%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL944^8 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 148.35s 78.90s
% Output : Refutation 149.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 86
% Syntax : Number of formulae : 195 ( 29 unt; 0 typ; 18 def)
% Number of atoms : 2472 ( 37 equ; 0 cnn)
% Maximal formula atoms : 88 ( 12 avg)
% Number of connectives : 7699 ( 665 ~; 683 |; 54 &;5629 @)
% ( 0 <=>; 668 =>; 0 <=; 0 <~>)
% Maximal formula depth : 123 ( 16 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 4 con; 0-6 aty)
% Number of variables : 1156 ( 195 ^; 946 !; 2 ?;1156 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% 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(mand_decl,type,
mand: ( 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(eiw_di_decl,type,
eiw_di: $i > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(r2_decl,type,
r2: mworld > $o ).
thf(r3_decl,type,
r3: mworld > $o ).
thf(r4_decl,type,
r4: mworld > $o ).
thf(r5_decl,type,
r5: mworld > $o ).
thf(equivalence_1_decl,type,
equivalence_1: mworld > $o ).
thf(equivalence_2_decl,type,
equivalence_2: mworld > $o ).
thf(cn2_decl,type,
cn2: mworld > $o ).
thf(cn1_decl,type,
cn1: mworld > $o ).
thf(cn3_decl,type,
cn3: mworld > $o ).
thf(kn2_decl,type,
kn2: mworld > $o ).
thf(kn1_decl,type,
kn1: mworld > $o ).
thf(kn3_decl,type,
kn3: mworld > $o ).
thf(equivalence_3_decl,type,
equivalence_3: mworld > $o ).
thf(op_implies_or_decl,type,
op_implies_or: mworld > $o ).
thf(op_and_decl,type,
op_and: mworld > $o ).
thf(and_2_decl,type,
and_2: mworld > $o ).
thf(and_3_decl,type,
and_3: mworld > $o ).
thf(and_1_decl,type,
and_1: mworld > $o ).
thf(implies_2_decl,type,
implies_2: mworld > $o ).
thf(implies_3_decl,type,
implies_3: mworld > $o ).
thf(op_implies_and_decl,type,
op_implies_and: mworld > $o ).
thf(implies_1_decl,type,
implies_1: mworld > $o ).
thf(substitution_of_equivalents_decl,type,
substitution_of_equivalents: mworld > $o ).
thf(op_or_decl,type,
op_or: mworld > $o ).
thf(modus_tollens_decl,type,
modus_tollens: mworld > $o ).
thf(or_1_decl,type,
or_1: mworld > $o ).
thf(or_2_decl,type,
or_2: mworld > $o ).
thf(or_3_decl,type,
or_3: mworld > $o ).
thf(op_equiv_decl,type,
op_equiv: mworld > $o ).
thf(modus_ponens_decl,type,
modus_ponens: mworld > $o ).
thf(r1_decl,type,
r1: mworld > $o ).
thf(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(is_a_theorem_decl,type,
is_a_theorem: $i > mworld > $o ).
thf(equiv_decl,type,
equiv: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(sk1_decl,type,
sk1: mworld ).
thf(sk2_decl,type,
sk2: mworld > $i ).
thf(sk3_decl,type,
sk3: mworld > $i > mworld > $i > mworld > mworld ).
thf(sk4_decl,type,
sk4: mworld > $i > mworld > $i > mworld > mworld ).
thf(sk159_decl,type,
sk159: mworld > $o ).
thf(sk160_decl,type,
sk160: mworld > mworld ).
thf(sk161_decl,type,
sk161: mworld > $i > mworld > $i > mworld > mworld > mworld ).
thf(sk162_decl,type,
sk162: mworld > $i > mworld > $i > mworld > mworld > mworld ).
thf(sk163_decl,type,
sk163: mworld > mworld ).
thf(sk164_decl,type,
sk164: mworld > $i ).
thf(sk165_decl,type,
sk165: mworld > mworld ).
thf(sk166_decl,type,
sk166: mworld > $i ).
thf(sk167_decl,type,
sk167: mworld > mworld ).
