
thf(18366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,12456]) ).
thf(18367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[18366]) ).
thf(18457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) ) ) ),
inference(simp,[status(thm)],[18367]) ).
thf(18475,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[18457]) ).
thf(2733,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)],[82,64]) ).
thf(2734,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)],[2733]) ).
thf(2735,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[2734:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(2762,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[2735]) ).
thf(194,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ $true
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[76,184]) ).
thf(195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ sk13 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ sk13 ))]]) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ sk13 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[196]) ).
thf(3275,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)],[90,1063]) ).
thf(3276,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)],[3275]) ).
thf(3277,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3276:[bind(A,$thf( H @ ( G @ sk15 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3406,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[3277]) ).
thf(4387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,3901]) ).
thf(4388,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4387]) ).
thf(4398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk14 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4388]) ).
thf(4407,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4398]) ).
thf(1426,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,1423]) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1426]) ).
thf(1434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= sk5 )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1427]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= sk5 ),
inference(simp,[status(thm)],[1434]) ).
thf(25989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,25316]) ).
thf(25990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[25989]) ).
thf(26093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[25990]) ).
thf(26113,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[26093]) ).
thf(12370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4103]) ).
thf(12371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[12370]) ).
thf(12426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[12371]) ).
thf(12457,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( sk5 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[12426]) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,1074]) ).
thf(1195,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk15 ) @ sk6 ) ),
inference(simp,[status(thm)],[1195]) ).
thf(3187,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)],[3042,128]) ).
thf(3188,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)],[3187]) ).
thf(3189,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[3188:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk8 @ sk6 )),bind(D,$thf( D ))]]) ).
thf(3237,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ sk6 @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[3189]) ).
thf(5673,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)],[90,3237]) ).
thf(5674,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)],[5673]) ).
thf(5675,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[5674:[bind(A,$thf( G @ sk8 @ sk6 )),bind(B,$thf( E @ sk13 )),bind(C,$thf( E )),bind(D,$thf( G ))]]) ).
thf(5697,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[5675]) ).
thf(10828,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)],[85,1720]) ).
thf(10829,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)],[10828]) ).
thf(10830,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10829:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk18 ) )),bind(D,$thf( H @ ( G @ sk15 ) ))]]) ).
thf(10922,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk15 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10830]) ).
thf(209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( D @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,184]) ).
thf(210,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( D @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( D @ sk7 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ sk7 ))]]) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( D @ sk7 @ r2 ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ sk20 ) @ ( C @ id ) )
| ( C @ ( B @ ( A @ r3 ) ) ) ),
inference(cnfConj,[status(thm)],[98]) ).
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(1044,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)],[85,140]) ).
thf(1045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk13 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1045]) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[1060]) ).
thf(77,plain,
! [A: $i] : ( A @ sk12 @ ( A @ sk13 @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(3785,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(3786,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)],[3785]) ).
thf(3787,plain,
! [A: $i] : ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) ),
inference(pattern_uni,[status(thm)],[3786:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ sk13 )),bind(D,$thf( F @ sk12 ))]]) ).
thf(3795,plain,
! [A: $i] : ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) ),
inference(simp,[status(thm)],[3787]) ).
thf(4649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk20 ) @ ( D @ id ) ) )
| ~ $true
| ( D @ ( C @ ( B @ r3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,102]) ).
thf(4650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ ( C @ sk20 ) @ ( D @ id ) ) )
| ( D @ ( C @ ( B @ r3 ) ) ) ),
inference(simp,[status(thm)],[4649]) ).
thf(4651,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ sk6 @ ( A @ ( B @ r3 ) ) ),
inference(pattern_uni,[status(thm)],[4650:[bind(A,$thf( G @ ( F @ sk20 ) )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk20 ) @ sk6 ))]]) ).
thf(4700,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ sk6 @ ( A @ ( B @ r3 ) ) ),
inference(simp,[status(thm)],[4651]) ).
thf(23188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,23144]) ).
thf(23189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) ),
inference(simp,[status(thm)],[23188]) ).
thf(23194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( D @ sk13 @ sk8 ) )
| ( B
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[23189]) ).
thf(23207,plain,
! [B: $i,A: $i] :
( ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[23194]) ).
thf(39475,plain,
( ( ( sk5 @ ( sk5 @ sk2 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,39076]) ).
thf(39476,plain,
( ( sk5 @ ( sk5 @ sk2 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[39475]) ).
thf(39481,plain,
( ( sk5 @ ( sk5 @ sk2 ) )
!= sk5 ),
inference(simp,[status(thm)],[39476]) ).
thf(10850,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ ( sk5 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[3042,1720]) ).
thf(10851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10850]) ).
thf(10852,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10851:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk6 ))]]) ).
thf(10943,plain,
! [A: $i] :
~ ( A @ sk8 @ sk6 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10852]) ).
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/sandbox/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(24560,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,23200]) ).
thf(24561,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[24560]) ).
thf(24649,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[24561]) ).
thf(24675,plain,
! [B: $i,A: $i] :
( ( B @ sk14 @ sk6 )
!= ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[24649]) ).
thf(248,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 ) ) )
!= ( G @ ( H @ ( J @ r4 ) ) ) )
| ~ ( K @ r1 )
| ~ ( K @ ( G @ id ) )
| ~ $true
| ~ ( J @ r1 )
| ~ ( H @ ( I @ r2 ) )
| ~ ( I @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[27,22]) ).
thf(249,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 ) ) )
!= ( G @ ( H @ ( J @ r4 ) ) ) )
| ~ ( K @ r1 )
| ~ ( K @ ( G @ id ) )
| ~ ( J @ r1 )
| ~ ( H @ ( I @ r2 ) )
| ~ ( I @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ r1 )
| ~ ( H @ ( F @ id ) )
| ~ ( D @ r1 )
| ~ ( E @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$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( F )),bind(H,$thf( E )),bind(I,$thf( I )),bind(J,$thf( D ))]]) ).
thf(270,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ r1 )
| ~ ( H @ ( F @ id ) )
| ~ ( D @ r1 )
| ~ ( E @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(6452,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)],[85,130]) ).
thf(6453,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)],[6452]) ).
thf(6454,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[6453:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk18 ) )),bind(D,$thf( I @ ( H @ sk15 ) )),bind(E,$thf( E ))]]) ).
thf(6550,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[6454]) ).
thf(256,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(257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ r4 ) ) )
| ~ ( B @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(260,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)],[257]) ).
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(18405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,12456]) ).
thf(18406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[18405]) ).
thf(18442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( sk5 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) ) ) ),
inference(simp,[status(thm)],[18406]) ).
thf(18471,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[18442]) ).
thf(272,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( F @ ( B @ id ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[78,22]) ).
thf(273,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( F @ ( B @ id ) ) )
| ~ ( F @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk14 @ r1 )
| ~ ( D @ sk12 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( H )),bind(B,$thf( H @ sk12 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H @ sk14 ))]]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk14 @ r1 )
| ~ ( D @ sk12 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[274]) ).
thf(31659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( D @ sk12 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(rewrite,[status(thm)],[287,79]) ).
thf(31660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk12 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[31659]) ).
thf(3994,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( G @ sk14 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,1291]) ).
thf(3995,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( G @ sk14 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3994]) ).
thf(3996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3995:[bind(A,$thf( H @ sk14 )),bind(B,$thf( J @ ( K @ sk13 @ sk3 ) )),bind(C,$thf( L @ sk14 )),bind(D,$thf( L )),bind(E,$thf( J )),bind(F,$thf( K )),bind(G,$thf( H ))]]) ).
thf(4091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ),
inference(simp,[status(thm)],[3996]) ).
thf(14400,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,650]) ).
thf(14401,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14400]) ).
thf(14468,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ ( F @ sk13 @ sk3 ) ) )
| ( B
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[14401]) ).
thf(14484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14468]) ).
thf(15052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,9473]) ).
thf(15053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[15052]) ).
thf(15154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[15053]) ).
thf(15169,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[15154]) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,1821]) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1825]) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( sk5 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1826]) ).
thf(1837,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1833]) ).
thf(24601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,23200]) ).
thf(24602,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[24601]) ).
thf(24636,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[24602]) ).
thf(24684,plain,
! [B: $i,A: $i] :
( ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[24636]) ).
thf(13578,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)],[90,6537]) ).
thf(13579,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)],[13578]) ).
thf(13580,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[13579:[bind(A,$thf( H @ ( G @ sk17 ) )),bind(B,$thf( F @ sk7 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(13612,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[13580]) ).
thf(4742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,3902]) ).
thf(4743,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4742]) ).
thf(4752,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk13 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4743]) ).
thf(4757,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4752]) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,512]) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) ),
inference(simp,[status(thm)],[517]) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(4391,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)],[36,3901]) ).
thf(4392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4391]) ).
thf(4400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk14 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4392]) ).
thf(4402,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4400]) ).
thf(4708,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,4513]) ).
thf(4709,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk12 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[4708]) ).
thf(4725,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk12 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[4709]) ).
thf(4732,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk12 ) ),
inference(simp,[status(thm)],[4725]) ).
thf(215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[49,184]) ).
thf(216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[215]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk7 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( F )),bind(B,$thf( F @ sk7 ))]]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk7 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[217]) ).
