%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL942^2 : TPTP v9.3.1. Released v8.1.0.
% 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:18 AM UTC 2026
% Result : Theorem 95.26s 22.49s
% Output : Refutation 100.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 49
% Syntax : Number of formulae : 1401 ( 219 unt; 0 typ; 30 def)
% Number of atoms : 7427 (1721 equ; 0 cnn)
% Maximal formula atoms : 240 ( 5 avg)
% Number of connectives : 23661 (2875 ~;2765 |; 292 &;17262 @)
% ( 0 <=>; 467 =>; 0 <=; 0 <~>)
% Maximal formula depth : 73 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 12 con; 0-3 aty)
% Number of variables : 1212 ( 52 ^;1137 !; 0 ?;1212 :)
% ( 0 !>; 0 ?*; 0 @-; 23 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_decl,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(unit_decl,type,
unit: $i ).
thf(e0_decl,type,
e0: $i ).
thf(e1_decl,type,
e1: $i ).
thf(e2_decl,type,
e2: $i ).
thf(e3_decl,type,
e3: $i ).
thf(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(inv_decl,type,
inv: $i > $i ).
thf(op_decl,type,
op: $i > $i > $i ).
thf(sk1_decl,type,
sk1: mworld ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: $o ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: mworld > $o ).
thf(sk6_decl,type,
sk6: mworld > mworld ).
thf(sk7_decl,type,
sk7: mworld > $o ).
thf(sk8_decl,type,
sk8: mworld > mworld ).
thf(sk9_decl,type,
sk9: mworld > mworld ).
thf(sk10_decl,type,
sk10: mworld > mworld ).
thf(sk11_decl,type,
sk11: mworld > $o ).
thf(sk12_decl,type,
sk12: mworld > mworld ).
thf(sk13_decl,type,
sk13: mworld > $o ).
thf(sk14_decl,type,
sk14: mworld > mworld ).
thf(sk15_decl,type,
sk15: mworld > mworld ).
thf(sk16_decl,type,
sk16: mworld > mworld ).
thf(sk17_decl,type,
sk17: mworld > $o ).
thf(sk18_decl,type,
sk18: mworld > mworld ).
thf(sk19_decl,type,
sk19: mworld > $o ).
thf(sk20_decl,type,
sk20: mworld > mworld ).
thf(sk21_decl,type,
sk21: mworld > mworld ).
thf(sk22_decl,type,
sk22: mworld > mworld ).
thf(sk23_decl,type,
sk23: mworld > $o ).
thf(sk24_decl,type,
sk24: mworld > mworld ).
thf(sk25_decl,type,
sk25: mworld > $o ).
thf(sk26_decl,type,
sk26: mworld > mworld ).
thf(sk27_decl,type,
sk27: mworld > mworld ).
thf(sk28_decl,type,
sk28: mworld > mworld ).
thf(sk29_decl,type,
sk29: mworld > mworld ).
thf(sk30_decl,type,
sk30: mworld > mworld ).
thf(sk31_decl,type,
sk31: mworld > mworld ).
thf(sk32_decl,type,
sk32: mworld > mworld ).
thf(sk33_decl,type,
sk33: mworld > mworld ).
thf(sk34_decl,type,
sk34: mworld > mworld ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: mworld] :
~ ( ( mrel @ mactual @ A )
=> ~ ( ( ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ B ) ) )
| ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ B ) ) )
| ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ B ) ) )
| ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ B ) ) ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ~ ( ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ C ) ) )
| ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ C ) ) )
| ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ C ) ) )
| ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ C ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ B ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ B ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ B ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ B ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ B ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ B ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ B ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ B ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ B ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ B ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ B ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ B ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ B ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ B ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ B ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ B ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ e0 @ e1 @ B ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ e0 @ e2 @ B ) ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ e0 @ e3 @ B ) ) ) ) ).
thf(sk32_def,definition,
( sk32
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ e1 @ e2 @ B ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ e1 @ e3 @ B ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( qmltpeq @ e2 @ e3 @ B ) ) ) ) ).
thf(1,conjecture,
mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ( ( ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ B ) ) )
| ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ B ) ) )
| ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ B ) ) )
| ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ B ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ B ) ) ) )
& ! [B: mworld] :
( ( mrel @ A @ B )
=> ~ ( ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ C ) ) )
| ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ C ) ) )
| ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ C ) ) )
| ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
! [Q: mworld,P: mworld,O: mworld,N: mworld,M: mworld,L: mworld,K: mworld,J: mworld,I: mworld,H: mworld,G: mworld,F: mworld,E: mworld,D: mworld,C: mworld,B: mworld,A: mworld] :
( ( mrel @ mactual @ sk1 )
& ( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2 )
& ( ~ ( mrel @ sk1 @ B )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ B )
| sk2 )
& ( ~ ( mrel @ sk1 @ C )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ C )
| sk2 )
& ( ~ ( mrel @ sk1 @ D )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ D )
| sk2 )
& ( ~ sk2
| ~ ( mrel @ sk1 @ E )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ E )
| sk3 )
& ( ~ sk2
| ~ ( mrel @ sk1 @ F )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ F )
| sk3 )
& ( ~ sk2
| ~ ( mrel @ sk1 @ G )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ G )
| sk3 )
& ( ~ sk2
| ~ ( mrel @ sk1 @ H )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ H )
| sk3 )
& ( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ I )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ I )
| sk4 )
& ( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ J )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ J )
| sk4 )
& ( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ K )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ K )
| sk4 )
& ( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ L )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ L )
| sk4 )
& ( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ M )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ M ) )
& ( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ N )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ N ) )
& ( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ O )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ O ) )
& ( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ P )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ P ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( mrel @ Q @ ( sk6 @ Q ) )
| ~ ( sk5 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ Q ) )
| ~ ( sk5 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk5 @ Q )
| ( mrel @ Q @ ( sk8 @ Q ) )
| ~ ( sk7 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk5 @ Q )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk8 @ Q ) )
| ~ ( sk7 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk5 @ Q )
| ( sk7 @ Q )
| ( mrel @ Q @ ( sk9 @ Q ) )
| ( mrel @ Q @ ( sk10 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk5 @ Q )
| ( sk7 @ Q )
| ( mrel @ Q @ ( sk9 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk10 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk5 @ Q )
| ( sk7 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk9 @ Q ) )
| ( mrel @ Q @ ( sk10 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk5 @ Q )
| ( sk7 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk9 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk10 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( mrel @ Q @ ( sk12 @ Q ) )
| ~ ( sk11 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sk12 @ Q ) )
| ~ ( sk11 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk11 @ Q )
| ( mrel @ Q @ ( sk14 @ Q ) )
| ~ ( sk13 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk11 @ Q )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sk14 @ Q ) )
| ~ ( sk13 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk11 @ Q )
| ( sk13 @ Q )
| ( mrel @ Q @ ( sk15 @ Q ) )
| ( mrel @ Q @ ( sk16 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk11 @ Q )
| ( sk13 @ Q )
| ( mrel @ Q @ ( sk15 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sk16 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk11 @ Q )
| ( sk13 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sk15 @ Q ) )
| ( mrel @ Q @ ( sk16 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk11 @ Q )
| ( sk13 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sk15 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sk16 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( mrel @ Q @ ( sk18 @ Q ) )
| ~ ( sk17 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sk18 @ Q ) )
| ~ ( sk17 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk17 @ Q )
| ( mrel @ Q @ ( sk20 @ Q ) )
| ~ ( sk19 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk17 @ Q )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sk20 @ Q ) )
| ~ ( sk19 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk17 @ Q )
| ( sk19 @ Q )
| ( mrel @ Q @ ( sk21 @ Q ) )
| ( mrel @ Q @ ( sk22 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk17 @ Q )
| ( sk19 @ Q )
| ( mrel @ Q @ ( sk21 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sk22 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk17 @ Q )
| ( sk19 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sk21 @ Q ) )
| ( mrel @ Q @ ( sk22 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk17 @ Q )
| ( sk19 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sk21 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sk22 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( mrel @ Q @ ( sk24 @ Q ) )
| ~ ( sk23 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ Q ) )
| ~ ( sk23 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk23 @ Q )
| ( mrel @ Q @ ( sk26 @ Q ) )
| ~ ( sk25 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk23 @ Q )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sk26 @ Q ) )
| ~ ( sk25 @ Q ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk23 @ Q )
| ( sk25 @ Q )
| ( mrel @ Q @ ( sk27 @ Q ) )
| ( mrel @ Q @ ( sk28 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk23 @ Q )
| ( sk25 @ Q )
| ( mrel @ Q @ ( sk27 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sk28 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk23 @ Q )
| ( sk25 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sk27 @ Q ) )
| ( mrel @ Q @ ( sk28 @ Q ) ) )
& ( ~ ( mrel @ sk1 @ Q )
| ( sk23 @ Q )
| ( sk25 @ Q )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sk27 @ Q ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sk28 @ Q ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(41,plain,
mrel @ mactual @ sk1,
inference(cnfConj,[status(thm)],[22]) ).
thf(3,axiom,
mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e1 @ e3 ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e2 @ e3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(119,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ e0 @ e1 @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ e0 @ e2 @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ e0 @ e3 @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ e1 @ e2 @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ e1 @ e3 @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ e2 @ e3 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(120,plain,
! [F: mworld,E: mworld,D: mworld,C: mworld,B: mworld,A: mworld] :
( ( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk29 @ A ) ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) ) )
& ( ~ ( mrel @ mactual @ B )
| ( mrel @ B @ ( sk30 @ B ) ) )
& ( ~ ( mrel @ mactual @ B )
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ B ) ) )
& ( ~ ( mrel @ mactual @ C )
| ( mrel @ C @ ( sk31 @ C ) ) )
& ( ~ ( mrel @ mactual @ C )
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ C ) ) )
& ( ~ ( mrel @ mactual @ D )
| ( mrel @ D @ ( sk32 @ D ) ) )
& ( ~ ( mrel @ mactual @ D )
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ D ) ) )
& ( ~ ( mrel @ mactual @ E )
| ( mrel @ E @ ( sk33 @ E ) ) )
& ( ~ ( mrel @ mactual @ E )
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ E ) ) )
& ( ~ ( mrel @ mactual @ F )
| ( mrel @ F @ ( sk34 @ F ) ) )
& ( ~ ( mrel @ mactual @ F )
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ F ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(127,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk29 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(19024,plain,
! [A: mworld] :
( ~ $true
| ( mrel @ A @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,127]) ).
thf(19025,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19024]) ).
thf(19026,plain,
mrel @ sk1 @ ( sk29 @ sk1 ),
inference(pattern_uni,[status(thm)],[19025:[bind(A,$thf( sk1 ))]]) ).
thf(125,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(133,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(19389,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,133]) ).
thf(19390,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19389]) ).
thf(19609,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19390]) ).
thf(19672,plain,
( ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19609]) ).
thf(27,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sk27 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sk28 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(101,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sk27 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sk28 @ A ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(9,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(512,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(513,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(cnf,[status(esa)],[512]) ).
thf(64,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk6 @ A ) )
| ~ ( sk5 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(96,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk6 @ A ) )
| ~ ( sk5 @ A ) ),
inference(simp,[status(thm)],[64]) ).
thf(11644,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk6 @ B ) )
| ~ ( sk5 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,96]) ).
thf(11645,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk6 @ B ) )
| ~ ( sk5 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[11644]) ).
thf(11646,plain,
( ( mrel @ sk1 @ ( sk6 @ sk1 ) )
| ~ ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[11645:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(36,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(34,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ A ) )
| ~ ( sk5 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(98,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ A ) )
| ~ ( sk5 @ A ) ),
inference(simp,[status(thm)],[34]) ).
thf(13042,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ B ) )
| ~ ( sk5 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,98]) ).
thf(13043,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ B ) )
| ~ ( sk5 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[13042]) ).
thf(13044,plain,
( ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ sk1 ) )
| ~ ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[13043:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(14275,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| sk2
| ~ $true
| ~ ( sk5 @ sk1 )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
!= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,13044]) ).
thf(14276,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| sk2
| ~ ( sk5 @ sk1 )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
!= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk6 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[14275]) ).
thf(14277,plain,
( ~ ( mrel @ sk1 @ ( sk6 @ sk1 ) )
| sk2
| ~ ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14276:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(14888,plain,
( ~ ( sk5 @ sk1 )
| ~ $true
| sk2
| ~ ( sk5 @ sk1 )
| ( ( mrel @ sk1 @ ( sk6 @ sk1 ) )
!= ( mrel @ sk1 @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11646,14277]) ).
thf(14889,plain,
( ~ ( sk5 @ sk1 )
| sk2
| ( ( mrel @ sk1 @ ( sk6 @ sk1 ) )
!= ( mrel @ sk1 @ ( sk6 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[14888]) ).
thf(14890,plain,
( ~ ( sk5 @ sk1 )
| sk2 ),
inference(pattern_uni,[status(thm)],[14889:[]]) ).
thf(128,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(138,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(907,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,138]) ).
thf(908,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[907]) ).
thf(909,plain,
~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[908:[bind(A,$thf( sk1 ))]]) ).
thf(62,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ A )
| sk2 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(118,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ A )
| sk2 ),
inference(simp,[status(thm)],[62]) ).
thf(35087,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,118]) ).
thf(35088,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[35087]) ).
thf(35089,plain,
( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ sk1 )
| sk2 ),
inference(pattern_uni,[status(thm)],[35088:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(15,axiom,
mlocal @ ( mbox @ ( qmltpeq @ ( inv @ unit ) @ unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(584,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ unit ) @ unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(585,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ unit ) @ unit @ A ) ),
inference(cnf,[status(esa)],[584]) ).
thf(132,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(135,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(799,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,135]) ).
thf(800,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(1118,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,801]) ).
thf(1119,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(simp,[status(thm)],[1118]) ).
thf(1157,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e1 )
| ( e3 != unit )
| ( A
!= ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[1119]) ).
thf(1179,plain,
( ~ ( mrel @ mactual @ ( sk33 @ mactual ) )
| ( ( inv @ unit )
!= e1 )
| ( e3 != unit ) ),
inference(simp,[status(thm)],[1157]) ).
thf(664,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,133]) ).
thf(665,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[664]) ).
thf(666,plain,
~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ),
inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(46,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( mrel @ A @ ( sk14 @ A ) )
| ~ ( sk13 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(88,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( mrel @ A @ ( sk14 @ A ) )
| ~ ( sk13 @ A ) ),
inference(simp,[status(thm)],[46]) ).
thf(57,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(89,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(669,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk5 @ B )
| ( sk7 @ B )
| ( mrel @ B @ ( sk9 @ B ) )
| ( mrel @ B @ ( sk10 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,89]) ).
thf(670,plain,
! [B: mworld,A: mworld] :
( ( sk5 @ B )
| ( sk7 @ B )
| ( mrel @ B @ ( sk9 @ B ) )
| ( mrel @ B @ ( sk10 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(671,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( mrel @ sk1 @ ( sk10 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[670:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(819,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ~ $true
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) )
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[671,89]) ).
thf(820,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) )
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[819]) ).