thf(sk168_decl,type,
sk168: mworld > mworld ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [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] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: mworld] :
~ ( ( mrel @ mactual @ A )
=> ( r2 @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: mworld] :
@+[B: $i] : ( eiw_di @ B @ A ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: mworld,B: $i,C: mworld,D: $i,E: mworld] :
@+[F: mworld] :
~ ( ( mrel @ A @ F )
=> ( qmltpeq @ D @ B @ F ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: mworld,B: $i,C: mworld,D: $i,E: mworld] :
@+[F: mworld] :
~ ( ( mrel @ A @ F )
=> ( is_a_theorem @ D @ F ) ) ) ) ).
thf(sk160_def,definition,
( sk160
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ( modus_ponens @ B ) ) ) ) ).
thf(sk161_def,definition,
( sk161
= ( ^ [A: mworld,B: $i,C: mworld,D: $i,E: mworld,F: mworld] :
@+[G: mworld] :
~ ( ( mrel @ A @ G )
=> ( is_a_theorem @ D @ G ) ) ) ) ).
thf(sk162_def,definition,
( sk162
= ( ^ [A: mworld,B: $i,C: mworld,D: $i,E: mworld,F: mworld] :
@+[G: mworld] :
~ ( ( mrel @ A @ G )
=> ( is_a_theorem @ ( implies @ D @ B ) @ G ) ) ) ) ).
thf(sk163_def,definition,
( sk163
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( ( ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ C @ G ) )
& ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ ( implies @ C @ E ) @ G ) ) )
=> ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ E @ G ) ) ) ) ) ) ) ) ) ) ).
thf(sk164_def,definition,
( sk164
= ( ^ [A: mworld] :
@+[B: $i] :
~ ( ( eiw_di @ B @ ( sk163 @ A ) )
=> ! [C: mworld] :
( ( mrel @ ( sk163 @ A ) @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( is_a_theorem @ B @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( is_a_theorem @ ( implies @ B @ D ) @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( is_a_theorem @ D @ F ) ) ) ) ) ) ) ) ) ).
thf(sk165_def,definition,
( sk165
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ ( sk163 @ A ) @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( ( ! [E: mworld] :
( ( mrel @ D @ E )
=> ( is_a_theorem @ ( sk164 @ A ) @ E ) )
& ! [E: mworld] :
( ( mrel @ D @ E )
=> ( is_a_theorem @ ( implies @ ( sk164 @ A ) @ C ) @ E ) ) )
=> ! [E: mworld] :
( ( mrel @ D @ E )
=> ( is_a_theorem @ C @ E ) ) ) ) ) ) ) ) ).
thf(sk166_def,definition,
( sk166
= ( ^ [A: mworld] :
@+[B: $i] :
~ ( ( eiw_di @ B @ ( sk165 @ A ) )
=> ! [C: mworld] :
( ( mrel @ ( sk165 @ A ) @ C )
=> ( ( ! [D: mworld] :
( ( mrel @ C @ D )
=> ( is_a_theorem @ ( sk164 @ A ) @ D ) )
& ! [D: mworld] :
( ( mrel @ C @ D )
=> ( is_a_theorem @ ( implies @ ( sk164 @ A ) @ B ) @ D ) ) )
=> ! [D: mworld] :
( ( mrel @ C @ D )
=> ( is_a_theorem @ B @ D ) ) ) ) ) ) ) ).
thf(sk167_def,definition,
( sk167
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ ( sk165 @ A ) @ B )
=> ( ( ! [C: mworld] :
( ( mrel @ B @ C )
=> ( is_a_theorem @ ( sk164 @ A ) @ C ) )
& ! [C: mworld] :
( ( mrel @ B @ C )
=> ( is_a_theorem @ ( implies @ ( sk164 @ A ) @ ( sk166 @ A ) ) @ C ) ) )
=> ! [C: mworld] :
( ( mrel @ B @ C )
=> ( is_a_theorem @ ( sk166 @ A ) @ C ) ) ) ) ) ) ).
thf(sk168_def,definition,
( sk168
= ( ^ [A: mworld] :
@+[B: mworld] :
~ ( ( mrel @ ( sk167 @ A ) @ B )
=> ( is_a_theorem @ ( sk166 @ A ) @ B ) ) ) ) ).