thf(1032,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)],[85,128]) ).
thf(1033,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)],[1032]) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[1033:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk18 ) )),bind(D,$thf( I @ ( H @ sk15 ) )),bind(E,$thf( E ))]]) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk15 ) @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[1034]) ).
thf(8616,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)],[3425,1069]) ).
thf(8617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[8616]) ).
thf(8686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk15 ) ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[8617]) ).
thf(8700,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[8686]) ).
thf(26144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[3043,10923]) ).
thf(26145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[26144]) ).
thf(26146,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[26145:[bind(A,$thf( D )),bind(B,$thf( D @ sk8 )),bind(C,$thf( D ))]]) ).
thf(26315,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk8 @ id ) ),
inference(simp,[status(thm)],[26146]) ).
thf(302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,142]) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk7 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[303]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[324]) ).
thf(820,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)],[36,128]) ).
thf(821,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)],[820]) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[821:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[822]) ).
thf(3861,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)],[3425,827]) ).
thf(3862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[3861]) ).
thf(3875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk3 ) ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[3862]) ).
thf(3894,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[3875]) ).
thf(25970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,25316]) ).
thf(25971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[25970]) ).
thf(26079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[25971]) ).
thf(26107,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[26079]) ).
thf(31414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,8925]) ).
thf(31415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[31414]) ).
thf(31456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[31415]) ).
thf(31493,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[31456]) ).
thf(3278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk14 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1354,90]) ).
thf(3279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk14 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3278]) ).
thf(3280,plain,
! [A: $i] : ( A @ sk14 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[3279:[bind(A,$thf( D )),bind(B,$thf( D @ sk14 )),bind(C,$thf( sk5 ))]]) ).
thf(3408,plain,
! [A: $i] : ( A @ sk14 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[3280]) ).
thf(314,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)],[36,118]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ r1 ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk3 ) )),bind(D,$thf( E ))]]) ).
thf(332,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ r1 ),
inference(simp,[status(thm)],[316]) ).
thf(1736,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,332]) ).
thf(1737,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1736]) ).
thf(1740,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) )
!= sk5 ),
inference(simp,[status(thm)],[1737]) ).
thf(3059,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,142]) ).
thf(3060,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3059]) ).
thf(3112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk7 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3060]) ).
thf(3122,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk7 ) ),
inference(simp,[status(thm)],[3112]) ).
thf(16128,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ $true
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[1664,3130]) ).
thf(16129,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( B @ sk8 @ ( A @ id ) ) ),
inference(simp,[status(thm)],[16128]) ).
thf(16130,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[16129:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B ))]]) ).
thf(16232,plain,
! [A: $i] :
~ ( A @ sk8 @ ( sk5 @ sk6 @ id ) ),
inference(simp,[status(thm)],[16130]) ).
thf(153,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ $true
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
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 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[153]) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( E @ sk13 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ sk13 ))]]) ).
thf(188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( E @ sk13 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[155]) ).
thf(2736,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)],[36,64]) ).
thf(2737,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)],[2736]) ).
thf(2738,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[2737:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(2764,plain,
! [B: $i,A: $i] : ( A @ sk8 @ ( B @ ( A @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[2738]) ).
thf(5810,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)],[2764,90]) ).
thf(5811,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)],[5810]) ).
thf(5812,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[5811:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ sk3 ) )),bind(D,$thf( G @ sk8 ))]]) ).
thf(5854,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[5812]) ).
thf(7461,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)],[3429,67]) ).
thf(7462,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)],[7461]) ).
thf(7463,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[7462:[bind(A,$thf( E @ sk8 )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk11 ))]]) ).
thf(7513,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[7463]) ).
thf(3999,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ ( G @ sk13 @ sk3 ) @ ( E @ sk7 @ r4 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[96,650]) ).
thf(4000,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( F @ ( G @ sk13 @ sk3 ) @ ( E @ sk7 @ r4 ) ) ) )
| ~ ( A @ ( B @ sk19 ) @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3999]) ).
thf(4001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[4000:[bind(A,$thf( H @ sk7 )),bind(B,$thf( J @ ( K @ sk13 @ sk3 ) )),bind(C,$thf( L @ sk14 )),bind(D,$thf( L )),bind(E,$thf( H )),bind(F,$thf( J )),bind(G,$thf( K ))]]) ).
thf(4095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ),
inference(simp,[status(thm)],[4001]) ).
thf(307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,141]) ).
thf(308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[307]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk14 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[308]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[323]) ).
thf(200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( D @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,184]) ).
thf(201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( D @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( D @ sk14 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ sk14 ))]]) ).
thf(225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( D @ sk14 @ r2 ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[49,42]) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[1330]) ).
thf(1332,plain,
! [A: $i] : ( sk5 @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[1331:[bind(A,$thf( C )),bind(B,$thf( C @ sk7 ))]]) ).
thf(1363,plain,
! [A: $i] : ( sk5 @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[1332]) ).
thf(4569,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk7 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1363,4348]) ).
thf(4570,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( A @ sk7 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[4569]) ).
thf(4582,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ sk14 )
!= sk5 )
| ( ( A @ sk7 )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[4570]) ).
thf(15102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,9473]) ).
thf(15103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[15102]) ).
thf(15130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[15103]) ).
thf(15162,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[15130]) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,1074]) ).
thf(1701,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1700]) ).
thf(1739,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[1701]) ).
thf(13268,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)],[7513,64]) ).
thf(13269,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)],[13268]) ).
thf(13270,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[13269:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk11 ))]]) ).
thf(13355,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[13270]) ).
thf(6500,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)],[36,130]) ).
thf(6501,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)],[6500]) ).
thf(6502,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[6501:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk3 ) ))]]) ).
thf(6539,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk3 ) @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[6502]) ).
thf(5636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,3237]) ).
thf(5637,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ sk6 @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[5636]) ).
thf(5692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 @ sk6 ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[5637]) ).
thf(5705,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[5692]) ).
thf(6573,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)],[82,6540]) ).
thf(6574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[6573]) ).
thf(6585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk7 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[6574]) ).
thf(6593,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6585]) ).
thf(4383,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)],[85,3901]) ).
thf(4384,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)],[4383]) ).
thf(4397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk14 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[4384]) ).
thf(4406,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4397]) ).
thf(4169,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)],[90,3120]) ).
thf(4170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk13 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[4169]) ).
thf(4171,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[4170:[bind(A,$thf( F @ sk8 )),bind(B,$thf( E @ sk13 )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(4191,plain,
! [B: $i,A: $i] :
~ ( A @ sk13 @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[4171]) ).
thf(1806,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,332]) ).
thf(1807,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1806]) ).
thf(1810,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1807]) ).
thf(496,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)],[82,146]) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[496]) ).
thf(498,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(505,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[498]) ).
thf(1721,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,505]) ).
thf(1722,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1721]) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[1722]) ).
thf(3645,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,3235]) ).
thf(3646,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3645]) ).
thf(3654,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ sk8 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[3646]) ).
thf(31524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,8945]) ).
thf(31525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[31524]) ).
thf(31625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[31525]) ).
thf(31647,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ sk6 )
!= ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[31625]) ).
thf(14439,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,3117]) ).
thf(14440,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14439]) ).
thf(14458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 ) )
| ( B
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[14440]) ).
thf(14509,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14458]) ).
thf(8661,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)],[90,1069]) ).
thf(8662,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)],[8661]) ).
thf(8663,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[8662:[bind(A,$thf( H @ ( G @ sk15 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(8690,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[8663]) ).
thf(10399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4085]) ).
thf(10400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[10399]) ).
thf(10426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[10400]) ).
thf(10455,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[10426]) ).
thf(14441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,1817]) ).
thf(14442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14441]) ).
thf(14477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( B
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[14442]) ).
thf(14494,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14477]) ).
thf(3153,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,3118]) ).
thf(3154,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3153]) ).
thf(3162,plain,
! [B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[3154]) ).
thf(3204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,140]) ).
thf(3205,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3204]) ).
thf(3224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk13 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3205]) ).
thf(3242,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[3224]) ).
thf(10882,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)],[82,1720]) ).
thf(10883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10882]) ).
thf(10884,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10883:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(10919,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10884]) ).
thf(3094,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,140]) ).
thf(3095,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk13 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3094]) ).
thf(3115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk13 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3095]) ).
thf(3126,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk13 ) ),
inference(simp,[status(thm)],[3115]) ).
thf(16713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,10452]) ).
thf(16714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[16713]) ).
thf(16809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[16714]) ).
thf(16822,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[16809]) ).
thf(3138,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,3128]) ).
thf(3139,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ r1 ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3147,plain,
! [B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[3139]) ).
thf(73,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ r2 ) )
| ( A @ sk9 @ r1 ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(39471,plain,
! [A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( sk5 @ ( sk5 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,39076]) ).
thf(39472,plain,
! [A: $i] :
( ( A @ sk7 @ r1 )
!= ( sk5 @ ( sk5 @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39471]) ).
thf(39485,plain,
! [A: $i] :
( ( A @ sk7 )
!= ( sk5 @ ( sk5 @ sk2 ) ) ),
inference(simp,[status(thm)],[39472]) ).
thf(4283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4123]) ).
thf(4284,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[4283]) ).
thf(4332,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[4284]) ).