thf(821,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[820:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(1344,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,36]) ).
thf(1345,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[1344]) ).
thf(1353,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( sk10 @ sk1 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1369,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| sk2
| ( ( sk10 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1353]) ).
thf(19039,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk29 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,127]) ).
thf(19040,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk29 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[19039]) ).
thf(19041,plain,
mrel @ mactual @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19040:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(10,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(514,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(515,plain,
! [D: mworld,C: mworld,B: mworld,A: mworld] :
( ( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A ) )
& ( ~ ( mrel @ mactual @ B )
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ B ) )
& ( ~ ( mrel @ mactual @ C )
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ C ) )
& ( ~ ( mrel @ mactual @ D )
| ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ D ) ) ),
inference(cnf,[status(esa)],[514]) ).
thf(518,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A ) ),
inference(cnfConj,[status(thm)],[515]) ).
thf(521,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A ) ),
inference(simp,[status(thm)],[518]) ).
thf(661,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,133]) ).
thf(662,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[661]) ).
thf(663,plain,
~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( sk1 ))]]) ).
thf(10745,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,663]) ).
thf(10746,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[10745]) ).
thf(10784,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( A
!= ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[10746]) ).
thf(10820,plain,
( ~ ( mrel @ mactual @ ( sk30 @ sk1 ) )
| ( ( inv @ ( inv @ e2 ) )
!= e0 ) ),
inference(simp,[status(thm)],[10784]) ).
thf(19873,plain,
( ~ $true
| ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,10820]) ).
thf(19874,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19873]) ).
thf(19958,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( mactual != mactual )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19874]) ).
thf(20095,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19958]) ).
thf(1108,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,585]) ).
thf(1109,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1108]) ).
thf(1110,plain,
qmltpeq @ ( inv @ unit ) @ unit @ sk1,
inference(pattern_uni,[status(thm)],[1109:[bind(A,$thf( sk1 ))]]) ).
thf(131,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(19576,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,131]) ).
thf(19577,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19576]) ).
thf(19657,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19577]) ).
thf(19687,plain,
( ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19657]) ).
thf(11,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) ) ) @ ( mbox @ ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(523,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(52,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(74,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ A ) ),
inference(simp,[status(thm)],[52]) ).
thf(1003,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,74]) ).
thf(1004,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[1003]) ).
thf(1005,plain,
( ~ sk2
| ~ sk3
| ~ sk4
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(51,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sk12 @ A ) )
| ~ ( sk11 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(115,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ ( sk12 @ A ) )
| ~ ( sk11 @ A ) ),
inference(simp,[status(thm)],[51]) ).
thf(519,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[515]) ).
thf(522,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A ) ),
inference(simp,[status(thm)],[519]) ).
thf(12219,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,522]) ).
thf(12220,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[12219]) ).
thf(12221,plain,
qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1,
inference(pattern_uni,[status(thm)],[12220:[bind(A,$thf( sk1 ))]]) ).
thf(19709,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,138]) ).
thf(19710,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19709]) ).
thf(19711,plain,
~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[19710:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(20841,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12221,19711]) ).
thf(20842,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20841]) ).
thf(21073,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[20842]) ).
thf(21114,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21073]) ).
thf(6,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ unit ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ unit ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e2 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ unit ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e3 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e3 @ unit ) @ e3 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e2 ) ) @ ( mbox @ ( qmltpeq @ unit @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(276,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ unit @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ unit @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ unit @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ unit @ e3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(277,plain,
! [L: mworld,K: mworld,J: mworld,I: mworld,H: mworld,G: mworld,F: mworld,E: mworld,D: mworld,C: mworld,B: mworld,A: mworld] :
( ( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A ) )
& ( ~ ( mrel @ mactual @ B )
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ B ) )
& ( ~ ( mrel @ mactual @ C )
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ C ) )
& ( ~ ( mrel @ mactual @ D )
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ D ) )
& ( ~ ( mrel @ mactual @ E )
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ E ) )
& ( ~ ( mrel @ mactual @ F )
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ F ) )
& ( ~ ( mrel @ mactual @ G )
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ G ) )
& ( ~ ( mrel @ mactual @ H )
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ H ) )
& ( ~ ( mrel @ mactual @ I )
| ( qmltpeq @ unit @ e0 @ I )
| ~ ( mrel @ mactual @ J )
| ( qmltpeq @ unit @ e1 @ J )
| ~ ( mrel @ mactual @ K )
| ( qmltpeq @ unit @ e2 @ K )
| ~ ( mrel @ mactual @ L )
| ( qmltpeq @ unit @ e3 @ L ) ) ),
inference(cnf,[status(esa)],[276]) ).
thf(282,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(291,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A ) ),
inference(simp,[status(thm)],[282]) ).
thf(19817,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,291]) ).
thf(19818,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19817]) ).
thf(19819,plain,
qmltpeq @ ( op @ e1 @ unit ) @ e1 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19818:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(524,plain,
! [B: mworld,A: mworld] :
( ( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A ) )
& ( ~ ( mrel @ mactual @ B )
| ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ B ) ) ),
inference(cnf,[status(esa)],[523]) ).
thf(526,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A ) ),
inference(cnfConj,[status(thm)],[524]) ).
thf(527,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A ) ),
inference(simp,[status(thm)],[526]) ).
thf(796,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,135]) ).
thf(797,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[796]) ).
thf(798,plain,
~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[797:[bind(A,$thf( sk1 ))]]) ).
thf(16897,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[527,798]) ).
thf(16898,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[16897]) ).
thf(16994,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e3 )
| ( A
!= ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[16898]) ).
thf(17038,plain,
( ~ ( mrel @ mactual @ ( sk33 @ sk1 ) )
| ( ( op @ e2 @ e3 )
!= e3 ) ),
inference(simp,[status(thm)],[16994]) ).
thf(19861,plain,
( ~ $true
| ( ( op @ e2 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,17038]) ).
thf(19862,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19861]) ).
thf(19993,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( mactual != mactual )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19862]) ).
thf(20046,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19993]) ).
thf(280,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(287,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A ) ),
inference(simp,[status(thm)],[280]) ).
thf(1712,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[287,798]) ).
thf(1713,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1712]) ).
thf(1770,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e3 )
!= e1 )
| ( e3 != e3 )
| ( A
!= ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[1713]) ).
thf(1793,plain,
( ~ ( mrel @ mactual @ ( sk33 @ sk1 ) )
| ( ( op @ unit @ e3 )
!= e1 ) ),
inference(simp,[status(thm)],[1770]) ).
thf(525,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A ) ),
inference(cnfConj,[status(thm)],[524]) ).
thf(14381,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[525,666]) ).
thf(14382,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(simp,[status(thm)],[14381]) ).
thf(14497,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( A
!= ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[14382]) ).
thf(14538,plain,
( ~ ( mrel @ mactual @ ( sk30 @ mactual ) )
| ( ( op @ e3 @ e3 )
!= e2 ) ),
inference(simp,[status(thm)],[14497]) ).
thf(516,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A ) ),
inference(cnfConj,[status(thm)],[515]) ).
thf(9096,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,516]) ).
thf(9097,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[9096]) ).
thf(9199,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[9097]) ).
thf(9233,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[9199]) ).
thf(14421,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,525]) ).
thf(14422,plain,
! [A: mworld] :
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[14421]) ).
thf(14423,plain,
qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1,
inference(pattern_uni,[status(thm)],[14422:[bind(A,$thf( sk1 ))]]) ).
thf(14605,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14423,663]) ).
thf(14606,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[14605]) ).
thf(14643,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[14606]) ).
thf(14665,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[14643]) ).
thf(10713,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,521]) ).
thf(10714,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[10713]) ).
thf(10715,plain,
qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1,
inference(pattern_uni,[status(thm)],[10714:[bind(A,$thf( sk1 ))]]) ).
thf(278,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(290,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A ) ),
inference(simp,[status(thm)],[278]) ).
thf(5071,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,798]) ).
thf(5072,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[5071]) ).
thf(5134,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e3 @ unit )
!= e1 )
| ( e3 != e3 )
| ( A
!= ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[5072]) ).
thf(5163,plain,
( ~ ( mrel @ mactual @ ( sk33 @ sk1 ) )
| ( ( op @ e3 @ unit )
!= e1 ) ),
inference(simp,[status(thm)],[5134]) ).
thf(129,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(137,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(877,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,137]) ).
thf(878,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[877]) ).
thf(879,plain,
~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ),
inference(pattern_uni,[status(thm)],[878:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(10707,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,879]) ).
thf(10708,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(simp,[status(thm)],[10707]) ).
thf(10791,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( e2 != e2 )
| ( A
!= ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[10708]) ).
thf(10827,plain,
( ~ ( mrel @ mactual @ ( sk32 @ mactual ) )
| ( ( inv @ ( inv @ e2 ) )
!= e1 ) ),
inference(simp,[status(thm)],[10791]) ).
thf(16901,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[527,879]) ).
thf(16902,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(simp,[status(thm)],[16901]) ).
thf(16978,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e2 )
| ( A
!= ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[16902]) ).
thf(17022,plain,
( ~ ( mrel @ mactual @ ( sk32 @ mactual ) )
| ( ( op @ e2 @ e3 )
!= e2 ) ),
inference(simp,[status(thm)],[16978]) ).
thf(19800,plain,
( ~ $true
| ( ( op @ e2 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,17022]) ).
thf(19801,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19800]) ).
thf(20010,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( mactual != mactual )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19801]) ).
thf(20063,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20010]) ).
thf(285,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(288,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A ) ),
inference(simp,[status(thm)],[285]) ).
thf(2643,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[288,663]) ).
thf(2644,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[2643]) ).
thf(2710,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( A
!= ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[2644]) ).
thf(2736,plain,
( ~ ( mrel @ mactual @ ( sk30 @ sk1 ) )
| ( ( op @ unit @ e2 )
!= e0 ) ),
inference(simp,[status(thm)],[2710]) ).
thf(19915,plain,
( ~ $true
| ( ( op @ unit @ e2 )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,2736]) ).
thf(19916,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19915]) ).
thf(20013,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( mactual != mactual )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19916]) ).
thf(20066,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20013]) ).
thf(19341,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,138]) ).
thf(19342,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19341]) ).
thf(19600,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19342]) ).
thf(19668,plain,
( ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19600]) ).
thf(5079,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,290]) ).
thf(5080,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[5079]) ).
thf(5081,plain,
qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1,
inference(pattern_uni,[status(thm)],[5080:[bind(A,$thf( sk1 ))]]) ).
thf(20911,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5081,19711]) ).
thf(20912,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20911]) ).
thf(21031,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[20912]) ).
thf(21096,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21031]) ).
thf(16913,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,527]) ).
thf(16914,plain,
! [A: mworld] :
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[16913]) ).
thf(16915,plain,
qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1,
inference(pattern_uni,[status(thm)],[16914:[bind(A,$thf( sk1 ))]]) ).
thf(121,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(134,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(767,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,134]) ).
thf(768,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(769,plain,
~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[768:[bind(A,$thf( sk1 ))]]) ).
thf(1138,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,769]) ).
thf(1139,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1138]) ).
thf(1174,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e2 )
| ( e3 != unit )
| ( A
!= ( sk34 @ sk1 ) ) ),
inference(simp,[status(thm)],[1139]) ).
thf(1196,plain,
( ~ ( mrel @ mactual @ ( sk34 @ sk1 ) )
| ( ( inv @ unit )
!= e2 )
| ( e3 != unit ) ),
inference(simp,[status(thm)],[1174]) ).
thf(19728,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,288]) ).
thf(19729,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19728]) ).
thf(19730,plain,
qmltpeq @ ( op @ unit @ e2 ) @ e2 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19729:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(655,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,131]) ).
thf(656,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[655]) ).
thf(657,plain,
~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ),
inference(pattern_uni,[status(thm)],[656:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(23080,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19730,657]) ).
thf(23081,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[23080]) ).
thf(23147,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[23081]) ).
thf(23184,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e1 ) ),
inference(simp,[status(thm)],[23147]) ).
thf(14455,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[525,663]) ).
thf(14456,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[14455]) ).
thf(14486,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( A
!= ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[14456]) ).
thf(14527,plain,
( ~ ( mrel @ mactual @ ( sk30 @ sk1 ) )
| ( ( op @ e3 @ e3 )
!= e2 ) ),
inference(simp,[status(thm)],[14486]) ).
thf(19753,plain,
( ~ $true
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,14527]) ).
thf(19754,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19753]) ).
thf(19965,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( mactual != mactual )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19754]) ).
thf(20102,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19965]) ).
thf(279,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(289,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A ) ),
inference(simp,[status(thm)],[279]) ).
thf(3604,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,289]) ).
thf(3605,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[3604]) ).
thf(3606,plain,
qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1,
inference(pattern_uni,[status(thm)],[3605:[bind(A,$thf( sk1 ))]]) ).
thf(3698,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[3606,666]) ).
thf(3699,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[3698]) ).
thf(3756,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[3699]) ).
thf(3766,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[3756]) ).
thf(283,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(292,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A ) ),
inference(simp,[status(thm)],[283]) ).
thf(19769,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,292]) ).
thf(19770,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19769]) ).
thf(19771,plain,
qmltpeq @ ( op @ e0 @ unit ) @ e0 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19770:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(24236,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19771,657]) ).
thf(24237,plain,
( ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[24236]) ).
thf(24287,plain,
( ( ( op @ e0 @ unit )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[24237]) ).
thf(24334,plain,
( ( ( op @ e0 @ unit )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[24287]) ).
thf(14430,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,525]) ).
thf(14431,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[14430]) ).
thf(14432,plain,
qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual,
inference(pattern_uni,[status(thm)],[14431:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(14712,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14432,663]) ).
thf(14713,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[14712]) ).
thf(14745,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[14713]) ).
thf(14769,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[14745]) ).
thf(910,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,138]) ).
thf(911,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[910]) ).
thf(912,plain,
~ ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ),
inference(pattern_uni,[status(thm)],[911:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(12247,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,912]) ).
thf(12248,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(simp,[status(thm)],[12247]) ).
thf(12300,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( A
!= ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[12248]) ).
thf(12324,plain,
( ~ ( mrel @ mactual @ ( sk31 @ mactual ) )
| ( ( inv @ ( inv @ e3 ) )
!= e0 ) ),
inference(simp,[status(thm)],[12300]) ).
thf(1228,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,912]) ).
thf(1229,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[1228]) ).
thf(1254,plain,
( ( ( inv @ unit )
!= e0 )
| ( e3 != unit )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1229]) ).
thf(7626,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,292]) ).
thf(7627,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[7626]) ).
thf(7628,plain,
qmltpeq @ ( op @ e0 @ unit ) @ e0 @ sk1,
inference(pattern_uni,[status(thm)],[7627:[bind(A,$thf( sk1 ))]]) ).
thf(5088,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,290]) ).
thf(5089,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[5088]) ).
thf(5090,plain,
qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual,
inference(pattern_uni,[status(thm)],[5089:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(5263,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5090,909]) ).
thf(5264,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[5263]) ).
thf(5311,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[5264]) ).
thf(5342,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[5311]) ).