thf(12,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(162,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(163,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(cnf,[status(esa)],[162]) ).
thf(60,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ modus_ponens )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ A ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ A @ B ) ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ A ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ A @ B ) ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) )
@ ( mbox @ modus_ponens ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_0) ).
thf(546,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( modus_ponens @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( ( ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ C @ G ) )
& ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ ( implies @ C @ E ) @ G ) ) )
=> ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ E @ G ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( ( ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ C @ G ) )
& ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ ( implies @ C @ E ) @ G ) ) )
=> ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ E @ G ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( modus_ponens @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(547,plain,
! [K: mworld,J: mworld,I: mworld,H: mworld,G: mworld,F: mworld,E: $i,D: mworld,C: $i,B: mworld,A: mworld] :
( ( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( modus_ponens @ ( sk160 @ A ) )
| ( sk159 @ A ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ( mrel @ F @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ( mrel @ F @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ( is_a_theorem @ E @ G ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ( mrel @ F @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ E ) @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ( is_a_theorem @ E @ G ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ~ ( is_a_theorem @ C @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ( mrel @ F @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ( is_a_theorem @ E @ G ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ~ ( is_a_theorem @ C @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ E ) @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ( is_a_theorem @ E @ G ) )
& ( ~ ( mrel @ mactual @ H )
| ( mrel @ H @ ( sk163 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ( eiw_di @ ( sk164 @ H ) @ ( sk163 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ( mrel @ ( sk163 @ H ) @ ( sk165 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ( eiw_di @ ( sk166 @ H ) @ ( sk165 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ( mrel @ ( sk165 @ H ) @ ( sk167 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ~ ( mrel @ ( sk167 @ H ) @ I )
| ( is_a_theorem @ ( sk164 @ H ) @ I )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ~ ( mrel @ ( sk167 @ H ) @ J )
| ( is_a_theorem @ ( implies @ ( sk164 @ H ) @ ( sk166 @ H ) ) @ J )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ( mrel @ ( sk167 @ H ) @ ( sk168 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) )
& ( ~ ( mrel @ mactual @ H )
| ~ ( is_a_theorem @ ( sk166 @ H ) @ ( sk168 @ H ) )
| ~ ( mrel @ H @ K )
| ( modus_ponens @ K ) ) ),
inference(cnf,[status(esa)],[546]) ).
thf(560,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A ) ),
inference(cnfConj,[status(thm)],[547]) ).
thf(928,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( mrel @ B @ ( sk160 @ B ) )
| ( sk159 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[163,560]) ).
thf(929,plain,
! [B: mworld,A: mworld] :
( ( mrel @ B @ ( sk160 @ B ) )
| ( sk159 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[928]) ).
thf(930,plain,
( ( mrel @ mactual @ ( sk160 @ mactual ) )
| ( sk159 @ mactual ) ),
inference(pattern_uni,[status(thm)],[929:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(23,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ cn1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) )
@ ( mbox @ cn1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn1_0) ).
thf(224,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( cn1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( cn1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(57,axiom,
mlocal @ ( mbox @ equivalence_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
thf(526,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( equivalence_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(26,axiom,
( mlocal
@ ( mbox
@ ( mimplies @ ( mbox @ op_and )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( and @ A @ B ) @ ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and_0) ).
thf(282,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( op_and @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( qmltpeq @ ( and @ C @ E ) @ ( not @ ( or @ ( not @ C ) @ ( not @ E ) ) ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
mlocal @ ( mbox @ op_equiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(170,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_equiv @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(49,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ r5 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) )
@ ( mbox @ r5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5_0) ).
thf(440,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r5 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r5 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(17,axiom,
mlocal @ ( mbox @ substitution_of_equivalents ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents_1) ).
thf(174,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( substitution_of_equivalents @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(436,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [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)],[48]) ).
thf(39,axiom,
mlocal @ ( mbox @ op_and ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
thf(372,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_and @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(55,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ r2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ r2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_0) ).
thf(504,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(50,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ r4 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) )
@ ( mbox @ r4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4_0) ).