thf(4352,plain,
! [B: $i,A: $i] :
( ( B @ sk14 )
!= ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[4332]) ).
thf(236,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
!= ( G @ ( H @ ( J @ r4 ) ) ) )
| ~ ( G @ r1 )
| ~ $true
| ~ ( J @ r1 )
| ~ ( H @ ( I @ r2 ) )
| ~ ( I @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[27,184]) ).
thf(237,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
!= ( G @ ( H @ ( J @ r4 ) ) ) )
| ~ ( G @ r1 )
| ~ ( J @ r1 )
| ~ ( H @ ( I @ r2 ) )
| ~ ( I @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ r1 )
| ~ ( D @ r1 )
| ~ ( E @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$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( F )),bind(H,$thf( E )),bind(I,$thf( I )),bind(J,$thf( D ))]]) ).
thf(266,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ r1 )
| ~ ( D @ r1 )
| ~ ( E @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(6972,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,6048]) ).
thf(6973,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[6972]) ).
thf(7038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[6973]) ).
thf(7052,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[7038]) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,140]) ).
thf(483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[482]) ).
thf(502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk13 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[483]) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[502]) ).
thf(22696,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,22625]) ).
thf(22697,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[22696]) ).
thf(22708,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( sk5 @ sk6 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[22697]) ).
thf(22714,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( sk5 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[22708]) ).
thf(524,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,505]) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[524]) ).
thf(530,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk17 ) @ sk6 ) ),
inference(simp,[status(thm)],[525]) ).
thf(39487,plain,
( ( ( sk5 @ ( sk5 @ sk6 @ sk2 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,39061]) ).
thf(39488,plain,
( ( sk5 @ ( sk5 @ sk6 @ sk2 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[39487]) ).
thf(39503,plain,
( ( sk5 @ ( sk5 @ sk6 @ sk2 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[39488]) ).
thf(2312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( C @ ( sk5 @ r4 ) ) ) )
| ~ $true
| ~ ( C @ ( E @ sk13 @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[33,1748]) ).
thf(2313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( D @ sk14 @ ( C @ ( sk5 @ r4 ) ) ) )
| ~ ( C @ ( E @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[2312]) ).
thf(2329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( D @ sk14 ) )
| ( B != C )
| ( A != sk5 )
| ~ ( C @ ( E @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[2313]) ).
thf(2338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk4 ) )
!= ( B @ sk14 ) )
| ~ ( A @ ( C @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[2329]) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ sk6 @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,146]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ sk6 @ r1 ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 )
!= ( C @ sk6 ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(5985,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4116]) ).
thf(5986,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[5985]) ).
thf(6040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( A
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[5986]) ).
thf(6053,plain,
! [B: $i,A: $i] :
( ( B @ sk14 @ sk6 )
!= ( sk5 @ ( A @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[6040]) ).
thf(86,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk18 ) @ ( B @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(4365,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk18 ) @ ( B @ ( A @ r3 ) ) )
!= ( E @ ( D @ ( C @ r3 ) ) ) )
| ~ $true
| ( C @ ( D @ sk20 ) @ ( E @ id ) ) ),
inference(paramod_ordered,[status(thm)],[86,99]) ).
thf(4366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk18 ) @ ( B @ ( A @ r3 ) ) )
!= ( E @ ( D @ ( C @ r3 ) ) ) )
| ( C @ ( D @ sk20 ) @ ( E @ id ) ) ),
inference(simp,[status(thm)],[4365]) ).
thf(4367,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ ( B @ ( A @ sk18 ) @ id ) ),
inference(pattern_uni,[status(thm)],[4366:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ sk18 ) ))]]) ).
thf(4380,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ ( B @ ( A @ sk18 ) @ id ) ),
inference(simp,[status(thm)],[4367]) ).
thf(3865,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)],[3425,991]) ).
thf(3866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3865]) ).
thf(3872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk17 ) ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[3866]) ).
thf(3890,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[3872]) ).
thf(230,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(231,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)],[230]) ).
thf(232,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( D @ r4 ) ) )
| ~ ( C @ ( A @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(264,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)],[232]) ).
thf(3056,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)],[3043,129]) ).
thf(3057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[3056]) ).
thf(3058,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk14 @ id ) ),
inference(pattern_uni,[status(thm)],[3057:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(3129,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk14 @ id ) ),
inference(simp,[status(thm)],[3058]) ).
thf(4213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,3129]) ).
thf(4214,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[4213]) ).
thf(4259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 ) )
| ( A
!= ( B @ sk14 ) ) ),
inference(simp,[status(thm)],[4214]) ).
thf(4269,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[4259]) ).
thf(4315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4123]) ).
thf(4316,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[4315]) ).
thf(4339,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[4316]) ).
thf(4354,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[4339]) ).
thf(2014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,1817]) ).
thf(2015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) ),
inference(simp,[status(thm)],[2014]) ).
thf(2024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( A
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[2015]) ).
thf(2028,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[2024]) ).
thf(3389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk7 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1363,90]) ).
thf(3390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk7 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[3389]) ).
thf(3391,plain,
! [A: $i] : ( A @ sk7 @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[3390:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 )),bind(C,$thf( sk5 ))]]) ).
thf(3433,plain,
! [A: $i] : ( A @ sk7 @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[3391]) ).
thf(4319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ ( sk5 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3433,4123]) ).
thf(4320,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ ( sk5 @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[4319]) ).
thf(4340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( ( C @ sk14 )
!= sk5 ) ),
inference(simp,[status(thm)],[4320]) ).
thf(174,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ $true
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[49,22]) ).
thf(175,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[174]) ).
thf(176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( E @ sk7 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G @ sk7 ))]]) ).
thf(180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( E @ sk7 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[176]) ).
thf(13808,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)],[90,6550]) ).
thf(13809,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)],[13808]) ).
thf(13810,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(pattern_uni,[status(thm)],[13809:[bind(A,$thf( H @ ( G @ sk15 ) )),bind(B,$thf( F @ sk7 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(13849,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk15 ) @ id ) ),
inference(simp,[status(thm)],[13810]) ).
thf(39493,plain,
( ( ( sk5 @ ( sk5 @ sk6 @ sk2 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,39061]) ).
thf(39494,plain,
( ( sk5 @ ( sk5 @ sk6 @ sk2 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[39493]) ).
thf(39501,plain,
( ( sk5 @ ( sk5 @ sk6 @ sk2 ) )
!= sk5 ),
inference(simp,[status(thm)],[39494]) ).
thf(14407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,1747]) ).
thf(14408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14407]) ).
thf(14466,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( B != sk5 ) ),
inference(simp,[status(thm)],[14408]) ).
thf(14481,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14466]) ).
thf(39477,plain,
! [A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( sk5 @ ( sk5 @ sk2 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,39076]) ).
thf(39478,plain,
! [A: $i] :
( ( A @ sk14 @ r1 )
!= ( sk5 @ ( sk5 @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39477]) ).
thf(39486,plain,
! [A: $i] :
( ( A @ sk14 )
!= ( sk5 @ ( sk5 @ sk2 ) ) ),
inference(simp,[status(thm)],[39478]) ).
thf(817,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)],[82,128]) ).
thf(818,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)],[817]) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk13 @ id ) ),
inference(pattern_uni,[status(thm)],[818:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ sk17 ) ))]]) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ sk17 ) @ ( A @ sk13 @ id ) ),
inference(simp,[status(thm)],[819]) ).
thf(24541,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,23200]) ).
thf(24542,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[24541]) ).
thf(24671,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[24542]) ).
thf(24681,plain,
! [B: $i,A: $i] :
( ( B @ sk14 )
!= ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[24671]) ).
thf(542,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk13 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,381]) ).
thf(543,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[542]) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( B @ sk13 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( I )),bind(B,$thf( J @ sk13 )),bind(C,$thf( I @ ( J @ sk13 @ sk3 ) )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ ( B @ sk13 @ r4 ) ) ),
inference(simp,[status(thm)],[544]) ).