thf(9114,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,516]) ).
thf(9115,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[9114]) ).
thf(9116,plain,
qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ sk1,
inference(pattern_uni,[status(thm)],[9115:[bind(A,$thf( sk1 ))]]) ).
thf(1226,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,769]) ).
thf(1227,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ) ),
inference(simp,[status(thm)],[1226]) ).
thf(1243,plain,
( ( ( inv @ unit )
!= e2 )
| ( e3 != unit )
| ( ( sk34 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1227]) ).
thf(7635,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,292]) ).
thf(7636,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[7635]) ).
thf(7637,plain,
qmltpeq @ ( op @ e0 @ unit ) @ e0 @ mactual,
inference(pattern_uni,[status(thm)],[7636:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(61,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ A )
| sk4 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(75,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ A )
| sk4 ),
inference(simp,[status(thm)],[61]) ).
thf(1389,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ sk3
| ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ B )
| sk4
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,75]) ).
thf(1390,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ sk3
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ B )
| sk4
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[1389]) ).
thf(1391,plain,
( ~ sk2
| ~ sk3
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ sk1 )
| sk4 ),
inference(pattern_uni,[status(thm)],[1390:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(284,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(1480,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,284]) ).
thf(1481,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1480]) ).
thf(1555,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[1481]) ).
thf(1576,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1555]) ).
thf(874,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,137]) ).
thf(875,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[874]) ).
thf(876,plain,
~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[875:[bind(A,$thf( sk1 ))]]) ).
thf(16957,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[527,876]) ).
thf(16958,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[16957]) ).
thf(16982,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e2 )
| ( A
!= ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[16958]) ).
thf(17026,plain,
( ~ ( mrel @ mactual @ ( sk32 @ sk1 ) )
| ( ( op @ e2 @ e3 )
!= e2 ) ),
inference(simp,[status(thm)],[16982]) ).
thf(2667,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,288]) ).
thf(2668,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[2667]) ).
thf(2669,plain,
qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1,
inference(pattern_uni,[status(thm)],[2668:[bind(A,$thf( sk1 ))]]) ).
thf(2761,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[2669,666]) ).
thf(2762,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[2761]) ).
thf(2817,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[2762]) ).
thf(2825,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[2817]) ).
thf(12228,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,522]) ).
thf(12229,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[12228]) ).
thf(12230,plain,
qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual,
inference(pattern_uni,[status(thm)],[12229:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(20977,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12230,19711]) ).
thf(20978,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20977]) ).
thf(21022,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[20978]) ).
thf(21092,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21022]) ).
thf(35,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(81,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2 ),
inference(simp,[status(thm)],[35]) ).
thf(3114,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,81]) ).
thf(3115,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[3114]) ).
thf(3116,plain,
( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ sk1 )
| sk2 ),
inference(pattern_uni,[status(thm)],[3115:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1721,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,287]) ).
thf(1722,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[1721]) ).
thf(1723,plain,
qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual,
inference(pattern_uni,[status(thm)],[1722:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(20901,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1723,19711]) ).
thf(20902,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20901]) ).
thf(21005,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[20902]) ).
thf(21086,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21005]) ).
thf(40,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ A )
| sk4 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(110,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ A )
| sk4 ),
inference(simp,[status(thm)],[40]) ).
thf(1111,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ unit ) @ unit @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,585]) ).
thf(1112,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( inv @ unit ) @ unit @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[1111]) ).
thf(1113,plain,
qmltpeq @ ( inv @ unit ) @ unit @ mactual,
inference(pattern_uni,[status(thm)],[1112:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(1271,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,801]) ).
thf(1272,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[1271]) ).
thf(1323,plain,
( ( ( inv @ unit )
!= e1 )
| ( e3 != unit )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1272]) ).
thf(5115,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,801]) ).
thf(5116,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(simp,[status(thm)],[5115]) ).
thf(5121,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e3 @ unit )
!= e1 )
| ( e3 != e3 )
| ( A
!= ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[5116]) ).
thf(5150,plain,
( ~ ( mrel @ mactual @ ( sk33 @ mactual ) )
| ( ( op @ e3 @ unit )
!= e1 ) ),
inference(simp,[status(thm)],[5121]) ).
thf(1275,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,909]) ).
thf(1276,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[1275]) ).
thf(1313,plain,
( ( ( inv @ unit )
!= e0 )
| ( e3 != unit )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1276]) ).
thf(19901,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,290]) ).
thf(19902,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19901]) ).
thf(19903,plain,
qmltpeq @ ( op @ e3 @ unit ) @ e3 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19902:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(26617,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19903,657]) ).
thf(26618,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[26617]) ).
thf(26698,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[26618]) ).
thf(26718,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e1 ) ),
inference(simp,[status(thm)],[26698]) ).
thf(39,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(79,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2 ),
inference(simp,[status(thm)],[39]) ).
thf(2464,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,79]) ).
thf(2465,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[2464]) ).
thf(2466,plain,
( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ sk1 )
| sk2 ),
inference(pattern_uni,[status(thm)],[2465:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(6609,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,291]) ).
thf(6610,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[6609]) ).
thf(6611,plain,
qmltpeq @ ( op @ e1 @ unit ) @ e1 @ sk1,
inference(pattern_uni,[status(thm)],[6610:[bind(A,$thf( sk1 ))]]) ).
thf(14670,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14432,909]) ).
thf(14671,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[14670]) ).
thf(14759,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[14671]) ).
thf(14773,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[14759]) ).
thf(7608,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,292]) ).
thf(7609,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[7608]) ).
thf(7697,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[7609]) ).
thf(7728,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e0 @ unit ) @ e0 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[7697]) ).
thf(2695,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[288,876]) ).
thf(2696,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[2695]) ).
thf(2708,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e2 )
!= e1 )
| ( e2 != e2 )
| ( A
!= ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[2696]) ).
thf(2734,plain,
( ~ ( mrel @ mactual @ ( sk32 @ sk1 ) )
| ( ( op @ unit @ e2 )
!= e1 ) ),
inference(simp,[status(thm)],[2708]) ).
thf(19815,plain,
( ~ $true
| ( ( op @ unit @ e2 )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,2734]) ).
thf(19816,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19815]) ).
thf(19996,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( mactual != mactual )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19816]) ).
thf(20049,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19996]) ).
thf(5275,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5090,798]) ).
thf(5276,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[5275]) ).
thf(5330,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[5276]) ).
thf(5338,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[5330]) ).
thf(70,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk18 @ A ) )
| ~ ( sk17 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(91,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk18 @ A ) )
| ~ ( sk17 @ A ) ),
inference(simp,[status(thm)],[70]) ).
thf(8052,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk18 @ B ) )
| ~ ( sk17 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,91]) ).
thf(8053,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk18 @ B ) )
| ~ ( sk17 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[8052]) ).
thf(8054,plain,
( ( mrel @ sk1 @ ( sk18 @ sk1 ) )
| ~ ( sk17 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[8053:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(3613,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,289]) ).
thf(3614,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[3613]) ).
thf(3615,plain,
qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual,
inference(pattern_uni,[status(thm)],[3614:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(3769,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3615,663]) ).
thf(3770,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[3769]) ).
thf(3821,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[3770]) ).
thf(3840,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[3821]) ).
thf(5181,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5081,909]) ).
thf(5182,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[5181]) ).
thf(5238,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[5182]) ).
thf(5256,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[5238]) ).
thf(19866,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,525]) ).
thf(19867,plain,
! [A: mworld] :
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19866]) ).
thf(19868,plain,
qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19867:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(28,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sk20 @ A ) )
| ~ ( sk19 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(93,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ ( sk20 @ A ) )
| ~ ( sk19 @ A ) ),
inference(simp,[status(thm)],[28]) ).
thf(770,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,134]) ).
thf(771,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(772,plain,
~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ),
inference(pattern_uni,[status(thm)],[771:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(5091,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,772]) ).
thf(5092,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(simp,[status(thm)],[5091]) ).
thf(5148,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e3 @ unit )
!= e2 )
| ( e3 != e3 )
| ( A
!= ( sk34 @ mactual ) ) ),
inference(simp,[status(thm)],[5092]) ).
thf(5177,plain,
( ~ ( mrel @ mactual @ ( sk34 @ mactual ) )
| ( ( op @ e3 @ unit )
!= e2 ) ),
inference(simp,[status(thm)],[5148]) ).
thf(124,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk34 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(136,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk34 @ A ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(35850,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk34 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,136]) ).
thf(35851,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk34 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[35850]) ).
thf(35852,plain,
mrel @ mactual @ ( sk34 @ mactual ),
inference(pattern_uni,[status(thm)],[35851:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(36535,plain,
( ~ $true
| ( ( op @ e3 @ unit )
!= e2 ) ),
inference(rewrite,[status(thm)],[5177,35852]) ).
thf(36536,plain,
( ( op @ e3 @ unit )
!= e2 ),
inference(simp,[status(thm)],[36535]) ).
thf(53,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sk15 @ A ) )
| ( mrel @ A @ ( sk16 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(78,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sk15 @ A ) )
| ( mrel @ A @ ( sk16 @ A ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(1718,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,287]) ).
thf(1719,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1720,plain,
qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1,
inference(pattern_uni,[status(thm)],[1719:[bind(A,$thf( sk1 ))]]) ).
thf(1840,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1720,912]) ).
thf(1841,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1859,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1841]) ).
thf(1875,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1859]) ).
thf(19863,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,516]) ).
thf(19864,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19863]) ).
thf(19865,plain,
qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19864:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(25888,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19865,657]) ).
thf(25889,plain,
( ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[25888]) ).
thf(25967,plain,
( ( ( inv @ ( inv @ e0 ) )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[25889]) ).
thf(25989,plain,
( ( ( inv @ ( inv @ e0 ) )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[25967]) ).
thf(66,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( mrel @ A @ ( sk26 @ A ) )
| ~ ( sk25 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(80,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( mrel @ A @ ( sk26 @ A ) )
| ~ ( sk25 @ A ) ),
inference(simp,[status(thm)],[66]) ).
thf(2948,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk23 @ B )
| ( mrel @ B @ ( sk26 @ B ) )
| ~ ( sk25 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,80]) ).
thf(2949,plain,
! [B: mworld,A: mworld] :
( ( sk23 @ B )
| ( mrel @ B @ ( sk26 @ B ) )
| ~ ( sk25 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[2948]) ).
thf(2950,plain,
( ( sk23 @ sk1 )
| ( mrel @ sk1 @ ( sk26 @ sk1 ) )
| ~ ( sk25 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2949:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(10681,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,666]) ).
thf(10682,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(simp,[status(thm)],[10681]) ).
thf(10782,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( A
!= ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[10682]) ).
thf(10818,plain,
( ~ ( mrel @ mactual @ ( sk30 @ mactual ) )
| ( ( inv @ ( inv @ e2 ) )
!= e0 ) ),
inference(simp,[status(thm)],[10782]) ).
thf(5053,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,909]) ).
thf(5054,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[5053]) ).
thf(5130,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( A
!= ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[5054]) ).
thf(5159,plain,
( ~ ( mrel @ mactual @ ( sk31 @ sk1 ) )
| ( ( op @ e3 @ unit )
!= e0 ) ),
inference(simp,[status(thm)],[5130]) ).
thf(19917,plain,
( ~ $true
| ( ( op @ e3 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,5159]) ).
thf(19918,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19917]) ).
thf(19968,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( mactual != mactual )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19918]) ).
thf(20021,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19968]) ).
thf(16922,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,527]) ).
thf(16923,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[16922]) ).
thf(16924,plain,
qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual,
inference(pattern_uni,[status(thm)],[16923:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(17087,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[16915,879]) ).
thf(17088,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[17087]) ).
thf(17163,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[17088]) ).
thf(17171,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[17163]) ).
thf(63,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ( mrel @ A @ ( sk27 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sk28 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(106,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ( mrel @ A @ ( sk27 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ ( sk28 @ A ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(71,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ( mrel @ A @ ( sk27 @ A ) )
| ( mrel @ A @ ( sk28 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(102,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ( mrel @ A @ ( sk27 @ A ) )
| ( mrel @ A @ ( sk28 @ A ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(16474,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk23 @ B )
| ( sk25 @ B )
| ( mrel @ B @ ( sk27 @ B ) )
| ( mrel @ B @ ( sk28 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,102]) ).
thf(16475,plain,
! [B: mworld,A: mworld] :
( ( sk23 @ B )
| ( sk25 @ B )
| ( mrel @ B @ ( sk27 @ B ) )
| ( mrel @ B @ ( sk28 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[16474]) ).
thf(16476,plain,
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( mrel @ sk1 @ ( sk28 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[16475:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(42,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ A )
| sk3 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(84,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ A )
| sk3 ),
inference(simp,[status(thm)],[42]) ).
thf(19757,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,133]) ).
thf(19758,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19757]) ).
thf(19759,plain,
~ ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[19758:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(1945,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1723,798]) ).
thf(1946,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[1945]) ).
thf(2004,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1946]) ).
thf(2017,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2004]) ).
thf(1124,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,666]) ).
thf(1125,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(simp,[status(thm)],[1124]) ).
thf(1161,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e0 )
| ( e2 != unit )
| ( A
!= ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[1125]) ).
thf(1183,plain,
( ~ ( mrel @ mactual @ ( sk30 @ mactual ) )
| ( ( inv @ unit )
!= e0 )
| ( e2 != unit ) ),
inference(simp,[status(thm)],[1161]) ).
thf(5221,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[5081,801]) ).
thf(5222,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[5221]) ).
thf(5242,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[5222]) ).
thf(5259,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[5242]) ).
thf(1136,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,657]) ).
thf(1137,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[1136]) ).
thf(1154,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e0 )
| ( e1 != unit )
| ( A
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[1137]) ).
thf(1176,plain,
( ~ ( mrel @ mactual @ ( sk29 @ mactual ) )
| ( ( inv @ unit )
!= e0 )
| ( e1 != unit ) ),
inference(simp,[status(thm)],[1154]) ).
thf(19699,plain,
( ~ $true
| ( ( inv @ unit )
!= e0 )
| ( e1 != unit ) ),
inference(rewrite,[status(thm)],[1176,19041]) ).
thf(19700,plain,
( ( ( inv @ unit )
!= e0 )
| ( e1 != unit ) ),
inference(simp,[status(thm)],[19699]) ).
thf(6591,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,291]) ).
thf(6592,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[6591]) ).
thf(6658,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[6592]) ).
thf(6685,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[6658]) ).
thf(12459,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12230,798]) ).
thf(12460,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[12459]) ).
thf(12519,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[12460]) ).
thf(12536,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[12519]) ).
thf(19910,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,287]) ).
thf(19911,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19910]) ).
thf(19912,plain,
qmltpeq @ ( op @ unit @ e3 ) @ e3 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19911:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(26775,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19912,657]) ).
thf(26776,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[26775]) ).
thf(26861,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[26776]) ).
thf(26887,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e1 ) ),
inference(simp,[status(thm)],[26861]) ).
thf(658,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,131]) ).