thf(460,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r4 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( or @ C @ ( or @ E @ G ) ) @ ( or @ E @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( or @ C @ ( or @ E @ G ) ) @ ( or @ E @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r4 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(13,axiom,
mlocal @ ( mbox @ implies_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
thf(164,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( implies_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(165,plain,
! [A: mworld] :
( ~ ( mrel @ mactual @ A )
| ( implies_3 @ A ) ),
inference(cnf,[status(esa)],[164]) ).
thf(1377,plain,
! [B: mworld,A: mworld] :
( ~ $true
| ( implies_3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(paramod_ordered,[status(thm)],[163,165]) ).
thf(1378,plain,
! [B: mworld,A: mworld] :
( ( implies_3 @ B )
| ( ( mrel @ A @ A )
!= ( mrel @ mactual @ B ) ) ),
inference(simp,[status(thm)],[1377]) ).
thf(1379,plain,
implies_3 @ mactual,
inference(pattern_uni,[status(thm)],[1378:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).
thf(46,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ and_3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ) ) ) ) )
@ ( mbox @ and_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3_0) ).
thf(416,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( and_3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( implies @ E @ ( and @ C @ E ) ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( implies @ E @ ( and @ C @ E ) ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( and_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( is_a_theorem @ A ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_a_theorem_substitution_1) ).
thf(76,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
& ! [F: mworld] :
( ( mrel @ E @ F )
=> ( is_a_theorem @ B @ F ) ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( is_a_theorem @ D @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(77,plain,
! [F: mworld,E: mworld,D: $i,C: mworld,B: $i,A: mworld] :
( ( ~ ( mrel @ mactual @ A )
| ~ ( eiw_di @ B @ A )
| ~ ( mrel @ A @ C )
| ~ ( eiw_di @ D @ C )
| ~ ( mrel @ C @ E )
| ( mrel @ E @ ( sk3 @ E @ D @ C @ B @ A ) )
| ( mrel @ E @ ( sk4 @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ F )
| ( is_a_theorem @ D @ F ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( eiw_di @ B @ A )
| ~ ( mrel @ A @ C )
| ~ ( eiw_di @ D @ C )
| ~ ( mrel @ C @ E )
| ( mrel @ E @ ( sk3 @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ B @ ( sk4 @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ F )
| ( is_a_theorem @ D @ F ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( eiw_di @ B @ A )
| ~ ( mrel @ A @ C )
| ~ ( eiw_di @ D @ C )
| ~ ( mrel @ C @ E )
| ~ ( qmltpeq @ B @ D @ ( sk3 @ E @ D @ C @ B @ A ) )
| ( mrel @ E @ ( sk4 @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ F )
| ( is_a_theorem @ D @ F ) )
& ( ~ ( mrel @ mactual @ A )
| ~ ( eiw_di @ B @ A )
| ~ ( mrel @ A @ C )
| ~ ( eiw_di @ D @ C )
| ~ ( mrel @ C @ E )
| ~ ( qmltpeq @ B @ D @ ( sk3 @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ B @ ( sk4 @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ F )
| ( is_a_theorem @ D @ F ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [F: mworld,E: mworld,D: $i,C: mworld,B: $i,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( eiw_di @ B @ A )
| ~ ( mrel @ A @ C )
| ~ ( eiw_di @ D @ C )
| ~ ( mrel @ C @ E )
| ( mrel @ E @ ( sk3 @ E @ D @ C @ B @ A ) )
| ( mrel @ E @ ( sk4 @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ F )
| ( is_a_theorem @ D @ F ) ),
inference(cnfConj,[status(thm)],[77]) ).
thf(41,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ cn2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ) ) ) ) )
@ ( mbox @ cn2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2_0) ).
thf(376,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( cn2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( implies @ ( not @ C ) @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( implies @ ( not @ C ) @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( cn2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(51,axiom,
mlocal @ ( mbox @ implies_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
thf(480,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( implies_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
( mlocal
@ ( mbox
@ ( mimplies @ ( mbox @ op_equiv )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( equiv @ A @ B ) @ ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv_0) ).