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(26227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[82,10923]) ).
thf(26228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( sk5 @ ( C @ id ) ) ),
inference(simp,[status(thm)],[26227]) ).
thf(26229,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ ( A @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[26228:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk17 ) )),bind(D,$thf( E ))]]) ).
thf(26335,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ ( A @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[26229]) ).
thf(3647,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,3235]) ).
thf(3648,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[3647]) ).
thf(3651,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[3648]) ).
thf(1619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( F @ sk14 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,1291]) ).
thf(1620,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( F @ sk14 @ r4 ) ) ) ),
inference(simp,[status(thm)],[1619]) ).
thf(1630,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( A
!= ( F @ sk14 ) ) ),
inference(simp,[status(thm)],[1620]) ).
thf(1635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[1630]) ).
thf(3073,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,1423]) ).
thf(3074,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( sk5 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3073]) ).
thf(3113,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 )
!= sk5 )
| ( A != B ) ),
inference(simp,[status(thm)],[3074]) ).
thf(3123,plain,
! [A: $i] :
( ( A @ sk8 )
!= sk5 ),
inference(simp,[status(thm)],[3113]) ).
thf(9428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4083]) ).
thf(9429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[9428]) ).
thf(9465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[9429]) ).
thf(9483,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[9465]) ).
thf(25298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( E @ sk14 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,23152]) ).
thf(25299,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( E @ sk14 @ r4 ) ) ) ),
inference(simp,[status(thm)],[25298]) ).
thf(25310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( D @ sk13 @ sk8 ) )
| ( B
!= ( E @ sk14 ) ) ),
inference(simp,[status(thm)],[25299]) ).
thf(25326,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[25310]) ).
thf(159,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( F @ ( B @ id ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[48,22]) ).
thf(160,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( F @ ( B @ id ) ) )
| ~ ( F @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ sk6 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( G )),bind(B,$thf( G @ sk6 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ sk6 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[161]) ).
thf(168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( F @ r1 ) )
| ~ $true
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[79,22]) ).
thf(169,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( F @ r1 ) )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk14 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ sk14 ))]]) ).
thf(187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk14 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[170]) ).
thf(10887,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)],[36,1720]) ).
thf(10888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ ( sk5 @ id ) ) ),
inference(simp,[status(thm)],[10887]) ).
thf(10889,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ ( sk5 @ id ) ),
inference(pattern_uni,[status(thm)],[10888:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(10921,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ ( sk5 @ id ) ),
inference(simp,[status(thm)],[10889]) ).
thf(191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( D @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,184]) ).
thf(192,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( D @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( D @ sk13 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ sk13 ))]]) ).
thf(219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( D @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(3185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,141]) ).
thf(3186,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk14 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[3185]) ).
thf(3221,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk14 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[3186]) ).
thf(3238,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk14 ) ),
inference(simp,[status(thm)],[3221]) ).
thf(4525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4348]) ).
thf(4526,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[4525]) ).
thf(4590,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( A
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[4526]) ).
thf(4601,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[4590]) ).
thf(39469,plain,
( ( ( sk5 @ ( sk5 @ sk2 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,39076]) ).
thf(39470,plain,
( ( sk5 @ ( sk5 @ sk2 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[39469]) ).
thf(39482,plain,
( ( sk5 @ ( sk5 @ sk2 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[39470]) ).
thf(251,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(252,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)],[251]) ).
thf(253,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( G @ r4 ) ) )
| ~ ( I @ ( F @ id ) )
| ~ ( H @ ( E @ id ) )
| ~ ( G @ ( D @ id ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$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(271,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)],[253]) ).
thf(26032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,25316]) ).
thf(26033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[26032]) ).
thf(26094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[26033]) ).
thf(26114,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[26094]) ).
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(10353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4085]) ).
thf(10354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[10353]) ).
thf(10440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[10354]) ).
thf(10448,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[10440]) ).
thf(34581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,31654]) ).
thf(34582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[34581]) ).
thf(34714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[34582]) ).
thf(34731,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[34714]) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,141]) ).
thf(481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk14 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[481]) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[503]) ).
thf(13753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,6550]) ).
thf(13754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk15 ) @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[13753]) ).
thf(13812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk15 ) ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[13754]) ).
thf(13851,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[13812]) ).
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(641,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk7 @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,383]) ).
thf(642,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( E @ sk13 @ r2 ) ) )
| ~ ( D @ sk14 @ ( C @ ( F @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[641]) ).
thf(643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk17 ) @ ( B @ sk7 @ r4 ) ) ),
inference(pattern_uni,[status(thm)],[642:[bind(A,$thf( I )),bind(B,$thf( J @ sk13 )),bind(C,$thf( I @ ( J @ sk13 @ sk17 ) )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( F ))]]) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( C @ ( D @ sk13 @ sk17 ) @ ( B @ sk7 @ r4 ) ) ),
inference(simp,[status(thm)],[643]) ).
thf(11367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,4086]) ).
thf(11368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[11367]) ).
thf(11369,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[11368:[bind(A,$thf( sk5 @ ( J @ ( K @ sk13 @ sk17 ) @ sk19 ) )),bind(B,$thf( F @ sk14 )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( F ))]]) ).
thf(11402,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk14 @ ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[11369]) ).
thf(17740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,11402]) ).
thf(17741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[17740]) ).
thf(17790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) ) ) ),
inference(simp,[status(thm)],[17741]) ).
thf(17813,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[17790]) ).
thf(13638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,6539]) ).
thf(13639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk3 ) @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[13638]) ).
thf(13714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk3 ) ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[13639]) ).
thf(13734,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[13714]) ).
thf(4716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,4513]) ).
thf(4717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4716]) ).
thf(4724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk12 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4717]) ).
thf(4731,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk12 ) ),
inference(simp,[status(thm)],[4724]) ).
thf(3155,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,3118]) ).
thf(3156,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3155]) ).
thf(3165,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[3156]) ).
thf(4606,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(4607,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)],[4606]) ).
thf(4608,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ ( A @ ( B @ r3 ) ) ),
inference(pattern_uni,[status(thm)],[4607:[bind(A,$thf( F @ ( E @ sk20 ) )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk20 ) ))]]) ).
thf(4684,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk20 ) @ ( A @ ( B @ r3 ) ) ),
inference(simp,[status(thm)],[4608]) ).
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/sandbox/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(39069,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( sk5 @ ( B @ sk2 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,39019]) ).
thf(39070,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( sk5 @ ( B @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39069]) ).
thf(39071,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk13 @ sk2 ) @ r1 ),
inference(pattern_uni,[status(thm)],[39070:[bind(A,$thf( C )),bind(B,$thf( C @ sk13 ))]]) ).
thf(39100,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk13 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[39071]) ).
thf(4247,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)],[90,3129]) ).
thf(4248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk14 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[4247]) ).
thf(4249,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[4248:[bind(A,$thf( F @ sk8 )),bind(B,$thf( E @ sk14 )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(4277,plain,
! [B: $i,A: $i] :
~ ( A @ sk14 @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[4249]) ).
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(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,140]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[309]) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk13 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[310]) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[325]) ).
thf(3374,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)],[90,827]) ).
thf(3375,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)],[3374]) ).
thf(3376,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3375:[bind(A,$thf( H @ ( G @ sk3 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3423,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[3376]) ).
thf(197,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[76,184]) ).
thf(198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk13 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( F )),bind(B,$thf( F @ sk13 ))]]) ).
thf(223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ sk13 @ ( A @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( A @ ( B @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[199]) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ sk6 @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,146]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ sk6 @ r1 ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 )
!= ( C @ sk6 ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(239,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( E @ ( B @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( F @ ( C @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,27]) ).
thf(240,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( E @ ( B @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( F @ ( C @ id ) ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ r4 ) ) )
| ~ ( B @ ( A @ ( E @ sk6 @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( H )),bind(B,$thf( H @ sk6 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H ))]]) ).
thf(267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ r4 ) ) )
| ~ ( B @ ( A @ ( E @ sk6 @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(8905,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,3233]) ).
thf(8906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[8905]) ).
thf(8918,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ sk13 @ sk8 @ sk6 ) )
| ( A
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[8906]) ).
thf(8922,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[8918]) ).
thf(666,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,545]) ).
thf(667,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[666]) ).
thf(678,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ ( F @ sk13 @ sk3 ) ) )
| ( A
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[667]) ).
thf(685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ ( D @ sk13 @ sk3 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[678]) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,512]) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk17 ) @ r1 ) ),
inference(simp,[status(thm)],[515]) ).
thf(521,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[516]) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,1074]) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1192]) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk15 ) @ sk6 ) ),
inference(simp,[status(thm)],[1193]) ).
thf(9382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4083]) ).
thf(9383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[9382]) ).
thf(9460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[9383]) ).
thf(9478,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[9460]) ).
thf(26763,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk9 @ ( sk5 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ~ $true
| ( sk5 @ sk11 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[24963,90]) ).
thf(26764,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk9 @ ( sk5 @ id ) )
!= ( B @ ( A @ id ) ) )
| ( A @ ( B @ id ) )
| ( sk5 @ sk11 @ r1 ) ),
inference(simp,[status(thm)],[26763]) ).
thf(26765,plain,
( ( sk5 @ ( sk5 @ sk9 @ id ) )
| ( sk5 @ sk11 @ r1 ) ),
inference(pattern_uni,[status(thm)],[26764:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk9 ))]]) ).
thf(203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ $true
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[79,184]) ).
thf(204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[203]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ sk14 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ sk14 ))]]) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ sk14 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[205]) ).
thf(33223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,31490]) ).
thf(33224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[33223]) ).
thf(33297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[33224]) ).
thf(33304,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[33297]) ).
thf(35,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk1 ) @ ( A @ ( A @ ( B @ sk4 ) @ r3 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(17701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,11402]) ).
thf(17702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[17701]) ).
thf(17768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( sk5 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) ) ) ),
inference(simp,[status(thm)],[17702]) ).
thf(17809,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[17768]) ).
thf(6963,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,6048]) ).
thf(6964,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[6963]) ).
thf(7034,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( A
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[6964]) ).
thf(7049,plain,
! [B: $i,A: $i] :
( ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[7034]) ).
thf(14417,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,545]) ).
thf(14418,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk3 ) @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14417]) ).
thf(14476,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ ( F @ sk13 @ sk3 ) ) )
| ( B
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[14418]) ).
thf(14493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14476]) ).
thf(4389,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)],[82,3901]) ).
thf(4390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4389]) ).
thf(4396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk14 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4390]) ).