thf(659,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(660,plain,
~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[659:[bind(A,$thf( sk1 ))]]) ).
thf(31,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ( mrel @ A @ ( sk15 @ A ) )
| ( mrel @ A @ ( sk16 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(109,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ( mrel @ A @ ( sk15 @ A ) )
| ( mrel @ A @ ( sk16 @ A ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(26305,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk11 @ B )
| ( sk13 @ B )
| ( mrel @ B @ ( sk15 @ B ) )
| ( mrel @ B @ ( sk16 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,109]) ).
thf(26306,plain,
! [B: mworld,A: mworld] :
( ( sk11 @ B )
| ( sk13 @ B )
| ( mrel @ B @ ( sk15 @ B ) )
| ( mrel @ B @ ( sk16 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[26305]) ).
thf(26307,plain,
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( mrel @ sk1 @ ( sk16 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[26306:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(28044,plain,
! [A: mworld] :
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk16 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26307,79]) ).
thf(28045,plain,
! [A: mworld] :
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk16 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[28044]) ).
thf(28046,plain,
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk16 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[28045:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(1198,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,798]) ).
thf(1199,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[1198]) ).
thf(1242,plain,
( ( ( inv @ unit )
!= e1 )
| ( e3 != unit )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1199]) ).
thf(47,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ( mrel @ A @ ( sk21 @ A ) )
| ( mrel @ A @ ( sk22 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(116,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ( mrel @ A @ ( sk21 @ A ) )
| ( mrel @ A @ ( sk22 @ A ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(19502,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,135]) ).
thf(19503,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19502]) ).
thf(19631,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19503]) ).
thf(19678,plain,
( ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19631]) ).
thf(10859,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[10715,879]) ).
thf(10860,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[10859]) ).
thf(10921,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[10860]) ).
thf(10932,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[10921]) ).
thf(517,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A ) ),
inference(cnfConj,[status(thm)],[515]) ).
thf(520,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A ) ),
inference(simp,[status(thm)],[517]) ).
thf(9915,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,520]) ).
thf(9916,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[9915]) ).
thf(9917,plain,
qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ mactual,
inference(pattern_uni,[status(thm)],[9916:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(68,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(117,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ A ) ),
inference(simp,[status(thm)],[68]) ).
thf(19722,plain,
( ~ $true
| ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,10827]) ).
thf(19723,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19722]) ).
thf(19972,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( mactual != mactual )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19723]) ).
thf(20025,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19972]) ).
thf(24,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(85,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(10695,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,521]) ).
thf(10696,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[10695]) ).
thf(10795,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[10696]) ).
thf(10831,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[10795]) ).
thf(5099,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,912]) ).
thf(5100,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(simp,[status(thm)],[5099]) ).
thf(5145,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( A
!= ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[5100]) ).
thf(5174,plain,
( ~ ( mrel @ mactual @ ( sk31 @ mactual ) )
| ( ( op @ e3 @ unit )
!= e0 ) ),
inference(simp,[status(thm)],[5145]) ).
thf(19851,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,521]) ).
thf(19852,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19851]) ).
thf(19853,plain,
qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19852:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(25738,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19853,657]) ).
thf(25739,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[25738]) ).
thf(25795,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[25739]) ).
thf(25834,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e1 ) ),
inference(simp,[status(thm)],[25795]) ).
thf(1277,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,666]) ).
thf(1278,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[1277]) ).
thf(1311,plain,
( ( ( inv @ unit )
!= e0 )
| ( e2 != unit )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1278]) ).
thf(3694,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3606,663]) ).
thf(3695,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[3694]) ).
thf(3757,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[3695]) ).
thf(3767,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[3757]) ).
thf(12381,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[12221,912]) ).
thf(12382,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[12381]) ).
thf(12428,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[12382]) ).
thf(12437,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[12428]) ).
thf(4395,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ $true
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ B )
| sk3
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,84]) ).
thf(4396,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ B )
| sk3
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[4395]) ).
thf(4397,plain,
( ~ sk2
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ sk1 )
| sk3 ),
inference(pattern_uni,[status(thm)],[4396:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(19742,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,289]) ).
thf(19743,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19742]) ).
thf(19744,plain,
qmltpeq @ ( op @ e2 @ unit ) @ e2 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19743:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(281,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A ) ),
inference(cnfConj,[status(thm)],[277]) ).
thf(294,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A ) ),
inference(simp,[status(thm)],[281]) ).
thf(8509,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,294]) ).
thf(8510,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[8509]) ).
thf(8611,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[8510]) ).
thf(8645,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[8611]) ).
thf(3582,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,666]) ).
thf(3583,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(simp,[status(thm)],[3582]) ).
thf(3648,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( A
!= ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[3583]) ).
thf(3668,plain,
( ~ ( mrel @ mactual @ ( sk30 @ mactual ) )
| ( ( op @ e2 @ unit )
!= e0 ) ),
inference(simp,[status(thm)],[3648]) ).
thf(19832,plain,
( ~ $true
| ( ( op @ e2 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,3668]) ).
thf(19833,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19832]) ).
thf(20004,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( mactual != mactual )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19833]) ).
thf(20057,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20004]) ).
thf(3634,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,876]) ).
thf(3635,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[3634]) ).
thf(3662,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e2 @ unit )
!= e1 )
| ( e2 != e2 )
| ( A
!= ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[3635]) ).
thf(3682,plain,
( ~ ( mrel @ mactual @ ( sk32 @ sk1 ) )
| ( ( op @ e2 @ unit )
!= e1 ) ),
inference(simp,[status(thm)],[3662]) ).
thf(1955,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1723,801]) ).
thf(1956,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[1955]) ).
thf(2000,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1956]) ).
thf(2015,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[2000]) ).
thf(6618,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,291]) ).
thf(6619,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[6618]) ).
thf(6620,plain,
qmltpeq @ ( op @ e1 @ unit ) @ e1 @ mactual,
inference(pattern_uni,[status(thm)],[6619:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(19840,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,520]) ).
thf(19841,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19840]) ).
thf(19842,plain,
qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19841:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(14708,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[14432,912]) ).
thf(14709,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[14708]) ).
thf(14734,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[14709]) ).
thf(14766,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[14734]) ).
thf(33,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ A )
| sk4 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(92,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ A )
| sk4 ),
inference(simp,[status(thm)],[33]) ).
thf(2647,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[288,666]) ).
thf(2648,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(simp,[status(thm)],[2647]) ).
thf(2727,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( A
!= ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[2648]) ).
thf(2753,plain,
( ~ ( mrel @ mactual @ ( sk30 @ mactual ) )
| ( ( op @ unit @ e2 )
!= e0 ) ),
inference(simp,[status(thm)],[2727]) ).
thf(19820,plain,
( ~ $true
| ( ( op @ unit @ e2 )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,2753]) ).
thf(19821,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19820]) ).
thf(19994,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( mactual != mactual )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19821]) ).
thf(20047,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19994]) ).
thf(19464,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,81]) ).
thf(19465,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[19464]) ).
thf(19466,plain,
( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk29 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[19465:[bind(A,$thf( sk29 @ sk1 ))]]) ).
thf(23208,plain,
( sk2
| ~ $true
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19466,660]) ).
thf(23209,plain,
( sk2
| ( ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[23208]) ).
thf(23289,plain,
( sk2
| ( ( op @ e2 @ e2 )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ sk1 )
!= ( sk29 @ sk1 ) ) ),
inference(simp,[status(thm)],[23209]) ).
thf(23336,plain,
( sk2
| ( ( op @ e2 @ e2 )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[23289]) ).
thf(19,axiom,
mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ ( inv @ e3 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(625,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ ( inv @ e3 ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(32,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk10 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(97,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(1728,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[287,801]) ).
thf(1729,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(simp,[status(thm)],[1728]) ).
thf(1764,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e3 )
!= e1 )
| ( e3 != e3 )
| ( A
!= ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[1729]) ).
thf(1787,plain,
( ~ ( mrel @ mactual @ ( sk33 @ mactual ) )
| ( ( op @ unit @ e3 )
!= e1 ) ),
inference(simp,[status(thm)],[1764]) ).
thf(21190,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3615,19759]) ).
thf(21191,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[21190]) ).
thf(21306,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21191]) ).
thf(21374,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21306]) ).
thf(2795,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2669,876]) ).
thf(2796,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[2795]) ).
thf(2823,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[2796]) ).
thf(2826,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[2823]) ).
thf(16965,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[527,801]) ).
thf(16966,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(simp,[status(thm)],[16965]) ).
thf(17013,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e3 )
| ( A
!= ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[16966]) ).
thf(17057,plain,
( ~ ( mrel @ mactual @ ( sk33 @ mactual ) )
| ( ( op @ e2 @ e3 )
!= e3 ) ),
inference(simp,[status(thm)],[17013]) ).
thf(19883,plain,
( ~ $true
| ( ( op @ e2 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,17057]) ).
thf(19884,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19883]) ).
thf(20012,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( mactual != mactual )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19884]) ).
thf(20065,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20012]) ).
thf(1102,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,798]) ).
thf(1103,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1173,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e1 )
| ( e3 != unit )
| ( A
!= ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[1103]) ).
thf(1195,plain,
( ~ ( mrel @ mactual @ ( sk33 @ sk1 ) )
| ( ( inv @ unit )
!= e1 )
| ( e3 != unit ) ),
inference(simp,[status(thm)],[1173]) ).
thf(19523,plain,
! [A: mworld] :
( ~ $true
| ( mrel @ A @ ( sk29 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,127]) ).
thf(19524,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk29 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19523]) ).
thf(19608,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk29 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19524]) ).
thf(19671,plain,
( ( mrel @ ( sk29 @ sk1 ) @ ( sk29 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19608]) ).
thf(1710,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,287]) ).
thf(1711,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1710]) ).
thf(1781,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1804,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1781]) ).
thf(19880,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,585]) ).
thf(19881,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19880]) ).
thf(19882,plain,
qmltpeq @ ( inv @ unit ) @ unit @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19881:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(37,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk24 @ A ) )
| ~ ( sk23 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(86,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk24 @ A ) )
| ~ ( sk23 @ A ) ),
inference(simp,[status(thm)],[37]) ).
thf(5473,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk24 @ B ) )
| ~ ( sk23 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,86]) ).
thf(5474,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk24 @ B ) )
| ~ ( sk23 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[5473]) ).
thf(5475,plain,
( ( mrel @ sk1 @ ( sk24 @ sk1 ) )
| ~ ( sk23 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[5474:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(14563,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14423,909]) ).
thf(14564,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[14563]) ).
thf(14646,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[14564]) ).
thf(14666,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[14646]) ).
thf(12267,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,801]) ).
thf(12268,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(simp,[status(thm)],[12267]) ).
thf(12305,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( e3 != e3 )
| ( A
!= ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[12268]) ).
thf(12329,plain,
( ~ ( mrel @ mactual @ ( sk33 @ mactual ) )
| ( ( inv @ ( inv @ e3 ) )
!= e1 ) ),
inference(simp,[status(thm)],[12305]) ).
thf(19813,plain,
( ~ $true
| ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,12329]) ).
thf(19814,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19813]) ).
thf(19979,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( mactual != mactual )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19814]) ).
thf(20032,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19979]) ).
thf(1491,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,284]) ).
thf(1492,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[1491]) ).
thf(1493,plain,
qmltpeq @ ( op @ unit @ e0 ) @ e0 @ mactual,
inference(pattern_uni,[status(thm)],[1492:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(19877,plain,
! [A: mworld] :
( ~ $true
| ( mrel @ A @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,127]) ).
thf(19878,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19877]) ).
thf(19879,plain,
mrel @ ( sk29 @ mactual ) @ ( sk29 @ ( sk29 @ mactual ) ),
inference(pattern_uni,[status(thm)],[19878:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(3139,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[671,81]) ).
thf(3140,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[3139]) ).
thf(3141,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk10 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[3140:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(65,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( mrel @ A @ ( sk8 @ A ) )
| ~ ( sk7 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(77,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( mrel @ A @ ( sk8 @ A ) )
| ~ ( sk7 @ A ) ),
inference(simp,[status(thm)],[65]) ).
thf(14379,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[525,909]) ).
thf(14380,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[14379]) ).
thf(14502,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( A
!= ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[14380]) ).
thf(14543,plain,
( ~ ( mrel @ mactual @ ( sk31 @ sk1 ) )
| ( ( op @ e3 @ e3 )
!= e3 ) ),
inference(simp,[status(thm)],[14502]) ).
thf(19893,plain,
( ~ $true
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,14543]) ).
thf(19894,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19893]) ).
thf(19980,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( mactual != mactual )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19894]) ).
thf(20033,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19980]) ).
thf(2676,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,288]) ).
thf(2677,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[2676]) ).
thf(2678,plain,
qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual,
inference(pattern_uni,[status(thm)],[2677:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(21238,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2678,19759]) ).
thf(21239,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[21238]) ).
thf(21298,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21239]) ).
thf(21370,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21298]) ).
thf(19762,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,527]) ).
thf(19763,plain,
! [A: mworld] :
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19762]) ).
thf(19764,plain,
qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19763:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(17,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(590,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ B @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19926,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,131]) ).
thf(19927,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19926]) ).
thf(19928,plain,
~ ( qmltpeq @ e0 @ e1 @ ( sk29 @ ( sk29 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[19927:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(17123,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[16915,801]) ).
thf(17124,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[17123]) ).
thf(17161,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[17124]) ).
thf(17170,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[17161]) ).
thf(1212,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,909]) ).
thf(1213,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[1212]) ).
thf(1249,plain,
( ( ( inv @ unit )
!= e0 )
| ( e3 != unit )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1213]) ).
thf(2485,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[671,79]) ).
thf(2486,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[2485]) ).
thf(2487,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk10 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[2486:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(2832,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2678,663]) ).
thf(2833,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[2832]) ).
thf(2883,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2833]) ).
thf(2900,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2883]) ).
thf(12445,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12230,909]) ).
thf(12446,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[12445]) ).
thf(12513,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[12446]) ).
thf(12532,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[12513]) ).
thf(3578,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,663]) ).
thf(3579,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[3578]) ).
thf(3667,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( A
!= ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[3579]) ).
thf(3687,plain,
( ~ ( mrel @ mactual @ ( sk30 @ sk1 ) )
| ( ( op @ e2 @ unit )
!= e0 ) ),
inference(simp,[status(thm)],[3667]) ).
thf(19845,plain,
( ~ $true
| ( ( op @ e2 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,3687]) ).
thf(19846,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19845]) ).
thf(19975,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( mactual != mactual )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19846]) ).
thf(20028,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19975]) ).
thf(50,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk12 @ A ) )
| ~ ( sk11 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(107,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( mrel @ A @ ( sk12 @ A ) )
| ~ ( sk11 @ A ) ),
inference(simp,[status(thm)],[50]) ).
thf(23494,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk12 @ B ) )
| ~ ( sk11 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,107]) ).
thf(23495,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk12 @ B ) )
| ~ ( sk11 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[23494]) ).
thf(23496,plain,
( ( mrel @ sk1 @ ( sk12 @ sk1 ) )
| ~ ( sk11 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[23495:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(14451,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[525,912]) ).