thf(396,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( op_equiv @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( qmltpeq @ ( equiv @ C @ E ) @ ( and @ ( implies @ C @ E ) @ ( implies @ E @ C ) ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(74,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ and_1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) )
@ ( mbox @ and_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1_0) ).
thf(206,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( and_1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( and_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
mlocal @ ( mbox @ implies_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
thf(366,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( implies_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(7,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ implies_3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) )
@ ( mbox @ implies_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3_0) ).
thf(102,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( implies_3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( implies_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ implies_2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ implies_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2_0) ).
thf(334,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( implies_2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ ( implies @ C @ E ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ ( implies @ C @ E ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( implies_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(25,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ substitution_of_equivalents )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ A @ B ) ) ) @ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ A @ B ) ) ) @ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ substitution_of_equivalents ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents_0) ).
thf(260,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( substitution_of_equivalents @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ ( equiv @ C @ E ) @ G ) )
=> ! [G: mworld] :
( ( mrel @ F @ G )
=> ( qmltpeq @ C @ E @ G ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( ! [G: mworld] :
( ( mrel @ F @ G )
=> ( is_a_theorem @ ( equiv @ C @ E ) @ G ) )
=> ! [G: mworld] :
( ( mrel @ F @ G )
=> ( qmltpeq @ C @ E @ G ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( substitution_of_equivalents @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(42,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(392,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ( qmltpeq @ B @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1,conjecture,
mlocal @ ( mbox @ r2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ r2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(70,plain,
~ ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( r2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ cn3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ) ) )
@ ( mbox @ cn3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3_0) ).
thf(192,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( cn3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( is_a_theorem @ ( implies @ ( implies @ ( not @ C ) @ C ) @ C ) @ D ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( is_a_theorem @ ( implies @ ( implies @ ( not @ C ) @ C ) @ C ) @ D ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( cn3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,plain,
( ( mrel @ mactual @ sk1 )
& ~ ( r2 @ sk1 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
~ ( r2 @ sk1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(24,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ equivalence_2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ) ) ) ) )
@ ( mbox @ equivalence_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2_0) ).
thf(244,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( equivalence_2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ E @ C ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ E @ C ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( equivalence_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(549,plain,
! [G: mworld,F: mworld,E: $i,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ~ ( is_a_theorem @ C @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ E ) @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ( is_a_theorem @ E @ G ) ),
inference(cnfConj,[status(thm)],[547]) ).
thf(674,plain,
! [N: mworld,M: mworld,L: $i,K: mworld,J: $i,I: mworld,H: mworld,G: mworld,F: mworld,E: $i,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ~ ( is_a_theorem @ C @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ E ) @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ~ ( mrel @ mactual @ H )
| ~ ( sk159 @ H )
| ~ ( mrel @ H @ I )
| ~ ( eiw_di @ J @ I )
| ~ ( mrel @ I @ K )
| ~ ( eiw_di @ L @ K )
| ~ ( mrel @ K @ M )
| ~ $true
| ~ ( is_a_theorem @ ( implies @ J @ L ) @ ( sk162 @ M @ L @ K @ J @ I @ H ) )
| ~ ( mrel @ M @ N )
| ( is_a_theorem @ L @ N )
| ( ( is_a_theorem @ E @ G )
!= ( is_a_theorem @ J @ ( sk161 @ M @ L @ K @ J @ I @ H ) ) ) ),
inference(paramod_ordered,[status(thm)],[549,549]) ).