thf(4405,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk14 @ sk6 ) ),
inference(simp,[status(thm)],[4396]) ).
thf(1790,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,505]) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1790]) ).
thf(1809,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1791]) ).
thf(3151,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,3118]) ).
thf(3152,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3151]) ).
thf(3161,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[3152]) ).
thf(31505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,8945]) ).
thf(31506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[31505]) ).
thf(31630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[31506]) ).
thf(31650,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( A @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[31630]) ).
thf(19106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,1817]) ).
thf(19107,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ sk6 @ r4 ) ) ) ),
inference(simp,[status(thm)],[19106]) ).
thf(19136,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( B
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[19107]) ).
thf(19150,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[19136]) ).
thf(3909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,3116]) ).
thf(3910,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[3909]) ).
thf(3920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ sk13 @ sk8 ) )
| ( A
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[3910]) ).
thf(3921,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[3920]) ).
thf(14956,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)],[13355,90]) ).
thf(14957,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)],[14956]) ).
thf(14958,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ sk8 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[14957:[bind(A,$thf( F )),bind(B,$thf( F @ sk8 @ sk11 )),bind(C,$thf( F @ sk8 ))]]) ).
thf(15048,plain,
! [A: $i] :
( ( A @ sk8 @ sk11 @ ( A @ sk8 @ id ) )
| ( A @ sk8 @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[14958]) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,327]) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[468]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk3 ) @ sk6 ) ),
inference(simp,[status(thm)],[469]) ).
thf(6440,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)],[3043,130]) ).
thf(6441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6440]) ).
thf(6442,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk7 @ id ) ),
inference(pattern_uni,[status(thm)],[6441:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 ))]]) ).
thf(6542,plain,
! [B: $i,A: $i] :
~ ( B @ sk8 @ ( A @ sk7 @ id ) ),
inference(simp,[status(thm)],[6442]) ).
thf(526,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,505]) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[526]) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk17 ) @ sk6 ) ),
inference(simp,[status(thm)],[527]) ).
thf(661,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,547]) ).
thf(662,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(682,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ ( F @ sk13 @ sk17 ) ) )
| ( A
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[662]) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ ( D @ sk13 @ sk17 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[682]) ).
thf(6607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk7 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,6542]) ).
thf(6608,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk7 @ id ) ) ),
inference(simp,[status(thm)],[6607]) ).
thf(6652,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 ) )
| ( A
!= ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[6608]) ).
thf(6683,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ sk6 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[6652]) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,512]) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1702]) ).
thf(1743,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) )
!= sk5 ),
inference(simp,[status(thm)],[1703]) ).
thf(38826,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ( B @ sk8 @ ( C @ id ) )
| ( A @ sk8 @ sk9 @ ( A @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[38209,64]) ).
thf(38827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk11 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ( B @ sk8 @ ( C @ id ) )
| ( A @ sk8 @ sk9 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[38826]) ).
thf(38828,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
| ( A @ sk8 @ sk9 @ ( A @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[38827:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ sk8 @ sk11 ))]]) ).
thf(38956,plain,
! [A: $i] :
( ( A @ sk8 @ ( A @ sk8 @ sk11 @ id ) )
| ( A @ sk8 @ sk9 @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[38828]) ).
thf(4135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk13 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,3120]) ).
thf(4136,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[4135]) ).
thf(4188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk8 ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[4136]) ).
thf(4200,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[4188]) ).
thf(2689,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(2690,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)],[2689]) ).
thf(2691,plain,
! [A: $i] :
( ( A @ sk10 @ sk8 @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[2690:[bind(A,$thf( E )),bind(B,$thf( E @ sk10 )),bind(C,$thf( E @ sk11 ))]]) ).
thf(2747,plain,
! [A: $i] :
( ( A @ sk10 @ sk8 @ ( A @ sk11 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[2691]) ).
thf(12890,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)],[2747,90]) ).
thf(12891,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)],[12890]) ).
thf(12892,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ sk8 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(pattern_uni,[status(thm)],[12891:[bind(A,$thf( F )),bind(B,$thf( F @ sk11 )),bind(C,$thf( F @ sk10 @ sk8 ))]]) ).
thf(12968,plain,
! [A: $i] :
( ( A @ sk11 @ ( A @ sk10 @ sk8 @ id ) )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[12892]) ).
thf(6562,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3043,6540]) ).
thf(6563,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[6562]) ).
thf(6588,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 )
!= ( C @ sk7 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[6563]) ).
thf(6597,plain,
! [B: $i,A: $i] :
( ( A @ sk8 )
!= ( B @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6588]) ).
thf(227,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(228,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)],[227]) ).
thf(229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( E @ ( C @ id ) )
| ~ ( D @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(263,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)],[229]) ).
thf(4546,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1365,4348]) ).
thf(4547,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( A @ sk13 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[4546]) ).
thf(4593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ sk14 )
!= sk5 )
| ( ( A @ sk13 )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[4547]) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,1074]) ).
thf(1770,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1769]) ).
thf(1813,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk15 ) @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1770]) ).
thf(177,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( F @ r1 ) )
| ~ $true
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[49,22]) ).
thf(178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( F @ r1 ) )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[177]) ).
thf(179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk7 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ sk7 ))]]) ).
thf(182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk7 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[179]) ).
thf(311,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ r2 ) ) )
| ~ ( G @ r1 )
| ~ ( G @ ( C @ id ) )
| ~ ( C @ ( D @ ( F @ r4 ) ) )
| ~ ( F @ r1 )
| ~ $true
| ~ ( E @ r1 ) ),
inference(paramod_ordered,[status(thm)],[36,22]) ).
thf(312,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( E @ r2 ) ) )
| ~ ( G @ r1 )
| ~ ( G @ ( C @ id ) )
| ~ ( C @ ( D @ ( F @ r4 ) ) )
| ~ ( F @ r1 )
| ~ ( E @ r1 ) ),
inference(simp,[status(thm)],[311]) ).
thf(313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ r1 )
| ~ ( C @ ( A @ id ) )
| ~ ( A @ ( E @ ( D @ sk3 ) @ ( B @ r4 ) ) )
| ~ ( B @ r1 )
| ~ ( D @ r1 ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( I @ ( H @ sk3 ) )),bind(E,$thf( H ))]]) ).
thf(331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ r1 )
| ~ ( C @ ( A @ id ) )
| ~ ( A @ ( E @ ( D @ sk3 ) @ ( B @ r4 ) ) )
| ~ ( B @ r1 )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[313]) ).
thf(3641,plain,
! [A: $i] :
( ( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,3235]) ).
thf(3642,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3641]) ).
thf(3655,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 @ sk6 )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[3642]) ).
thf(457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,332]) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[457]) ).
thf(463,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[458]) ).
thf(1731,plain,
! [B: $i,A: $i] :
( ( ( B @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,146]) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ( ( B @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[1731]) ).
thf(1738,plain,
! [B: $i,A: $i] :
( ( ( B @ sk6 )
!= sk5 )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[1732]) ).
thf(3643,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,3235]) ).
thf(3644,plain,
! [B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( B @ sk8 @ sk6 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3643]) ).
thf(3652,plain,
! [B: $i,A: $i] :
( ( A @ sk7 )
!= ( B @ sk8 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[3644]) ).
thf(14386,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,2335]) ).
thf(14387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk17 ) @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14386]) ).
thf(14467,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( D @ ( E @ sk13 @ sk17 ) ) )
| ( B != sk5 ) ),
inference(simp,[status(thm)],[14387]) ).
thf(14482,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( B @ ( C @ sk13 @ sk17 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14467]) ).
thf(33157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,31490]) ).
thf(33158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[33157]) ).
thf(33279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[33158]) ).
thf(33312,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[33279]) ).
thf(19966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk20 ) @ ( B @ ( A @ sk18 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4380,90]) ).
thf(19967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk20 ) @ ( B @ ( A @ sk18 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[19966]) ).
thf(19968,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk18 ) @ ( B @ ( A @ sk20 ) @ id ) ),
inference(pattern_uni,[status(thm)],[19967:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ sk18 ) )),bind(D,$thf( H @ ( G @ sk20 ) ))]]) ).
thf(20030,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk18 ) @ ( B @ ( A @ sk20 ) @ id ) ),
inference(simp,[status(thm)],[19968]) ).
thf(19050,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,3233]) ).
thf(19051,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[19050]) ).
thf(19147,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 @ sk6 ) )
| ( B
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[19051]) ).
thf(19164,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[19147]) ).
thf(6948,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ( ( A @ sk14 )
!= sk5 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,4600]) ).
thf(6949,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ( ( A @ sk14 )
!= sk5 ) ),
inference(simp,[status(thm)],[6948]) ).
thf(6960,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= ( sk5 @ sk6 ) )
| ( ( A @ sk14 )
!= sk5 ) ),
inference(simp,[status(thm)],[6949]) ).
thf(34600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,31654]) ).
thf(34601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[34600]) ).
thf(34703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[34601]) ).
thf(34727,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[34703]) ).
thf(1829,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,1821]) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1829]) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( sk5 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1835]) ).
thf(4287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,4123]) ).
thf(4288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[4287]) ).
thf(4333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= sk5 )
| ( A
!= ( C @ sk14 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[4288]) ).
thf(4353,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) )
!= sk5 )
| ~ ( B @ sk14 @ r1 ) ),
inference(simp,[status(thm)],[4333]) ).