thf(14452,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(simp,[status(thm)],[14451]) ).
thf(14485,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( A
!= ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[14452]) ).
thf(14526,plain,
( ~ ( mrel @ mactual @ ( sk31 @ mactual ) )
| ( ( op @ e3 @ e3 )
!= e3 ) ),
inference(simp,[status(thm)],[14485]) ).
thf(1820,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1720,801]) ).
thf(1821,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1858,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1874,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1858]) ).
thf(14428,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[525,657]) ).
thf(14429,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[14428]) ).
thf(14508,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e1 )
| ( A
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[14429]) ).
thf(14549,plain,
( ~ ( mrel @ mactual @ ( sk29 @ mactual ) )
| ( ( op @ e3 @ e3 )
!= e1 ) ),
inference(simp,[status(thm)],[14508]) ).
thf(19693,plain,
( ~ $true
| ( ( op @ e3 @ e3 )
!= e1 ) ),
inference(rewrite,[status(thm)],[14549,19041]) ).
thf(19694,plain,
( ( op @ e3 @ e3 )
!= e1 ),
inference(simp,[status(thm)],[19693]) ).
thf(19802,plain,
( ~ $true
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,14526]) ).
thf(19803,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19802]) ).
thf(19960,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( mactual != mactual )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19803]) ).
thf(20097,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19960]) ).
thf(56,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sk14 @ A ) )
| ~ ( sk13 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(73,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ ( sk14 @ A ) )
| ~ ( sk13 @ A ) ),
inference(simp,[status(thm)],[56]) ).
thf(48,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sk18 @ A ) )
| ~ ( sk17 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(105,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ ( sk18 @ A ) )
| ~ ( sk17 @ A ) ),
inference(simp,[status(thm)],[48]) ).
thf(10885,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10715,876]) ).
thf(10886,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[10885]) ).
thf(10907,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[10886]) ).
thf(10929,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[10907]) ).
thf(17982,plain,
! [A: mworld] :
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk28 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16476,36]) ).
thf(17983,plain,
! [A: mworld] :
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk28 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[17982]) ).
thf(17984,plain,
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk28 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[17983:[bind(A,$thf( sk28 @ sk1 ))]]) ).
thf(3090,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,81]) ).
thf(3091,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[3090]) ).
thf(3165,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( sk10 @ sk1 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[3091]) ).
thf(3190,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| sk2
| ( ( sk10 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[3165]) ).
thf(1148,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,876]) ).
thf(1149,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1148]) ).
thf(1163,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e1 )
| ( e2 != unit )
| ( A
!= ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[1149]) ).
thf(1185,plain,
( ~ ( mrel @ mactual @ ( sk32 @ sk1 ) )
| ( ( inv @ unit )
!= e1 )
| ( e2 != unit ) ),
inference(simp,[status(thm)],[1163]) ).
thf(16,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inv_substitution_1) ).
thf(586,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( inv @ B ) @ ( inv @ D ) @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12205,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,798]) ).
thf(12206,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[12205]) ).
thf(12294,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( e3 != e3 )
| ( A
!= ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[12206]) ).
thf(12318,plain,
( ~ ( mrel @ mactual @ ( sk33 @ sk1 ) )
| ( ( inv @ ( inv @ e3 ) )
!= e1 ) ),
inference(simp,[status(thm)],[12294]) ).
thf(12349,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12221,909]) ).
thf(12350,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[12349]) ).
thf(12411,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[12350]) ).
thf(12442,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[12411]) ).
thf(21164,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3606,19759]) ).
thf(21165,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[21164]) ).
thf(21319,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21165]) ).
thf(21380,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21319]) ).
thf(2836,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[2678,666]) ).
thf(2837,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[2836]) ).
thf(2876,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[2837]) ).
thf(2904,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[2876]) ).
thf(17989,plain,
! [A: mworld] :
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk28 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16476,79]) ).
thf(17990,plain,
! [A: mworld] :
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk28 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[17989]) ).
thf(17991,plain,
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk28 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[17990:[bind(A,$thf( sk28 @ sk1 ))]]) ).
thf(17198,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[16924,879]) ).
thf(17199,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[17198]) ).
thf(17267,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[17199]) ).
thf(17282,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[17267]) ).
thf(3809,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3615,876]) ).
thf(3810,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[3809]) ).
thf(3820,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[3810]) ).
thf(3839,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[3820]) ).
thf(12397,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[12221,801]) ).
thf(12398,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[12397]) ).
thf(12407,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[12398]) ).
thf(12441,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[12407]) ).
thf(3712,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[3606,879]) ).
thf(3713,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[3712]) ).
thf(3741,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[3713]) ).
thf(3768,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[3741]) ).
thf(1204,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,772]) ).
thf(1205,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ),
inference(simp,[status(thm)],[1204]) ).
thf(1256,plain,
( ( ( inv @ unit )
!= e2 )
| ( e3 != unit )
| ( ( sk34 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1205]) ).
thf(2757,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2669,663]) ).
thf(2758,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[2757]) ).
thf(2804,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[2758]) ).
thf(2827,plain,
( ( ( op @ unit @ e2 )
!= e0 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[2804]) ).
thf(14565,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[14423,666]) ).
thf(14566,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[14565]) ).
thf(14647,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[14566]) ).
thf(14667,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[14647]) ).
thf(9123,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,516]) ).
thf(9124,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[9123]) ).
thf(9125,plain,
qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 @ mactual,
inference(pattern_uni,[status(thm)],[9124:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(2653,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,288]) ).
thf(2654,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[2653]) ).
thf(2712,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[2654]) ).
thf(2738,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2712]) ).
thf(10722,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,521]) ).
thf(10723,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[10722]) ).
thf(10724,plain,
qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual,
inference(pattern_uni,[status(thm)],[10723:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(10969,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10724,663]) ).
thf(10970,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[10969]) ).
thf(11014,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[10970]) ).
thf(11018,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[11014]) ).
thf(27944,plain,
! [A: mworld] :
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk16 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26307,81]) ).
thf(27945,plain,
! [A: mworld] :
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk16 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[27944]) ).
thf(27946,plain,
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk16 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[27945:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(3600,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[289,879]) ).
thf(3601,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(simp,[status(thm)],[3600]) ).
thf(3654,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e2 @ unit )
!= e1 )
| ( e2 != e2 )
| ( A
!= ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[3601]) ).
thf(3674,plain,
( ~ ( mrel @ mactual @ ( sk32 @ mactual ) )
| ( ( op @ e2 @ unit )
!= e1 ) ),
inference(simp,[status(thm)],[3654]) ).
thf(19847,plain,
( ~ $true
| ( ( op @ e2 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,3674]) ).
thf(19848,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19847]) ).
thf(19988,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( mactual != mactual )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19848]) ).
thf(20041,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19988]) ).
thf(19568,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,79]) ).
thf(19569,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[19568]) ).
thf(19570,plain,
( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk29 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[19569:[bind(A,$thf( sk29 @ sk1 ))]]) ).
thf(6616,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[291,657]) ).
thf(6617,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ e1 @ unit ) @ e1 @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[6616]) ).
thf(6671,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ e1 @ unit )
!= e0 )
| ( e1 != e1 )
| ( A
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[6617]) ).
thf(6698,plain,
( ~ ( mrel @ mactual @ ( sk29 @ mactual ) )
| ( ( op @ e1 @ unit )
!= e0 ) ),
inference(simp,[status(thm)],[6671]) ).
thf(19701,plain,
( ~ $true
| ( ( op @ e1 @ unit )
!= e0 ) ),
inference(rewrite,[status(thm)],[6698,19041]) ).
thf(19702,plain,
( ( op @ e1 @ unit )
!= e0 ),
inference(simp,[status(thm)],[19701]) ).
thf(19739,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,284]) ).
thf(19740,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19739]) ).
thf(19741,plain,
qmltpeq @ ( op @ unit @ e0 ) @ e0 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19740:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(8534,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[294,657]) ).
thf(8535,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[8534]) ).
thf(8599,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e1 )
!= e0 )
| ( e1 != e1 )
| ( A
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[8535]) ).
thf(8633,plain,
( ~ ( mrel @ mactual @ ( sk29 @ mactual ) )
| ( ( op @ unit @ e1 )
!= e0 ) ),
inference(simp,[status(thm)],[8599]) ).
thf(19697,plain,
( ~ $true
| ( ( op @ unit @ e1 )
!= e0 ) ),
inference(rewrite,[status(thm)],[8633,19041]) ).
thf(19698,plain,
( ( op @ unit @ e1 )
!= e0 ),
inference(simp,[status(thm)],[19697]) ).
thf(23,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(113,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ sk4
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ A ) ),
inference(simp,[status(thm)],[23]) ).
thf(35040,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,118]) ).
thf(35041,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[35040]) ).
thf(35042,plain,
( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk29 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[35041:[bind(A,$thf( sk29 @ sk1 ))]]) ).
thf(35514,plain,
( sk2
| ~ $true
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[35042,660]) ).
thf(35515,plain,
( sk2
| ( ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[35514]) ).
thf(35627,plain,
( sk2
| ( ( op @ e3 @ e3 )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ sk1 )
!= ( sk29 @ sk1 ) ) ),
inference(simp,[status(thm)],[35515]) ).
thf(35662,plain,
( sk2
| ( ( op @ e3 @ e3 )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[35627]) ).
thf(3734,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[3606,876]) ).
thf(3735,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[3734]) ).
thf(3753,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[3735]) ).
thf(3764,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[3753]) ).
thf(6441,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk11 @ B )
| ( mrel @ B @ ( sk14 @ B ) )
| ~ ( sk13 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,88]) ).
thf(6442,plain,
! [B: mworld,A: mworld] :
( ( sk11 @ B )
| ( mrel @ B @ ( sk14 @ B ) )
| ~ ( sk13 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[6441]) ).
thf(6443,plain,
( ( sk11 @ sk1 )
| ( mrel @ sk1 @ ( sk14 @ sk1 ) )
| ~ ( sk13 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6442:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2095,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk5 @ B )
| ( mrel @ B @ ( sk8 @ B ) )
| ~ ( sk7 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,77]) ).
thf(2096,plain,
! [B: mworld,A: mworld] :
( ( sk5 @ B )
| ( mrel @ B @ ( sk8 @ B ) )
| ~ ( sk7 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[2095]) ).
thf(2097,plain,
( ( sk5 @ sk1 )
| ( mrel @ sk1 @ ( sk8 @ sk1 ) )
| ~ ( sk7 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2096:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(60,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sk27 @ A ) )
| ( mrel @ A @ ( sk28 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(76,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ( sk25 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ ( sk27 @ A ) )
| ( mrel @ A @ ( sk28 @ A ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(20,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ C ) ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(649,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
& ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ D @ F @ H ) ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ F @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19779,plain,
( ~ $true
| ( ( op @ e2 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,3682]) ).
thf(19780,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19779]) ).
thf(19946,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( mactual != mactual )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19780]) ).
thf(20083,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19946]) ).
thf(1269,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,663]) ).
thf(1270,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[1269]) ).
thf(1307,plain,
( ( ( inv @ unit )
!= e0 )
| ( e2 != unit )
| ( ( sk30 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1270]) ).
thf(1724,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[287,772]) ).
thf(1725,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(simp,[status(thm)],[1724]) ).
thf(1785,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e3 )
!= e2 )
| ( e3 != e3 )
| ( A
!= ( sk34 @ mactual ) ) ),
inference(simp,[status(thm)],[1725]) ).
thf(1808,plain,
( ~ ( mrel @ mactual @ ( sk34 @ mactual ) )
| ( ( op @ unit @ e3 )
!= e2 ) ),
inference(simp,[status(thm)],[1785]) ).
thf(36533,plain,
( ~ $true
| ( ( op @ unit @ e3 )
!= e2 ) ),
inference(rewrite,[status(thm)],[1808,35852]) ).
thf(36534,plain,
( ( op @ unit @ e3 )
!= e2 ),
inference(simp,[status(thm)],[36533]) ).
thf(19720,plain,
( ~ $true
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,14538]) ).
thf(19721,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19720]) ).
thf(20015,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( mactual != mactual )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19721]) ).
thf(20068,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20015]) ).
thf(689,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,36]) ).
thf(690,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ B )
| sk2
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[689]) ).
thf(691,plain,
( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 )
| sk2 ),
inference(pattern_uni,[status(thm)],[690:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(745,plain,
( sk2
| ~ $true
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[691,663]) ).
thf(746,plain,
( sk2
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[745]) ).
thf(758,plain,
( sk2
| ( ( op @ e0 @ e0 )
!= e0 )
| ( e2 != e0 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[746]) ).
thf(54,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ( mrel @ A @ ( sk15 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sk16 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(103,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ( mrel @ A @ ( sk15 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sk16 @ A ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(5293,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[5090,912]) ).
thf(5294,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[5293]) ).
thf(5320,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[5294]) ).
thf(5335,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[5320]) ).
thf(1732,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[287,909]) ).
thf(1733,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1732]) ).
thf(1767,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( A
!= ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[1733]) ).
thf(1790,plain,
( ~ ( mrel @ mactual @ ( sk31 @ sk1 ) )
| ( ( op @ unit @ e3 )
!= e0 ) ),
inference(simp,[status(thm)],[1767]) ).
thf(19875,plain,
( ~ $true
| ( ( op @ unit @ e3 )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,1790]) ).
thf(19876,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19875]) ).
thf(20008,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( mactual != mactual )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19876]) ).
thf(20061,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20008]) ).
thf(67,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( mrel @ A @ ( sk20 @ A ) )
| ~ ( sk19 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(108,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( mrel @ A @ ( sk20 @ A ) )
| ~ ( sk19 @ A ) ),
inference(simp,[status(thm)],[67]) ).
thf(2663,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[288,879]) ).
thf(2664,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(simp,[status(thm)],[2663]) ).
thf(2706,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e2 )
!= e1 )
| ( e2 != e2 )
| ( A
!= ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[2664]) ).
thf(2732,plain,
( ~ ( mrel @ mactual @ ( sk32 @ mactual ) )
| ( ( op @ unit @ e2 )
!= e1 ) ),
inference(simp,[status(thm)],[2706]) ).
thf(19871,plain,
( ~ $true
| ( ( op @ unit @ e2 )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,2732]) ).
thf(19872,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19871]) ).
thf(19956,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( mactual != mactual )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19872]) ).
thf(20093,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( sk32 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19956]) ).
thf(33827,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( sk17 @ B )
| ( sk19 @ B )
| ( mrel @ B @ ( sk21 @ B ) )
| ( mrel @ B @ ( sk22 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,116]) ).
thf(33828,plain,
! [B: mworld,A: mworld] :
( ( sk17 @ B )
| ( sk19 @ B )
| ( mrel @ B @ ( sk21 @ B ) )
| ( mrel @ B @ ( sk22 @ B ) )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[33827]) ).
thf(33829,plain,
( ( sk17 @ sk1 )
| ( sk19 @ sk1 )
| ( mrel @ sk1 @ ( sk21 @ sk1 ) )
| ( mrel @ sk1 @ ( sk22 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[33828:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(20919,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1720,19711]) ).