thf(675,plain,
! [N: mworld,M: mworld,L: $i,K: mworld,J: $i,I: mworld,H: mworld,G: mworld,F: mworld,E: $i,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ E @ D )
| ~ ( mrel @ D @ F )
| ~ ( is_a_theorem @ C @ ( sk161 @ F @ E @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ E ) @ ( sk162 @ F @ E @ D @ C @ B @ A ) )
| ~ ( mrel @ F @ G )
| ~ ( mrel @ mactual @ H )
| ~ ( sk159 @ H )
| ~ ( mrel @ H @ I )
| ~ ( eiw_di @ J @ I )
| ~ ( mrel @ I @ K )
| ~ ( eiw_di @ L @ K )
| ~ ( mrel @ K @ M )
| ~ ( is_a_theorem @ ( implies @ J @ L ) @ ( sk162 @ M @ L @ K @ J @ I @ H ) )
| ~ ( mrel @ M @ N )
| ( is_a_theorem @ L @ N )
| ( ( is_a_theorem @ E @ G )
!= ( is_a_theorem @ J @ ( sk161 @ M @ L @ K @ J @ I @ H ) ) ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
! [L: mworld,K: mworld,J: $i,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ J @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ J @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ J ) @ ( sk162 @ E @ J @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ mactual @ L )
| ~ ( sk159 @ L )
| ~ ( mrel @ L @ K )
| ~ ( eiw_di @ J @ K )
| ~ ( mrel @ K @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( is_a_theorem @ ( implies @ J @ H ) @ ( sk162 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ G @ F )
| ( is_a_theorem @ H @ F ) ),
inference(pattern_uni,[status(thm)],[675:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( R )),bind(F,$thf( F )),bind(G,$thf( sk161 @ O @ P @ Q @ R @ S @ T )),bind(H,$thf( T )),bind(I,$thf( S )),bind(J,$thf( R )),bind(K,$thf( Q )),bind(L,$thf( P )),bind(M,$thf( O ))]]) ).
thf(694,plain,
! [L: mworld,K: mworld,J: $i,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ J @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ J @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ J ) @ ( sk162 @ E @ J @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ mactual @ L )
| ~ ( sk159 @ L )
| ~ ( mrel @ L @ K )
| ~ ( eiw_di @ J @ K )
| ~ ( mrel @ K @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( is_a_theorem @ ( implies @ J @ H ) @ ( sk162 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ G @ F )
| ( is_a_theorem @ H @ F ) ),
inference(simp,[status(thm)],[676]) ).
thf(707,plain,
! [X: mworld,W: mworld,V: $i,U: mworld,T: $i,S: mworld,R: mworld,Q: mworld,P: mworld,O: $i,N: mworld,M: mworld,L: mworld,K: mworld,J: $i,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ J @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ J @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ J ) @ ( sk162 @ E @ J @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ mactual @ L )
| ~ ( sk159 @ L )
| ~ ( mrel @ L @ K )
| ~ ( eiw_di @ J @ K )
| ~ ( mrel @ K @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( is_a_theorem @ ( implies @ J @ H ) @ ( sk162 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ G @ F )
| ~ ( mrel @ mactual @ M )
| ~ ( sk159 @ M )
| ~ ( mrel @ M @ N )
| ~ ( eiw_di @ O @ N )
| ~ ( mrel @ N @ P )
| ~ ( eiw_di @ V @ P )
| ~ ( mrel @ P @ Q )
| ~ $true
| ~ ( is_a_theorem @ ( implies @ O @ V ) @ ( sk162 @ Q @ V @ P @ O @ N @ M ) )
| ~ ( mrel @ Q @ ( sk161 @ S @ T @ U @ V @ W @ X ) )
| ~ ( mrel @ mactual @ X )
| ~ ( sk159 @ X )
| ~ ( mrel @ X @ W )
| ~ ( eiw_di @ V @ W )
| ~ ( mrel @ W @ U )
| ~ ( eiw_di @ T @ U )
| ~ ( mrel @ U @ S )
| ~ ( is_a_theorem @ ( implies @ V @ T ) @ ( sk162 @ S @ T @ U @ V @ W @ X ) )
| ~ ( mrel @ S @ R )
| ( is_a_theorem @ T @ R )
| ( ( is_a_theorem @ H @ F )
!= ( is_a_theorem @ O @ ( sk161 @ Q @ V @ P @ O @ N @ M ) ) ) ),
inference(paramod_ordered,[status(thm)],[694,694]) ).