thf(6424,plain,
! [A: $i] :
( ( ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[4353,79]) ).
thf(6425,plain,
! [A: $i] :
( ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[6424]) ).
thf(12405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4103]) ).
thf(12406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[12405]) ).
thf(12453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) )
| ( ( A @ sk6 )
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[12406]) ).
thf(12467,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) @ sk6 )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[12453]) ).
thf(4738,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)],[85,3902]) ).
thf(4739,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)],[4738]) ).
thf(4751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk13 @ sk6 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[4739]) ).
thf(4763,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk13 @ sk6 ) ),
inference(simp,[status(thm)],[4751]) ).
thf(16698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,10452]) ).
thf(16699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[16698]) ).
thf(16785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( A
!= ( D @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[16699]) ).
thf(16814,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk7 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[16785]) ).
thf(1183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,1071]) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk15 ) @ r1 ) ),
inference(simp,[status(thm)],[1183]) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk15 ) ) ),
inference(simp,[status(thm)],[1184]) ).
thf(23183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,23144]) ).
thf(23184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( sk5 @ sk6 @ r4 ) ) ) ),
inference(simp,[status(thm)],[23183]) ).
thf(23193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( D @ sk13 @ sk8 ) )
| ( B
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[23184]) ).
thf(23205,plain,
! [B: $i,A: $i] :
( ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[23193]) ).
thf(16151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ id ) ) )
| ~ ( C @ r1 )
| ~ $true
| ~ ( B @ ( A @ r2 ) ) ),
inference(paramod_ordered,[status(thm)],[64,3130]) ).
thf(16152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ id ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[16151]) ).
thf(16153,plain,
! [B: $i,A: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[16152:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,332]) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[461]) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[462]) ).
thf(14430,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,649]) ).
thf(14431,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14430]) ).
thf(14464,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ ( F @ sk13 @ sk17 ) ) )
| ( B
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[14431]) ).
thf(14479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ ( D @ sk13 @ sk17 ) @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14464]) ).
thf(3266,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)],[2762,90]) ).
thf(3267,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)],[3266]) ).
thf(3268,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[3267:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F @ ( G @ sk17 ) )),bind(D,$thf( G @ sk8 ))]]) ).
thf(3401,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[3268]) ).
thf(13693,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk3 ) @ ( C @ sk7 @ id ) ) )
| ~ $true
| ~ ( B @ ( A @ id ) ) ),
inference(paramod_ordered,[status(thm)],[90,6539]) ).
thf(13694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( E @ ( D @ sk3 ) @ ( C @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[13693]) ).
thf(13695,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[13694:[bind(A,$thf( H @ ( G @ sk3 ) )),bind(B,$thf( F @ sk7 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(13739,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk7 @ ( C @ ( B @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[13695]) ).
thf(34779,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ $true
| ~ ( A @ ( B @ sk8 @ id ) ) ),
inference(paramod_ordered,[status(thm)],[1664,16236]) ).
thf(34780,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ r1 )
!= ( A @ r1 ) )
| ~ ( A @ ( B @ sk8 @ id ) ) ),
inference(simp,[status(thm)],[34779]) ).
thf(34781,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ ( A @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[34780:[bind(A,$thf( sk5 @ sk6 )),bind(B,$thf( B ))]]) ).
thf(34956,plain,
! [A: $i] :
~ ( sk5 @ sk6 @ ( A @ sk8 @ id ) ),
inference(simp,[status(thm)],[34781]) ).
thf(7001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,6048]) ).
thf(7002,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[7001]) ).
thf(7025,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[7002]) ).
thf(7044,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[7025]) ).
thf(1030,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)],[85,141]) ).
thf(1031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1030]) ).
thf(1056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk14 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[1056]) ).
thf(16287,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk8 @ ( sk5 @ sk6 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,16232]) ).
thf(16288,plain,
! [B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( B @ sk8 @ ( sk5 @ sk6 @ id ) ) ),
inference(simp,[status(thm)],[16287]) ).
thf(16364,plain,
! [B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( B @ sk8 ) )
| ( A
!= ( sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[16288]) ).
thf(16388,plain,
! [A: $i] :
( ( A @ sk8 )
!= ( sk5 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[16364]) ).
thf(150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( D @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ $true ),
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 )
!= ( D @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( E @ sk13 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ sk13 ))]]) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( E @ sk13 @ r2 ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(39064,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( sk5 @ ( B @ sk2 ) @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,39019]) ).
thf(39065,plain,
! [B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( sk5 @ ( B @ sk2 ) @ r1 ) ),
inference(simp,[status(thm)],[39064]) ).
thf(39066,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk7 @ sk2 ) @ r1 ),
inference(pattern_uni,[status(thm)],[39065:[bind(A,$thf( C )),bind(B,$thf( C @ sk7 ))]]) ).
thf(39099,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk7 @ sk2 ) @ r1 ),
inference(simp,[status(thm)],[39066]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A @ r1 )
| ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[111]) ).
thf(33065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ sk6 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,29875]) ).
thf(33066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ sk6 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[33065]) ).
thf(33124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( sk5 @ sk6 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) ) ) ),
inference(simp,[status(thm)],[33066]) ).
thf(33149,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[33124]) ).
thf(3832,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)],[3425,826]) ).
thf(3833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( D @ ( C @ sk17 ) @ ( B @ sk13 @ id ) ) ),
inference(simp,[status(thm)],[3832]) ).
thf(3877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( D @ ( C @ sk17 ) ) )
| ( A
!= ( B @ sk13 ) ) ),
inference(simp,[status(thm)],[3833]) ).
thf(3896,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ sk6 )
!= ( C @ ( B @ sk17 ) ) ),
inference(simp,[status(thm)],[3877]) ).
thf(17578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( B @ ( A @ sk4 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3794,90]) ).
thf(17579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( B @ ( A @ sk4 ) @ id ) )
!= ( D @ ( C @ id ) ) )
| ( C @ ( D @ id ) ) ),
inference(simp,[status(thm)],[17578]) ).
thf(17580,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk4 ) @ ( B @ ( A @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[17579:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ sk4 ) )),bind(D,$thf( H @ ( G @ sk19 ) ))]]) ).
thf(17653,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk4 ) @ ( B @ ( A @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[17580]) ).
thf(26232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( C @ id ) ) ),
inference(paramod_ordered,[status(thm)],[36,10923]) ).
thf(26233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( sk5 @ ( C @ id ) ) ),
inference(simp,[status(thm)],[26232]) ).
thf(26234,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ ( A @ sk3 ) @ id ) ),
inference(pattern_uni,[status(thm)],[26233:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk3 ) )),bind(D,$thf( E ))]]) ).
thf(26336,plain,
! [B: $i,A: $i] :
~ ( sk5 @ ( B @ ( A @ sk3 ) @ id ) ),
inference(simp,[status(thm)],[26234]) ).
thf(281,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( G @ ( D @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ $true
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[78,27]) ).
thf(282,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ ( A @ sk12 @ id ) )
!= ( G @ ( D @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ sk14 @ ( D @ ( C @ r4 ) ) )
| ~ ( E @ sk12 @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( I @ sk12 )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( I @ sk14 ))]]) ).
thf(290,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ sk14 @ ( D @ ( C @ r4 ) ) )
| ~ ( E @ sk12 @ ( B @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(29724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4087]) ).
thf(29725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[29724]) ).
thf(29849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ sk6 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[29725]) ).
thf(29868,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( sk5 @ sk6 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[29849]) ).
thf(475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,142]) ).
thf(476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[475]) ).
thf(504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk7 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[476]) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[504]) ).
thf(1430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,1423]) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( sk5 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1430]) ).
thf(1436,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= sk5 )
| ( B != C ) ),
inference(simp,[status(thm)],[1431]) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= sk5 ),
inference(simp,[status(thm)],[1436]) ).
thf(3140,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,3128]) ).
thf(3141,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( B @ sk8 @ r1 ) ),
inference(simp,[status(thm)],[3140]) ).
thf(3149,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ sk8 ) ),
inference(simp,[status(thm)],[3141]) ).
thf(25303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( E @ sk14 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,23152]) ).
thf(25304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( D @ sk13 @ sk8 @ ( E @ sk14 @ r4 ) ) ) ),
inference(simp,[status(thm)],[25303]) ).
thf(25307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( D @ sk13 @ sk8 ) )
| ( B
!= ( E @ sk14 ) ) ),
inference(simp,[status(thm)],[25304]) ).
thf(25323,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[25307]) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ sk6 @ r1 ) )
| ~ ( C @ ( B @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,146]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ sk6 @ r1 ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 )
!= ( C @ sk6 ) )
| ~ ( C @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[297]) ).
thf(1665,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(1666,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A != B )
| ( B @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[1666]) ).
thf(1678,plain,
! [A: $i] :
( ( ( A @ sk11 )
!= sk5 )
| ( A @ r1 )
| ( A @ sk9 @ r1 ) ),
inference(simp,[status(thm)],[1671]) ).
thf(4292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3425,4123]) ).
thf(4293,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk6 @ ( A @ id ) )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[4292]) ).
thf(4342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) ) )
| ( A
!= ( C @ sk14 ) ) ),
inference(simp,[status(thm)],[4293]) ).