thf(20920,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20919]) ).
thf(21003,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[20920]) ).
thf(21084,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21003]) ).
thf(27058,plain,
( sk2
| ~ $true
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19570,660]) ).
thf(27059,plain,
( sk2
| ( ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[27058]) ).
thf(27144,plain,
( sk2
| ( ( op @ e1 @ e1 )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ sk1 )
!= ( sk29 @ sk1 ) ) ),
inference(simp,[status(thm)],[27059]) ).
thf(27177,plain,
( sk2
| ( ( op @ e1 @ e1 )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[27144]) ).
thf(17117,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16915,876]) ).
thf(17118,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[17117]) ).
thf(17154,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[17118]) ).
thf(17169,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[17154]) ).
thf(12363,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12221,798]) ).
thf(12364,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[12363]) ).
thf(12429,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[12364]) ).
thf(12438,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[12429]) ).
thf(8527,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,294]) ).
thf(8528,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[8527]) ).
thf(8529,plain,
qmltpeq @ ( op @ unit @ e1 ) @ e1 @ sk1,
inference(pattern_uni,[status(thm)],[8528:[bind(A,$thf( sk1 ))]]) ).
thf(2440,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,79]) ).
thf(2441,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[2440]) ).
thf(2494,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A )
| sk2
| ( ( sk10 @ sk1 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[2441]) ).
thf(2542,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| sk2
| ( ( sk10 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[2494]) ).
thf(12477,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[12230,912]) ).
thf(12478,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[12477]) ).
thf(12515,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[12478]) ).
thf(12534,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[12515]) ).
thf(14601,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[14423,912]) ).
thf(14602,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[14601]) ).
thf(14628,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[14602]) ).
thf(14660,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[14628]) ).
thf(19408,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,137]) ).
thf(19409,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19408]) ).
thf(19634,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19409]) ).
thf(19680,plain,
( ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19634]) ).
thf(1202,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,879]) ).
thf(1203,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1250,plain,
( ( ( inv @ unit )
!= e1 )
| ( e2 != unit )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1203]) ).
thf(19718,plain,
( ~ $true
| ( ( op @ unit @ e3 )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,1793]) ).
thf(19719,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19718]) ).
thf(19950,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( mactual != mactual )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19719]) ).
thf(20087,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19950]) ).
thf(17894,plain,
! [A: mworld] :
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk28 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16476,81]) ).
thf(17895,plain,
! [A: mworld] :
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk28 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[17894]) ).
thf(17896,plain,
( ( sk23 @ sk1 )
| ( sk25 @ sk1 )
| ( mrel @ sk1 @ ( sk27 @ sk1 ) )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk28 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[17895:[bind(A,$thf( sk28 @ sk1 ))]]) ).
thf(19767,plain,
( ~ $true
| ( ( op @ e3 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,5174]) ).
thf(19768,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19767]) ).
thf(19963,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( mactual != mactual )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19768]) ).
thf(20100,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19963]) ).
thf(3787,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[3615,879]) ).
thf(3788,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[3787]) ).
thf(3818,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[3788]) ).
thf(3838,plain,
( ( ( op @ e2 @ unit )
!= e1 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[3818]) ).
thf(21248,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14432,19759]) ).
thf(21249,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[21248]) ).
thf(21283,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21249]) ).
thf(21365,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21283]) ).
thf(19561,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,36]) ).
thf(19562,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[19561]) ).
thf(19563,plain,
( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk29 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[19562:[bind(A,$thf( sk29 @ sk1 ))]]) ).
thf(20875,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14423,19711]) ).
thf(20876,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20875]) ).
thf(21032,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[20876]) ).
thf(21097,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21032]) ).
thf(3588,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,289]) ).
thf(3589,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[3588]) ).
thf(3652,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[3589]) ).
thf(3672,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[3652]) ).
thf(19804,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,134]) ).
thf(19805,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19804]) ).
thf(19806,plain,
~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ ( sk29 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[19805:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(8,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ ( inv @ e0 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e0 ) @ e0 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ ( inv @ e1 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e1 ) @ e1 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ ( inv @ e2 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e2 ) @ e2 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e3 @ ( inv @ e3 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e3 ) @ e3 ) @ unit ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(487,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ ( inv @ e0 ) ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( inv @ e0 ) @ e0 ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ ( inv @ e1 ) ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( inv @ e1 ) @ e1 ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ ( inv @ e2 ) ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( inv @ e2 ) @ e2 ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ ( inv @ e3 ) ) @ unit @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( inv @ e3 ) @ e3 ) @ unit @ A ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e0 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e0 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e0 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e0 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e1 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e1 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e1 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e1 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e2 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e2 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e2 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e2 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e3 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e3 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e3 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( inv @ e3 ) @ e3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ( mrel @ A @ ( sk21 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sk22 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(112,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ( mrel @ A @ ( sk21 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sk22 @ A ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(17234,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[16924,801]) ).
thf(17235,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[17234]) ).
thf(17266,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[17235]) ).
thf(17281,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[17266]) ).
thf(1122,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,909]) ).
thf(1123,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1122]) ).
thf(1159,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e0 )
| ( e3 != unit )
| ( A
!= ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1181,plain,
( ~ ( mrel @ mactual @ ( sk31 @ sk1 ) )
| ( ( inv @ unit )
!= e0 )
| ( e3 != unit ) ),
inference(simp,[status(thm)],[1159]) ).
thf(10755,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[521,876]) ).
thf(10756,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ A )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[10755]) ).
thf(10788,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( e2 != e2 )
| ( A
!= ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[10756]) ).
thf(10824,plain,
( ~ ( mrel @ mactual @ ( sk32 @ sk1 ) )
| ( ( inv @ ( inv @ e2 ) )
!= e1 ) ),
inference(simp,[status(thm)],[10788]) ).
thf(19787,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,522]) ).
thf(19788,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19787]) ).
thf(19789,plain,
qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19788:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(5063,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,290]) ).
thf(5064,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[5063]) ).
thf(5136,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[5064]) ).
thf(5165,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[5136]) ).
thf(19776,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,137]) ).
thf(19777,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19776]) ).
thf(19778,plain,
~ ( qmltpeq @ e1 @ e2 @ ( sk32 @ ( sk29 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[19777:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(7,axiom,
mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e1 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(295,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e1 @ e0 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e2 @ e0 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e3 @ e0 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e2 @ e0 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e3 @ e0 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e3 @ e0 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e1 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e2 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e3 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e2 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e3 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e3 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e1 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e2 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e3 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e2 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e3 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e3 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e1 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e2 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e3 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e2 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e3 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e3 ) @ ( op @ e3 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e0 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e1 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e2 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e1 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e2 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e3 ) @ B ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( op @ e3 @ e2 ) @ ( op @ e3 @ e3 ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24382,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19789,657]) ).
thf(24383,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[24382]) ).
thf(24477,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[24383]) ).
thf(24492,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e1 ) ),
inference(simp,[status(thm)],[24477]) ).
thf(3773,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[3615,666]) ).
thf(3774,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[3773]) ).
thf(3828,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[3774]) ).
thf(3842,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[3828]) ).
thf(14672,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[14432,666]) ).
thf(14673,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[14672]) ).
thf(14762,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[14673]) ).
thf(14775,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[14762]) ).
thf(35978,plain,
! [A: mworld] :
( ~ $true
| ( mrel @ A @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,136]) ).
thf(35979,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[35978]) ).
thf(35980,plain,
mrel @ ( sk29 @ mactual ) @ ( sk34 @ ( sk29 @ mactual ) ),
inference(pattern_uni,[status(thm)],[35979:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(19731,plain,
( ~ $true
| ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,12324]) ).
thf(19732,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19731]) ).
thf(19943,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( mactual != mactual )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19732]) ).
thf(20080,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19943]) ).
thf(19923,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,294]) ).
thf(19924,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ A )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19923]) ).
thf(19925,plain,
qmltpeq @ ( op @ unit @ e1 ) @ e1 @ ( sk29 @ mactual ),
inference(pattern_uni,[status(thm)],[19924:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(45,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ A )
| sk3 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(95,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ A )
| sk3 ),
inference(simp,[status(thm)],[45]) ).
thf(19790,plain,
( ~ $true
| ( ( op @ unit @ e3 )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,1787]) ).
thf(19791,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19790]) ).
thf(20002,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( mactual != mactual )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19791]) ).
thf(20055,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20002]) ).
thf(19733,plain,
( ~ $true
| ( ( op @ e2 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,17026]) ).
thf(19734,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19733]) ).
thf(19991,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( mactual != mactual )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19734]) ).
thf(20044,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19991]) ).
thf(10951,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[10724,879]) ).
thf(10952,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[10951]) ).
thf(10997,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[10952]) ).
thf(11022,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[10997]) ).
thf(1267,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,772]) ).
thf(1268,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ),
inference(simp,[status(thm)],[1267]) ).
thf(1317,plain,
( ( ( inv @ unit )
!= e2 )
| ( e3 != unit )
| ( ( sk34 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1268]) ).
thf(2870,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2678,876]) ).
thf(2871,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[2870]) ).
thf(2890,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2871]) ).
thf(2903,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2890]) ).
thf(12493,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[12230,801]) ).
thf(12494,plain,
( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[12493]) ).
thf(12501,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[12494]) ).
thf(12529,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[12501]) ).
thf(24089,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19764,657]) ).
thf(24090,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[24089]) ).
thf(24142,plain,
( ( e1 != e0 )
| ( ( op @ e2 @ e3 )
!= e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[24090]) ).
thf(24186,plain,
( ( e1 != e0 )
| ( ( op @ e2 @ e3 )
!= e1 ) ),
inference(simp,[status(thm)],[24142]) ).
thf(29,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ A ) )
| ~ ( sk23 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(90,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ A ) )
| ~ ( sk23 @ A ) ),
inference(simp,[status(thm)],[29]) ).
thf(7241,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ B ) )
| ~ ( sk23 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,90]) ).
thf(7242,plain,
! [B: mworld,A: mworld] :
( ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ B ) )
| ~ ( sk23 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[7241]) ).
thf(7243,plain,
( ~ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ sk1 ) )
| ~ ( sk23 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[7242:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1214,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,666]) ).
thf(1215,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[1214]) ).
thf(1257,plain,
( ( ( inv @ unit )
!= e0 )
| ( e2 != unit )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1215]) ).
thf(19724,plain,
( ~ $true
| ( ( op @ e3 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,5163]) ).
thf(19725,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19724]) ).
thf(20009,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( mactual != mactual )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19725]) ).
thf(20062,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20009]) ).
thf(19859,plain,
( ~ $true
| ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,10824]) ).
thf(19860,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk32 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19859]) ).
thf(19940,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( mactual != mactual )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19860]) ).
thf(20077,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( sk32 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19940]) ).
thf(9888,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,520]) ).
thf(9889,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[9888]) ).
thf(9982,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[9889]) ).
thf(10028,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[9982]) ).
thf(19438,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,134]) ).
thf(19439,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19438]) ).
thf(19647,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ A ) )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19439]) ).
thf(19682,plain,
( ~ ( qmltpeq @ e2 @ e3 @ ( sk34 @ ( sk29 @ sk1 ) ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19647]) ).
thf(1750,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[287,912]) ).
thf(1751,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(simp,[status(thm)],[1750]) ).
thf(1774,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( A
!= ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[1751]) ).
thf(1797,plain,
( ~ ( mrel @ mactual @ ( sk31 @ mactual ) )
| ( ( op @ unit @ e3 )
!= e0 ) ),
inference(simp,[status(thm)],[1774]) ).
thf(19747,plain,
( ~ $true
| ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,10818]) ).
thf(19748,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk30 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19747]) ).
thf(19966,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( mactual != mactual )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19748]) ).
thf(20103,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19966]) ).
thf(1332,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,89]) ).
thf(1333,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[1332]) ).
thf(1356,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( sk5 @ A )
| ( sk7 @ A )
| ( mrel @ A @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) )
| ( ( sk10 @ sk1 )
!= sk1 )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[1333]) ).
thf(1372,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( sk5 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( sk7 @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( mrel @ ( sk10 @ ( sk10 @ sk1 ) ) @ ( sk9 @ ( sk10 @ ( sk10 @ sk1 ) ) ) )
| ( mrel @ ( sk10 @ ( sk10 @ sk1 ) ) @ ( sk10 @ ( sk10 @ ( sk10 @ sk1 ) ) ) )
| ( ( sk10 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1356]) ).
thf(12231,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,772]) ).
thf(12232,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ mactual ) ) ) ),
inference(simp,[status(thm)],[12231]) ).
thf(12277,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e3 ) )
!= e2 )
| ( e3 != e3 )
| ( A
!= ( sk34 @ mactual ) ) ),
inference(simp,[status(thm)],[12232]) ).
thf(12338,plain,
( ~ ( mrel @ mactual @ ( sk34 @ mactual ) )
| ( ( inv @ ( inv @ e3 ) )
!= e2 ) ),
inference(simp,[status(thm)],[12277]) ).
thf(36537,plain,
( ~ $true
| ( ( inv @ ( inv @ e3 ) )
!= e2 ) ),
inference(rewrite,[status(thm)],[12338,35852]) ).
thf(36538,plain,
( ( inv @ ( inv @ e3 ) )
!= e2 ),
inference(simp,[status(thm)],[36537]) ).
thf(10935,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[10724,666]) ).
thf(10936,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[10935]) ).
thf(11009,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[10936]) ).
thf(11017,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[11009]) ).
thf(1236,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,876]) ).
thf(1237,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[1236]) ).
thf(1240,plain,
( ( ( inv @ unit )
!= e1 )
| ( e2 != unit )
| ( ( sk32 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1237]) ).
thf(69,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk9 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk10 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(72,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk9 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(21158,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14423,19759]) ).
thf(21159,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[21158]) ).
thf(21318,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21159]) ).
thf(21379,plain,
( ( ( op @ e3 @ e3 )
!= e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21318]) ).
thf(4,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e0 ) @ ( op @ e0 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e1 ) @ ( op @ e0 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e2 ) @ ( op @ e0 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e3 ) @ ( op @ e0 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e0 ) @ ( op @ e0 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e1 ) @ ( op @ e0 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e2 ) @ ( op @ e0 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e3 ) @ ( op @ e0 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e0 ) @ ( op @ e0 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e1 ) @ ( op @ e0 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e2 ) @ ( op @ e0 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e3 ) @ ( op @ e0 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e0 ) @ ( op @ e0 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e1 ) @ ( op @ e0 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e2 ) @ ( op @ e0 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e3 ) @ ( op @ e0 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e0 ) @ ( op @ e1 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e1 ) @ ( op @ e1 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e2 ) @ ( op @ e1 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e3 ) @ ( op @ e1 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e0 ) @ ( op @ e1 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e1 ) @ ( op @ e1 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e2 ) @ ( op @ e1 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e3 ) @ ( op @ e1 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e0 ) @ ( op @ e1 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e1 ) @ ( op @ e1 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e2 ) @ ( op @ e1 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e3 ) @ ( op @ e1 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e0 ) @ ( op @ e1 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e1 ) @ ( op @ e1 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e2 ) @ ( op @ e1 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e3 ) @ ( op @ e1 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e0 ) @ ( op @ e2 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e1 ) @ ( op @ e2 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e2 ) @ ( op @ e2 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e3 ) @ ( op @ e2 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e0 ) @ ( op @ e2 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e1 ) @ ( op @ e2 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e2 ) @ ( op @ e2 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e3 ) @ ( op @ e2 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e0 ) @ ( op @ e2 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e1 ) @ ( op @ e2 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e2 ) @ ( op @ e2 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e3 ) @ ( op @ e2 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e0 ) @ ( op @ e2 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e1 ) @ ( op @ e2 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e2 ) @ ( op @ e2 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e3 ) @ ( op @ e2 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e0 ) @ ( op @ e3 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e1 ) @ ( op @ e3 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e2 ) @ ( op @ e3 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e3 ) @ ( op @ e3 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e0 ) @ ( op @ e3 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e1 ) @ ( op @ e3 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e2 ) @ ( op @ e3 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e3 ) @ ( op @ e3 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e0 ) @ ( op @ e3 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e1 ) @ ( op @ e3 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e2 ) @ ( op @ e3 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e3 ) @ ( op @ e3 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e0 ) @ ( op @ e3 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e1 ) @ ( op @ e3 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e2 ) @ ( op @ e3 @ ( op @ e3 @ e2 ) ) ) ) @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e3 ) @ ( op @ e3 @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(143,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e0 ) @ ( op @ e0 @ ( op @ e0 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e1 ) @ ( op @ e0 @ ( op @ e0 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e2 ) @ ( op @ e0 @ ( op @ e0 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e3 ) @ ( op @ e0 @ ( op @ e0 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e0 ) @ ( op @ e0 @ ( op @ e1 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e1 ) @ ( op @ e0 @ ( op @ e1 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e2 ) @ ( op @ e0 @ ( op @ e1 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e3 ) @ ( op @ e0 @ ( op @ e1 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e0 ) @ ( op @ e0 @ ( op @ e2 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e1 ) @ ( op @ e0 @ ( op @ e2 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e2 ) @ ( op @ e0 @ ( op @ e2 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e3 ) @ ( op @ e0 @ ( op @ e2 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e0 ) @ ( op @ e0 @ ( op @ e3 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e1 ) @ ( op @ e0 @ ( op @ e3 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e2 ) @ ( op @ e0 @ ( op @ e3 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e3 ) @ ( op @ e0 @ ( op @ e3 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e0 ) @ ( op @ e1 @ ( op @ e0 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e1 ) @ ( op @ e1 @ ( op @ e0 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e2 ) @ ( op @ e1 @ ( op @ e0 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e3 ) @ ( op @ e1 @ ( op @ e0 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e0 ) @ ( op @ e1 @ ( op @ e1 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e1 ) @ ( op @ e1 @ ( op @ e1 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e2 ) @ ( op @ e1 @ ( op @ e1 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e3 ) @ ( op @ e1 @ ( op @ e1 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e0 ) @ ( op @ e1 @ ( op @ e2 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e1 ) @ ( op @ e1 @ ( op @ e2 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e2 ) @ ( op @ e1 @ ( op @ e2 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e3 ) @ ( op @ e1 @ ( op @ e2 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e0 ) @ ( op @ e1 @ ( op @ e3 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e1 ) @ ( op @ e1 @ ( op @ e3 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e2 ) @ ( op @ e1 @ ( op @ e3 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e3 ) @ ( op @ e1 @ ( op @ e3 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e0 ) @ ( op @ e2 @ ( op @ e0 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e1 ) @ ( op @ e2 @ ( op @ e0 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e2 ) @ ( op @ e2 @ ( op @ e0 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e3 ) @ ( op @ e2 @ ( op @ e0 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e0 ) @ ( op @ e2 @ ( op @ e1 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e1 ) @ ( op @ e2 @ ( op @ e1 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e2 ) @ ( op @ e2 @ ( op @ e1 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e3 ) @ ( op @ e2 @ ( op @ e1 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e0 ) @ ( op @ e2 @ ( op @ e2 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e1 ) @ ( op @ e2 @ ( op @ e2 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e2 ) @ ( op @ e2 @ ( op @ e2 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e3 ) @ ( op @ e2 @ ( op @ e2 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e0 ) @ ( op @ e2 @ ( op @ e3 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e1 ) @ ( op @ e2 @ ( op @ e3 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e2 ) @ ( op @ e2 @ ( op @ e3 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e3 ) @ ( op @ e2 @ ( op @ e3 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e0 ) @ ( op @ e3 @ ( op @ e0 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e1 ) @ ( op @ e3 @ ( op @ e0 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e2 ) @ ( op @ e3 @ ( op @ e0 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e3 ) @ ( op @ e3 @ ( op @ e0 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e0 ) @ ( op @ e3 @ ( op @ e1 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e1 ) @ ( op @ e3 @ ( op @ e1 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e2 ) @ ( op @ e3 @ ( op @ e1 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e3 ) @ ( op @ e3 @ ( op @ e1 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e0 ) @ ( op @ e3 @ ( op @ e2 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e1 ) @ ( op @ e3 @ ( op @ e2 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e2 ) @ ( op @ e3 @ ( op @ e2 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e3 ) @ ( op @ e3 @ ( op @ e2 @ e3 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e0 ) @ ( op @ e3 @ ( op @ e3 @ e0 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e1 ) @ ( op @ e3 @ ( op @ e3 @ e1 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e2 ) @ ( op @ e3 @ ( op @ e3 @ e2 ) ) @ A ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e3 ) @ ( op @ e3 @ ( op @ e3 @ e3 ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(99,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ( sk7 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ ( sk9 @ A ) )
| ( mrel @ A @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(20921,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5090,19711]) ).
thf(20922,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20921]) ).
thf(21007,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[20922]) ).
thf(21088,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21007]) ).
thf(2773,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[2669,879]) ).
thf(2774,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ sk1 )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[2773]) ).
thf(2807,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[2774]) ).
thf(2828,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( sk32 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[2807]) ).
thf(1261,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,798]) ).
thf(1262,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[1261]) ).
thf(1321,plain,
( ( ( inv @ unit )
!= e1 )
| ( e3 != unit )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1262]) ).
thf(741,plain,
( sk2
| ~ $true
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[691,666]) ).
thf(742,plain,
( sk2
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(simp,[status(thm)],[741]) ).
thf(759,plain,
( sk2
| ( ( op @ e0 @ e0 )
!= e0 )
| ( e2 != e0 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[742]) ).
thf(49,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sk15 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sk16 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(104,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk11 @ A )
| ( sk13 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ ( sk15 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ ( sk16 @ A ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(10843,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[10715,666]) ).
thf(10844,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ mactual ) ) ),
inference(simp,[status(thm)],[10843]) ).
thf(10906,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[10844]) ).
thf(10928,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[10906]) ).
thf(25,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ A )
| sk4 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(87,plain,
! [A: mworld] :
( ~ sk2
| ~ sk3
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ A )
| sk4 ),
inference(simp,[status(thm)],[25]) ).
thf(5211,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[5081,912]) ).
thf(5212,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[5211]) ).
thf(5241,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[5212]) ).
thf(5258,plain,
( ( ( op @ e3 @ unit )
!= e0 )
| ( ( sk31 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[5241]) ).
thf(11074,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ $true
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ B )
| sk3
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,95]) ).
thf(11075,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ B )
| sk3
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[11074]) ).
thf(11076,plain,
( ~ sk2
| ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ sk1 )
| sk3 ),
inference(pattern_uni,[status(thm)],[11075:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(12181,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[522,909]) ).
thf(12182,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 @ A )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[12181]) ).
thf(12299,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( e3 != e3 )
| ( A
!= ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[12182]) ).
thf(12323,plain,
( ~ ( mrel @ mactual @ ( sk31 @ sk1 ) )
| ( ( inv @ ( inv @ e3 ) )
!= e0 ) ),
inference(simp,[status(thm)],[12299]) ).
thf(19906,plain,
( ~ $true
| ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,12323]) ).
thf(19907,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19906]) ).
thf(19997,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( mactual != mactual )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19907]) ).
thf(20050,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e0 )
| ( ( sk31 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19997]) ).
thf(19525,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19026,585]) ).
thf(19526,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ sk1 @ ( sk29 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19525]) ).
thf(19656,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( sk1 != mactual )
| ( ( sk29 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[19526]) ).
thf(19686,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ ( sk29 @ sk1 ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[19656]) ).
thf(30,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sk21 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sk22 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(114,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sk21 @ A ) )
| ~ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ ( sk22 @ A ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(130,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk30 @ A ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(139,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk30 @ A ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(23939,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19744,657]) ).
thf(23940,plain,
( ( qmltpeq @ ( op @ e2 @ unit ) @ e2 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[23939]) ).
thf(24029,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e1 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[23940]) ).
thf(24042,plain,
( ( ( op @ e2 @ unit )
!= e0 )
| ( e2 != e1 ) ),
inference(simp,[status(thm)],[24029]) ).
thf(24852,plain,
( sk2
| ~ $true
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19563,660]) ).
thf(24853,plain,
( sk2
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk29 @ sk1 ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[24852]) ).
thf(24949,plain,
( sk2
| ( ( op @ e0 @ e0 )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ sk1 )
!= ( sk29 @ sk1 ) ) ),
inference(simp,[status(thm)],[24853]) ).
thf(24977,plain,
( sk2
| ( ( op @ e0 @ e0 )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[24949]) ).
thf(1206,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,663]) ).
thf(1207,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[1206]) ).
thf(1244,plain,
( ( ( inv @ unit )
!= e0 )
| ( e2 != unit )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1207]) ).
thf(19811,plain,
( ~ $true
| ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,12318]) ).
thf(19812,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ sk1 ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19811]) ).
thf(19957,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( mactual != mactual )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19812]) ).
thf(20094,plain,
( ( ( inv @ ( inv @ e3 ) )
!= e1 )
| ( ( sk33 @ sk1 )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19957]) ).
thf(9906,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,520]) ).
thf(9907,plain,
! [A: mworld] :
( ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[9906]) ).
thf(9908,plain,
qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ sk1,
inference(pattern_uni,[status(thm)],[9907:[bind(A,$thf( sk1 ))]]) ).
thf(1291,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,912]) ).
thf(1292,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[1291]) ).
thf(1308,plain,
( ( ( inv @ unit )
!= e0 )
| ( e3 != unit )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1292]) ).
thf(20965,plain,
( ~ $true
| ( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14432,19711]) ).
thf(20966,plain,
( ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[20965]) ).
thf(21024,plain,
( ( e0 != e0 )
| ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[20966]) ).
thf(21093,plain,
( ( ( op @ e3 @ e3 )
!= e3 )
| ( ( sk31 @ ( sk29 @ mactual ) )
!= mactual ) ),
inference(simp,[status(thm)],[21024]) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(272,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ D @ B @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2848,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[2678,879]) ).
thf(2849,plain,
( ( qmltpeq @ ( op @ unit @ e2 ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[2848]) ).
thf(2888,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[2849]) ).
thf(2902,plain,
( ( ( op @ unit @ e2 )
!= e1 )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[2888]) ).
thf(1265,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,879]) ).
thf(1266,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ mactual ) ) ),
inference(simp,[status(thm)],[1265]) ).
thf(1309,plain,
( ( ( inv @ unit )
!= e1 )
| ( e2 != unit )
| ( ( sk32 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1266]) ).
thf(5303,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[5090,801]) ).
thf(5304,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[5303]) ).
thf(5323,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[5304]) ).
thf(5336,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( sk33 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[5323]) ).
thf(14,axiom,
mlocal @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(536,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ e1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ e0 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ e2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ e0 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ e3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e3 ) @ e0 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ e0 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ e1 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ e2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ e1 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ e3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e3 ) @ e1 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ e0 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ e2 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ e1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ e2 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ e3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e3 ) @ e2 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e3 ) @ e0 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e0 ) @ e3 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e3 ) @ e1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e1 ) @ e3 @ B ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e3 ) @ e2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( qmltpeq @ ( inv @ e2 ) @ e3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1959,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1723,909]) ).
thf(1960,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[1959]) ).
thf(2006,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1960]) ).
thf(2019,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[2006]) ).
thf(17228,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16924,876]) ).
thf(17229,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[17228]) ).
thf(17250,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[17229]) ).
thf(17279,plain,
( ( ( op @ e2 @ e3 )
!= e2 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[17250]) ).
thf(43,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ A )
| sk3 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(82,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ A )
| sk3 ),
inference(simp,[status(thm)],[43]) ).
thf(17194,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16924,798]) ).
thf(17195,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ mactual )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[17194]) ).
thf(17278,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[17195]) ).
thf(17284,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[17278]) ).
thf(35830,plain,
! [A: mworld] :
( ~ $true
| ( mrel @ A @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,136]) ).
thf(35831,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk34 @ A ) )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[35830]) ).
thf(35832,plain,
mrel @ sk1 @ ( sk34 @ sk1 ),
inference(pattern_uni,[status(thm)],[35831:[bind(A,$thf( sk1 ))]]) ).
thf(816,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[671,36]) ).
thf(817,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk10 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[816]) ).
thf(818,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk10 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[817:[bind(A,$thf( sk10 @ sk1 ))]]) ).
thf(28034,plain,
! [A: mworld] :
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ~ $true
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk16 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[26307,36]) ).
thf(28035,plain,
! [A: mworld] :
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A )
| sk2
| ( ( mrel @ sk1 @ ( sk16 @ sk1 ) )
!= ( mrel @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[28034]) ).
thf(28036,plain,
( ( sk11 @ sk1 )
| ( sk13 @ sk1 )
| ( mrel @ sk1 @ ( sk15 @ sk1 ) )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ ( sk16 @ sk1 ) )
| sk2 ),
inference(pattern_uni,[status(thm)],[28035:[bind(A,$thf( sk16 @ sk1 ))]]) ).
thf(1824,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1720,909]) ).
thf(1825,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ sk1 ) ) ),
inference(simp,[status(thm)],[1824]) ).
thf(1867,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1825]) ).
thf(1876,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1867]) ).
thf(1208,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1110,801]) ).
thf(1209,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ mactual ) ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1248,plain,
( ( ( inv @ unit )
!= e1 )
| ( e3 != unit )
| ( ( sk33 @ mactual )
!= sk1 ) ),
inference(simp,[status(thm)],[1209]) ).
thf(9913,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[520,657]) ).
thf(9914,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 @ A )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[9913]) ).
thf(9978,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ ( inv @ e1 ) )
!= e0 )
| ( e1 != e1 )
| ( A
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[9914]) ).
thf(10024,plain,
( ~ ( mrel @ mactual @ ( sk29 @ mactual ) )
| ( ( inv @ ( inv @ e1 ) )
!= e0 ) ),
inference(simp,[status(thm)],[9978]) ).
thf(19695,plain,
( ~ $true
| ( ( inv @ ( inv @ e1 ) )
!= e0 ) ),
inference(rewrite,[status(thm)],[10024,19041]) ).