thf(4356,plain,
! [B: $i,A: $i] :
( ( B @ sk14 @ sk6 )
!= ( sk5 @ ( A @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[4342]) ).
thf(254,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(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( C @ r4 ) ) )
| ~ ( B @ ( A @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[254:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(262,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)],[259]) ).
thf(156,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( F @ r1 ) )
| ~ $true
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[76,22]) ).
thf(157,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( F @ r1 ) )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk13 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ sk13 ))]]) ).
thf(190,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ sk13 @ ( A @ id ) )
| ~ ( A @ ( B @ ( D @ r4 ) ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[158]) ).
thf(162,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( D @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ $true ),
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 )
!= ( D @ r1 ) )
| ~ ( F @ r1 )
| ~ ( F @ ( B @ id ) )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( E @ sk14 @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G @ sk14 ))]]) ).
thf(183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ r1 )
| ~ ( D @ ( A @ id ) )
| ~ ( A @ ( B @ ( C @ r4 ) ) )
| ~ ( C @ r1 )
| ~ ( B @ ( E @ sk14 @ r2 ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(3159,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,3118]) ).
thf(3160,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( B @ sk8 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[3159]) ).
thf(3164,plain,
! [B: $i,A: $i] :
( ( A @ sk14 )
!= ( B @ sk8 @ sk6 ) ),
inference(simp,[status(thm)],[3160]) ).
thf(4561,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,4348]) ).
thf(4562,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[4561]) ).
thf(4578,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( sk5 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[4562]) ).
thf(4596,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( sk5 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[4578]) ).
thf(1844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,1747]) ).
thf(1845,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( D @ ( E @ sk13 @ sk3 ) @ ( sk5 @ r4 ) ) ) ),
inference(simp,[status(thm)],[1844]) ).
thf(1854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( D @ ( E @ sk13 @ sk3 ) ) )
| ( A != sk5 ) ),
inference(simp,[status(thm)],[1845]) ).
thf(1859,plain,
! [C: $i,B: $i,A: $i] :
( ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[1854]) ).
thf(242,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( F @ ( C @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ $true
| ~ ( E @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[48,27]) ).
thf(243,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( F @ ( C @ id ) ) )
| ( G @ ( F @ ( E @ r4 ) ) )
| ~ ( D @ ( C @ ( B @ r4 ) ) )
| ~ ( G @ ( D @ id ) )
| ~ ( E @ ( B @ id ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( C @ r4 ) ) )
| ~ ( B @ ( E @ sk6 @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ sk6 )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H ))]]) ).
thf(268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( C @ r4 ) ) )
| ~ ( B @ ( E @ sk6 @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(22690,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,22625]) ).
thf(22691,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( sk5 @ sk6 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[22690]) ).
thf(22702,plain,
! [B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( sk5 @ sk6 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[22691]) ).
thf(22716,plain,
! [A: $i] :
( ( A @ sk8 @ sk6 )
!= ( sk5 @ sk6 @ sk6 ) ),
inference(simp,[status(thm)],[22702]) ).
thf(4130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk13 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,3120]) ).
thf(4131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( C @ sk8 @ ( B @ sk13 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[4130]) ).
thf(4176,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ sk8 )
!= sk5 )
| ( A
!= ( B @ sk13 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[4131]) ).
thf(4193,plain,
! [B: $i,A: $i] :
( ( ( B @ sk8 )
!= sk5 )
| ~ ( A @ sk13 @ r1 ) ),
inference(simp,[status(thm)],[4176]) ).
thf(6257,plain,
! [A: $i] :
( ( ( A @ sk8 )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[4193,76]) ).
thf(6258,plain,
! [A: $i] :
( ( A @ sk8 )
!= sk5 ),
inference(simp,[status(thm)],[6257]) ).
thf(6649,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)],[90,6542]) ).
thf(6650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ id ) )
!= ( D @ sk8 @ ( C @ sk7 @ id ) ) )
| ~ ( B @ ( A @ id ) ) ),
inference(simp,[status(thm)],[6649]) ).
thf(6651,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ id ) ),
inference(pattern_uni,[status(thm)],[6650:[bind(A,$thf( F @ sk8 )),bind(B,$thf( E @ sk7 )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(6682,plain,
! [B: $i,A: $i] :
~ ( A @ sk7 @ ( B @ sk8 @ id ) ),
inference(simp,[status(thm)],[6651]) ).
thf(31350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,8925]) ).
thf(31351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[31350]) ).
thf(31445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[31351]) ).
thf(31491,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( A @ sk13 @ ( B @ sk13 @ sk8 @ sk6 @ sk19 ) ) ),
inference(simp,[status(thm)],[31445]) ).
thf(12357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4103]) ).
thf(12358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) @ ( D @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[12357]) ).
thf(12448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( sk5 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) )
| ( A
!= ( D @ sk14 ) ) ),
inference(simp,[status(thm)],[12358]) ).
thf(12466,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ sk14 )
!= ( sk5 @ ( A @ ( B @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[12448]) ).
thf(1723,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1639,327]) ).
thf(1724,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 @ r1 )
!= ( sk5 @ r1 ) ),
inference(simp,[status(thm)],[1723]) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk3 ) @ sk6 )
!= sk5 ),
inference(simp,[status(thm)],[1724]) ).
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(24746,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,24683]) ).
thf(24747,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ sk6 @ id ) )
!= ( B @ sk14 @ ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) @ id ) ) ),
inference(simp,[status(thm)],[24746]) ).
thf(24791,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 ) )
| ( ( A @ sk6 )
!= ( sk5 @ sk6 @ ( C @ sk13 @ sk8 @ sk19 ) ) ) ),
inference(simp,[status(thm)],[24747]) ).
thf(24824,plain,
! [B: $i,A: $i] :
( ( A @ sk14 @ sk6 )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) ) ),
inference(simp,[status(thm)],[24791]) ).
thf(470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,327]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[470]) ).
thf(474,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk3 ) @ sk6 ) ),
inference(simp,[status(thm)],[471]) ).
thf(6575,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)],[36,6540]) ).
thf(6576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ sk6 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[6575]) ).
thf(6582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk7 @ sk6 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[6576]) ).
thf(6590,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6582]) ).
thf(26189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ $true
| ~ ( sk5 @ ( B @ id ) ) ),
inference(paramod_ordered,[status(thm)],[3042,10923]) ).
thf(26190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ ( sk5 @ ( B @ id ) ) ),
inference(simp,[status(thm)],[26189]) ).
thf(26191,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk8 @ sk6 @ id ) ),
inference(pattern_uni,[status(thm)],[26190:[bind(A,$thf( E )),bind(B,$thf( E @ sk8 @ sk6 )),bind(C,$thf( E ))]]) ).
thf(26332,plain,
! [A: $i] :
~ ( sk5 @ ( A @ sk8 @ sk6 @ id ) ),
inference(simp,[status(thm)],[26191]) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,505]) ).
thf(529,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk17 ) @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[528]) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk17 ) @ sk6 ) ),
inference(simp,[status(thm)],[529]) ).
thf(1026,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)],[85,142]) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[1026]) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk15 ) )
!= ( D @ sk7 ) )
| ( ( A @ ( B @ sk18 ) )
!= C ) ),
inference(simp,[status(thm)],[1027]) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk15 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[1058]) ).
thf(728,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33,649]) ).
thf(729,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
!= ( C @ sk14 @ ( E @ ( F @ sk13 @ sk17 ) @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[728]) ).
thf(735,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) )
!= ( C @ sk14 ) )
| ( B
!= ( E @ ( F @ sk13 @ sk17 ) ) )
| ( A
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[729]) ).
thf(740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ ( D @ sk13 @ sk17 ) @ sk4 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[735]) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,332]) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[459]) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[460]) ).
thf(24553,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ $true
| ~ ( A @ r1 ) ),
inference(paramod_ordered,[status(thm)],[42,23200]) ).
thf(24554,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ ( A @ id ) )
!= ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) @ ( C @ sk14 @ id ) ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[24553]) ).
thf(24645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk5 @ sk6 @ ( B @ sk13 @ sk8 @ sk19 ) )
!= sk5 )
| ( A
!= ( C @ sk14 ) )
| ~ ( A @ r1 ) ),
inference(simp,[status(thm)],[24554]) ).
thf(24673,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) )
!= sk5 )
| ~ ( B @ sk14 @ r1 ) ),
inference(simp,[status(thm)],[24645]) ).
thf(26892,plain,
! [A: $i] :
( ( ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) )
!= sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[24673,79]) ).
thf(26893,plain,
! [A: $i] :
( ( sk5 @ sk6 @ ( A @ sk13 @ sk8 @ sk19 ) )
!= sk5 ),
inference(simp,[status(thm)],[26892]) ).
thf(6568,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3042,6540]) ).
thf(6569,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk8 @ sk6 @ ( A @ r2 ) )
!= ( C @ sk7 @ sk6 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[6568]) ).
thf(6587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk8 @ sk6 )
!= ( C @ sk7 @ sk6 ) )
| ( A != B ) ),
inference(simp,[status(thm)],[6569]) ).
thf(6595,plain,
! [B: $i,A: $i] :
( ( A @ sk8 @ sk6 )
!= ( B @ sk7 @ sk6 ) ),
inference(simp,[status(thm)],[6587]) ).