thf(19696,plain,
( ( inv @ ( inv @ e1 ) )
!= e0 ),
inference(simp,[status(thm)],[19695]) ).
thf(3467,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ~ $true
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ B )
| sk3
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,82]) ).
thf(3468,plain,
! [B: mworld,A: mworld] :
( ~ sk2
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ B )
| sk3
| ( ( mrel @ A @ A )
!= ( mrel @ sk1 @ B ) ) ),
inference(simp,[status(thm)],[3467]) ).
thf(3469,plain,
( ~ sk2
| ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ sk1 )
| sk3 ),
inference(pattern_uni,[status(thm)],[3468:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1289,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,769]) ).
thf(1290,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e2 @ e3 @ ( sk34 @ sk1 ) ) ),
inference(simp,[status(thm)],[1289]) ).
thf(1303,plain,
( ( ( inv @ unit )
!= e2 )
| ( e3 != unit )
| ( ( sk34 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1290]) ).
thf(23793,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19741,657]) ).
thf(23794,plain,
( ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ ( sk29 @ mactual ) )
!= ( qmltpeq @ e0 @ e1 @ ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[23793]) ).
thf(23848,plain,
( ( ( op @ unit @ e0 )
!= e0 )
| ( e1 != e0 )
| ( ( sk29 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[23794]) ).
thf(23895,plain,
( ( ( op @ unit @ e0 )
!= e0 )
| ( e1 != e0 ) ),
inference(simp,[status(thm)],[23848]) ).
thf(5193,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5081,798]) ).
thf(5194,plain,
( ( qmltpeq @ ( op @ e3 @ unit ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[5193]) ).
thf(5250,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[5194]) ).
thf(5251,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[5250]) ).
thf(13,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( op @ C @ A ) @ ( op @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_substitution_2) ).
thf(532,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( op @ F @ B ) @ ( op @ F @ D ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(38,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk8 @ A ) )
| ~ ( sk7 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(94,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk5 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ ( sk8 @ A ) )
| ~ ( sk7 @ A ) ),
inference(simp,[status(thm)],[38]) ).
thf(17083,plain,
( ~ $true
| ( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[16915,798]) ).
thf(17084,plain,
( ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[17083]) ).
thf(17165,plain,
( ( e1 != e1 )
| ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[17084]) ).
thf(17172,plain,
( ( ( op @ e2 @ e3 )
!= e3 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[17165]) ).
thf(19887,plain,
( ~ $true
| ( ( op @ unit @ e3 )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,1797]) ).
thf(19888,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( mrel @ mactual @ ( sk31 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19887]) ).
thf(20005,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( mactual != mactual )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19888]) ).
thf(20058,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[20005]) ).
thf(7518,plain,
( sk2
| ~ $true
| ~ ( sk23 @ sk1 )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ sk1 ) )
!= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[691,7243]) ).
thf(7519,plain,
( sk2
| ~ ( sk23 @ sk1 )
| ( ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ ( sk24 @ sk1 ) )
!= ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ sk1 ) ) ),
inference(simp,[status(thm)],[7518]) ).
thf(7530,plain,
( sk2
| ~ ( sk23 @ sk1 )
| ( ( op @ e0 @ e0 )
!= ( op @ e0 @ e0 ) )
| ( e3 != e0 )
| ( ( sk24 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[7519]) ).
thf(7584,plain,
( sk2
| ~ ( sk23 @ sk1 )
| ( e3 != e0 )
| ( ( sk24 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[7530]) ).
thf(12,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( op @ A @ C ) @ ( op @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_substitution_1) ).
thf(528,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i,C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i,E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i,G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( op @ B @ F ) @ ( op @ D @ F ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1810,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1720,798]) ).
thf(1811,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ sk1 )
!= ( qmltpeq @ e1 @ e3 @ ( sk33 @ sk1 ) ) ),
inference(simp,[status(thm)],[1810]) ).
thf(1854,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( e3 != e3 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1811]) ).
thf(1880,plain,
( ( ( op @ unit @ e3 )
!= e1 )
| ( ( sk33 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[1854]) ).
thf(10977,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10724,876]) ).
thf(10978,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[10977]) ).
thf(10994,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( e2 != e2 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[10978]) ).
thf(11021,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e1 )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[10994]) ).
thf(10877,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[10715,663]) ).
thf(10878,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[10877]) ).
thf(10919,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[10878]) ).
thf(10931,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[10919]) ).
thf(1299,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1113,876]) ).
thf(1300,plain,
( ( qmltpeq @ ( inv @ unit ) @ unit @ mactual )
!= ( qmltpeq @ e1 @ e2 @ ( sk32 @ sk1 ) ) ),
inference(simp,[status(thm)],[1299]) ).
thf(1320,plain,
( ( ( inv @ unit )
!= e1 )
| ( e2 != unit )
| ( ( sk32 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1300]) ).
thf(1326,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ~ $true
| ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[821,585]) ).
thf(1327,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( mrel @ ( sk10 @ sk1 ) @ ( sk10 @ ( sk10 @ sk1 ) ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1326]) ).
thf(1351,plain,
! [A: mworld] :
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ unit ) @ unit @ A )
| ( ( sk10 @ sk1 )
!= mactual )
| ( ( sk10 @ ( sk10 @ sk1 ) )
!= A ) ),
inference(simp,[status(thm)],[1327]) ).
thf(1367,plain,
( ( sk5 @ sk1 )
| ( sk7 @ sk1 )
| ( mrel @ sk1 @ ( sk9 @ sk1 ) )
| ( sk5 @ ( sk10 @ sk1 ) )
| ( sk7 @ ( sk10 @ sk1 ) )
| ( mrel @ ( sk10 @ sk1 ) @ ( sk9 @ ( sk10 @ sk1 ) ) )
| ( qmltpeq @ ( inv @ unit ) @ unit @ ( sk10 @ ( sk10 @ sk1 ) ) )
| ( ( sk10 @ sk1 )
!= mactual ) ),
inference(simp,[status(thm)],[1351]) ).
thf(19854,plain,
! [A: mworld] :
( ~ $true
| ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19041,135]) ).
thf(19855,plain,
! [A: mworld] :
( ~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ A ) )
| ( ( mrel @ mactual @ ( sk29 @ mactual ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[19854]) ).
thf(19856,plain,
~ ( qmltpeq @ e1 @ e3 @ ( sk33 @ ( sk29 @ mactual ) ) ),
inference(pattern_uni,[status(thm)],[19855:[bind(A,$thf( sk29 @ mactual ))]]) ).
thf(58,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sk21 @ A ) )
| ( mrel @ A @ ( sk22 @ A ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(83,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk17 @ A )
| ( sk19 @ A )
| ~ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ ( sk21 @ A ) )
| ( mrel @ A @ ( sk22 @ A ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(1116,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ $true
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[585,663]) ).
thf(1117,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( qmltpeq @ ( inv @ unit ) @ unit @ A )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[1116]) ).
thf(1162,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( ( inv @ unit )
!= e0 )
| ( e2 != unit )
| ( A
!= ( sk30 @ sk1 ) ) ),
inference(simp,[status(thm)],[1117]) ).
thf(1184,plain,
( ~ ( mrel @ mactual @ ( sk30 @ sk1 ) )
| ( ( inv @ unit )
!= e0 )
| ( e2 != unit ) ),
inference(simp,[status(thm)],[1162]) ).
thf(19735,plain,
( ~ $true
| ( ( op @ e3 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[19041,5150]) ).
thf(19736,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( mrel @ mactual @ ( sk33 @ mactual ) )
!= ( mrel @ mactual @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[19735]) ).
thf(19949,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( mactual != mactual )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19736]) ).
thf(20086,plain,
( ( ( op @ e3 @ unit )
!= e1 )
| ( ( sk33 @ mactual )
!= ( sk29 @ mactual ) ) ),
inference(simp,[status(thm)],[19949]) ).
thf(1977,plain,
( ~ $true
| ( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ) ),
inference(paramod_ordered,[status(thm)],[1723,912]) ).
thf(1978,plain,
( ( qmltpeq @ ( op @ unit @ e3 ) @ e3 @ mactual )
!= ( qmltpeq @ e0 @ e3 @ ( sk31 @ mactual ) ) ),
inference(simp,[status(thm)],[1977]) ).
thf(2005,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( e3 != e3 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[1978]) ).
thf(2018,plain,
( ( ( op @ unit @ e3 )
!= e0 )
| ( ( sk31 @ mactual )
!= mactual ) ),
inference(simp,[status(thm)],[2005]) ).
thf(21128,plain,
( ~ $true
| ( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10715,19759]) ).
thf(21129,plain,
( ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 @ sk1 )
!= ( qmltpeq @ e0 @ e2 @ ( sk30 @ ( sk29 @ mactual ) ) ) ),
inference(simp,[status(thm)],[21128]) ).
thf(21328,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( e2 != e2 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21129]) ).
thf(21385,plain,
( ( ( inv @ ( inv @ e2 ) )
!= e0 )
| ( ( sk30 @ ( sk29 @ mactual ) )
!= sk1 ) ),
inference(simp,[status(thm)],[21328]) ).
thf(1488,plain,
! [A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,284]) ).
thf(1489,plain,
! [A: mworld] :
( ( qmltpeq @ ( op @ unit @ e0 ) @ e0 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1488]) ).
thf(1490,plain,
qmltpeq @ ( op @ unit @ e0 ) @ e0 @ sk1,
inference(pattern_uni,[status(thm)],[1489:[bind(A,$thf( sk1 ))]]) ).
thf(18,axiom,
mlocal @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(592,plain,
( ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e1 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e2 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e0 @ e3 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e0 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e2 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e3 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e3 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e3 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e1 @ e3 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e0 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e1 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e3 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e3 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e3 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e2 @ e3 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e0 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e1 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e1 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e1 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e1 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e2 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e2 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e2 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e2 ) @ e3 @ A ) ) )
& ( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 @ A ) )
| ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8536,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[513,294]) ).
thf(8537,plain,
! [B: mworld,A: mworld] :
( ( qmltpeq @ ( op @ unit @ e1 ) @ e1 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[8536]) ).
thf(8538,plain,
qmltpeq @ ( op @ unit @ e1 ) @ e1 @ mactual,
inference(pattern_uni,[status(thm)],[8537:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(59,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sk26 @ A ) )
| ~ ( sk25 @ A ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(100,plain,
! [A: mworld] :
( ~ ( mrel @ sk1 @ A )
| ( sk23 @ A )
| ~ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 @ ( sk26 @ A ) )
| ~ ( sk25 @ A ) ),
inference(simp,[status(thm)],[59]) ).
thf(26,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ A )
| sk3 ),
inference(cnfConj,[status(thm)],[22]) ).
thf(111,plain,
! [A: mworld] :
( ~ sk2
| ~ ( mrel @ sk1 @ A )
| ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 @ A )
| sk3 ),
inference(simp,[status(thm)],[26]) ).
thf(53697,plain,
$false,
inference(e,[status(thm)],[19672,101,14890,909,35089,1179,666,88,1369,138,20095,1110,19687,523,1005,115,21114,276,19819,20046,1793,12221,14538,9233,14665,10715,5163,10827,20063,20066,19668,21096,16915,1196,23184,20102,3766,24334,14769,288,12324,1254,7628,5342,9116,1243,7637,1391,1576,17026,2825,21092,3116,21086,110,1323,5150,1313,26718,2466,6611,14773,284,7728,289,20049,13044,5338,8054,3840,5256,19868,93,36536,78,1875,25989,2950,10818,20021,16924,17171,14423,106,514,16476,84,19759,2017,1183,5259,821,19700,14527,6685,12536,26887,660,28046,1242,3606,89,133,116,19678,10932,527,74,9917,292,117,512,20025,85,19903,10831,35852,798,5174,25834,1311,3767,19771,102,12437,4397,19744,8645,20057,3682,2015,6620,1723,19026,19842,14766,21,137,92,20047,23336,625,879,97,522,1787,11646,21374,2826,20065,1195,19671,3615,1804,19882,5081,5475,14666,20032,109,1493,19879,3141,77,20033,21370,19764,590,19928,96,17170,1249,2487,2900,12532,17022,19711,20028,23496,14526,1874,1720,41,19694,20097,73,105,10929,5090,657,17984,3190,1185,586,12318,134,26307,12442,12329,21380,2904,17991,513,17282,3839,2734,584,12441,3768,772,291,118,1256,2827,14667,9125,2738,11018,27946,20041,19570,19466,2753,86,19702,19741,19698,113,35662,3764,6443,81,2097,76,2669,649,20083,1307,98,36534,20068,758,103,5335,91,20061,19853,108,20093,33829,3668,21084,27177,17169,520,12438,8529,769,2542,12534,3687,14660,19680,1250,20087,17896,912,521,20100,3838,21365,3674,135,1113,19912,80,19563,21097,663,3672,19806,487,112,17281,1181,10824,17038,516,19789,5165,19778,295,24492,3842,14775,2732,35980,20080,525,19925,95,2678,20055,35042,1790,20044,11022,10724,127,1317,2903,12529,10820,24186,7243,585,17057,1257,20062,20077,10028,19682,1797,20103,1372,36538,11017,1240,72,21379,143,876,14543,99,21088,2828,671,1321,759,104,10928,87,14432,5258,11076,20050,19041,19686,114,139,24042,24977,1244,20094,75,9908,12323,1308,21093,272,2902,1309,290,119,5336,536,2019,17279,82,12230,287,17284,36,35832,818,28036,1876,1248,19696,3469,2736,1303,107,23895,5159,79,5251,532,19865,94,294,801,136,17172,20058,7584,528,19730,131,1880,691,11021,10931,1320,1367,19856,83,1184,20086,2018,21385,1490,592,8538,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL942^2 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % 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
% 0.10/0.21 % Computer : n001.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 10:50:05 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.02/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.23/1.21 % [INFO] Parsing done (374ms).
% 2.23/1.22 % [INFO] Running in sequential loop mode.
% 3.39/1.61 % [INFO] eprover registered as external prover.
% 3.39/1.62 % [INFO] Scanning for conjecture ...
% 3.96/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 4.26/1.96 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 5.24/2.17 % [INFO] Problem is higher-order (TPTP THF).
% 5.24/2.17 % [INFO] Type checking passed.
% 5.24/2.18 % [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 ...
% 95.26/22.48 % External prover 'e' found a proof!
% 95.26/22.48 % [INFO] Killing All external provers ...
% 95.26/22.48 % Time passed: 22119ms (effective reasoning time: 21253ms)
% 95.26/22.48 % 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)>
% 95.26/22.49 % Axioms used in derivation (18): ax4, ax9, ax6, op_substitution_2, ax8, reflexivity, ax11, ax2, transitivity, inv_substitution_1, symmetry, mrel_reflexive, ax10, op_substitution_1, ax1, ax7, ax3, ax5
% 95.26/22.49 % No. of inferences in proof: 1371
% 95.26/22.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 22119 ms resp. 21253 ms w/o parsing
% 100.46/23.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 100.46/23.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------