thf(14396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk13 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,3233]) ).
thf(14397,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk13 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14396]) ).
thf(14470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 @ sk6 ) )
| ( B
!= ( D @ sk13 ) ) ),
inference(simp,[status(thm)],[14397]) ).
thf(14486,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk13 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14470]) ).
thf(14412,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4111,3234]) ).
thf(14413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ sk6 @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[14412]) ).
thf(14459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 @ sk6 ) )
| ( B
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[14413]) ).
thf(14511,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk6 @ sk19 ) )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[14459]) ).
thf(9315,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)],[3795,90]) ).
thf(9316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk13 @ sk19 ) @ ( A @ sk12 @ id ) )
!= ( C @ ( B @ id ) ) )
| ( B @ ( C @ id ) ) ),
inference(simp,[status(thm)],[9315]) ).
thf(9317,plain,
! [A: $i] : ( A @ sk12 @ ( A @ ( A @ sk13 @ sk19 ) @ id ) ),
inference(pattern_uni,[status(thm)],[9316:[bind(A,$thf( F )),bind(B,$thf( F @ sk12 )),bind(C,$thf( F @ ( F @ sk13 @ sk19 ) ))]]) ).
thf(9370,plain,
! [A: $i] : ( A @ sk12 @ ( A @ ( A @ sk13 @ sk19 ) @ id ) ),
inference(simp,[status(thm)],[9317]) ).
thf(38412,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ ( E @ sk14 @ id ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,4091]) ).
thf(38413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ id ) )
!= ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) @ ( E @ sk14 @ id ) ) ),
inference(simp,[status(thm)],[38412]) ).
thf(38550,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( B @ sk14 @ ( C @ ( D @ sk13 @ sk3 ) @ sk19 ) ) )
| ( A
!= ( E @ sk14 ) ) ),
inference(simp,[status(thm)],[38413]) ).
thf(38572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ sk14 )
!= ( A @ sk14 @ ( B @ ( C @ sk13 @ sk3 ) @ sk19 ) ) ),
inference(simp,[status(thm)],[38550]) ).
thf(83,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk16 ) @ ( A @ ( B @ sk17 ) @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(1771,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1664,512]) ).
thf(1772,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) @ r1 )
!= ( sk5 @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[1771]) ).
thf(1812,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk17 ) )
!= ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[1772]) ).
thf(212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ $true
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(paramod_ordered,[status(thm)],[49,184]) ).
thf(213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( E @ r1 ) )
| ~ ( B @ r1 )
| ~ ( B @ ( C @ ( E @ r4 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[212]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ sk7 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ sk7 ))]]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ r1 )
| ~ ( A @ ( B @ ( D @ sk7 @ r4 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[214]) ).
thf(4718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,4513]) ).
thf(4719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk12 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[4718]) ).
thf(4727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk12 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[4719]) ).
thf(4734,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk12 ) ),
inference(simp,[status(thm)],[4727]) ).
thf(19104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk7 @ r4 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4084,3117]) ).
thf(19105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk19 ) @ sk6 @ ( A @ ( B @ r4 ) ) )
!= ( C @ sk14 @ ( E @ sk13 @ sk8 @ ( D @ sk7 @ r4 ) ) ) ),
inference(simp,[status(thm)],[19104]) ).
thf(19130,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk19 ) @ sk6 )
!= ( C @ sk14 ) )
| ( A
!= ( E @ sk13 @ sk8 ) )
| ( B
!= ( D @ sk7 ) ) ),
inference(simp,[status(thm)],[19105]) ).
thf(19188,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ sk7 @ ( C @ sk13 @ sk8 @ sk19 ) @ sk6 )
!= ( A @ sk14 ) ),
inference(simp,[status(thm)],[19130]) ).
thf(1657,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(1658,plain,
! [B: $i,A: $i] :
( ( ( A @ sk9 @ ( A @ id ) )
!= ( sk5 @ ( B @ id ) ) )
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[1657]) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ( ( A @ sk9 )
!= sk5 )
| ( A != B )
| ( B @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[1658]) ).
thf(1681,plain,
! [A: $i] :
( ( ( A @ sk9 )
!= sk5 )
| ( A @ r1 )
| ( A @ sk11 @ ( A @ sk10 @ r2 ) ) ),
inference(simp,[status(thm)],[1674]) ).
thf(3338,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)],[90,826]) ).
thf(3339,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)],[3338]) ).
thf(3340,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(pattern_uni,[status(thm)],[3339:[bind(A,$thf( H @ ( G @ sk17 ) )),bind(B,$thf( F @ sk13 )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(3405,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ sk13 @ ( C @ ( B @ sk17 ) @ id ) ),
inference(simp,[status(thm)],[3340]) ).
thf(51939,plain,
$false,
inference(e,[status(thm)],[24963,3883,1190,39098,4729,333,1840,29876,35029,88,3399,31656,10452,36422,40043,523,10446,3230,11409,34729,39484,3402,269,5614,1200,33309,6057,22717,1808,2659,3417,3942,142,8947,3121,1354,4762,9481,3794,4403,384,38209,3120,3429,11399,13623,16817,472,1063,16236,19191,3895,28769,23144,185,10923,42,1441,3777,288,14488,8330,24683,37,5621,4760,7761,3891,52,3263,4348,3425,184,3116,24826,110,25324,3125,14515,1191,3043,22710,4761,3148,3653,23057,14487,6049,38380,189,39061,26326,46,93,1741,3902,7047,8703,289,78,11404,261,4595,4329,1811,4600,31500,4733,3163,10918,1677,84,2335,12981,3431,10324,29875,756,1664,6591,39076,19165,4087,89,23208,3243,29865,3226,265,15165,7758,18475,2762,221,31490,74,3406,1074,6529,512,4407,1438,26113,12457,85,1199,5697,381,10922,220,102,1067,3795,4700,23207,39481,10943,60,24675,270,25316,6550,260,28,18471,31660,4091,3233,21,14484,33,15169,70,1423,1837,1365,24684,13612,4757,522,4402,4732,224,8700,26315,97,329,3894,26107,31493,1291,3408,1740,37658,7777,3413,3122,650,16232,188,53,141,3237,4123,5854,7513,4095,3119,328,225,4582,77,15162,1739,13355,6539,96,5705,6593,4406,4191,4513,1810,3428,547,1744,3654,31647,14509,8690,10455,14494,129,1720,4086,3162,3242,10919,3126,16822,3147,73,128,39485,4352,266,7052,508,22714,1071,8945,530,39503,2338,298,3130,6053,4380,3042,3890,1747,264,45,64,4269,4116,4354,32,34,2028,4340,180,13849,39501,3234,22,14481,39486,826,24681,545,27,59,118,71,26335,3651,1635,3123,9483,3118,54,49,25326,181,3416,86,6048,187,10921,219,3238,4601,39482,271,26114,113,10448,76,34731,509,13851,39,649,17813,13734,31654,4731,3165,4684,3133,4103,103,39100,1821,140,4277,91,108,330,827,3423,4085,223,299,267,505,80,8922,685,521,1198,130,9478,26765,226,33304,11402,35,17809,4084,7049,14493,4405,1809,6540,3161,31650,19150,3921,15048,473,6542,531,1748,48,690,6683,39019,1743,38956,327,4200,3129,12968,22625,6597,263,4593,9473,67,1813,182,331,3655,463,1738,2747,50,3652,72,14482,4111,991,33312,20030,3117,19164,6960,34727,3433,1839,6425,99,12467,87,4763,1817,16814,218,1189,23205,16153,465,14479,3401,13739,34956,1639,40,7044,1062,16388,186,3235,2764,39099,23,55,114,33149,3896,17653,383,26336,23200,82,290,29868,8925,510,3430,25259,1440,3149,25323,300,1678,4378,4356,36,262,146,51,190,183,23152,2768,3164,30,4596,1859,1363,33486,268,4083,22716,6258,6682,31491,12466,6537,1742,326,107,358,79,24824,474,6590,7402,26332,532,1065,740,464,26893,992,6595,68,62,3128,332,14486,14511,9370,38572,83,1812,222,12456,1069,26106,4734,90,3901,19188,1681,3405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN086+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/0.50 % Computer : n016.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 04:37:14 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.51/1.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.03/1.74 % [INFO] Parsing done (323ms).
% 2.03/1.76 % [INFO] Running in sequential loop mode.
% 3.28/2.40 % [INFO] eprover registered as external prover.
% 3.28/2.41 % [INFO] Scanning for conjecture ...
% 3.48/2.56 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.63/2.66 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.85/2.76 % [INFO] Problem is first-order (TPTP FOF).
% 3.85/2.77 % [INFO] Type checking passed.
% 3.85/2.77 % [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 ...
% 169.47/42.33 % External prover 'e' found a proof!
% 169.47/42.33 % [INFO] Killing All external provers ...
% 169.47/42.33 % Time passed: 41611ms (effective reasoning time: 40562ms)
% 169.47/42.33 % 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)>
% 169.47/42.33 % 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
% 169.47/42.33 % No. of inferences in proof: 1820
% 169.47/42.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 41611 ms resp. 40562 ms w/o parsing
% 165.84/42.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 165.84/42.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------