thf(708,plain,
! [X: mworld,W: mworld,V: $i,U: mworld,T: $i,S: mworld,R: mworld,Q: mworld,P: mworld,O: $i,N: mworld,M: mworld,L: mworld,K: mworld,J: $i,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ J @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ J @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ J ) @ ( sk162 @ E @ J @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ mactual @ L )
| ~ ( sk159 @ L )
| ~ ( mrel @ L @ K )
| ~ ( eiw_di @ J @ K )
| ~ ( mrel @ K @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( is_a_theorem @ ( implies @ J @ H ) @ ( sk162 @ G @ H @ I @ J @ K @ L ) )
| ~ ( mrel @ G @ F )
| ~ ( mrel @ mactual @ M )
| ~ ( sk159 @ M )
| ~ ( mrel @ M @ N )
| ~ ( eiw_di @ O @ N )
| ~ ( mrel @ N @ P )
| ~ ( eiw_di @ V @ P )
| ~ ( mrel @ P @ Q )
| ~ ( is_a_theorem @ ( implies @ O @ V ) @ ( sk162 @ Q @ V @ P @ O @ N @ M ) )
| ~ ( mrel @ Q @ ( sk161 @ S @ T @ U @ V @ W @ X ) )
| ~ ( mrel @ mactual @ X )
| ~ ( sk159 @ X )
| ~ ( mrel @ X @ W )
| ~ ( eiw_di @ V @ W )
| ~ ( mrel @ W @ U )
| ~ ( eiw_di @ T @ U )
| ~ ( mrel @ U @ S )
| ~ ( is_a_theorem @ ( implies @ V @ T ) @ ( sk162 @ S @ T @ U @ V @ W @ X ) )
| ~ ( mrel @ S @ R )
| ( is_a_theorem @ T @ R )
| ( ( is_a_theorem @ H @ F )
!= ( is_a_theorem @ O @ ( sk161 @ Q @ V @ P @ O @ N @ M ) ) ) ),
inference(simp,[status(thm)],[707]) ).
thf(709,plain,
! [V: mworld,U: mworld,T: $i,S: mworld,R: $i,Q: mworld,P: mworld,O: mworld,N: mworld,M: $i,L: mworld,K: mworld,J: mworld,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ H @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ H @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ H ) @ ( sk162 @ E @ H @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ mactual @ J )
| ~ ( sk159 @ J )
| ~ ( mrel @ J @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( eiw_di @ T @ G )
| ~ ( mrel @ G @ F )
| ~ ( is_a_theorem @ ( implies @ H @ T ) @ ( sk162 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ F @ ( sk161 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ mactual @ V )
| ~ ( sk159 @ V )
| ~ ( mrel @ V @ U )
| ~ ( eiw_di @ T @ U )
| ~ ( mrel @ U @ S )
| ~ ( eiw_di @ R @ S )
| ~ ( mrel @ S @ Q )
| ~ ( is_a_theorem @ ( implies @ T @ R ) @ ( sk162 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ Q @ ( sk161 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ mactual @ P )
| ~ ( sk159 @ P )
| ~ ( mrel @ P @ O )
| ~ ( eiw_di @ R @ O )
| ~ ( mrel @ O @ N )
| ~ ( eiw_di @ M @ N )
| ~ ( mrel @ N @ L )
| ~ ( is_a_theorem @ ( implies @ R @ M ) @ ( sk162 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ L @ K )
| ( is_a_theorem @ M @ K ) ),
inference(pattern_uni,[status(thm)],[708:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( sk161 @ Y @ Z @ ZA @ ZB @ ZC @ ZD )),bind(G,$thf( G )),bind(H,$thf( ZB )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( L )),bind(M,$thf( ZD )),bind(N,$thf( ZC )),bind(O,$thf( ZB )),bind(P,$thf( ZA )),bind(Q,$thf( Y )),bind(R,$thf( R )),bind(S,$thf( S )),bind(T,$thf( T )),bind(U,$thf( U )),bind(V,$thf( Z ))]]) ).
thf(871,plain,
! [V: mworld,U: mworld,T: $i,S: mworld,R: $i,Q: mworld,P: mworld,O: mworld,N: mworld,M: $i,L: mworld,K: mworld,J: mworld,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ H @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ H @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ H ) @ ( sk162 @ E @ H @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ mactual @ J )
| ~ ( sk159 @ J )
| ~ ( mrel @ J @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( eiw_di @ T @ G )
| ~ ( mrel @ G @ F )
| ~ ( is_a_theorem @ ( implies @ H @ T ) @ ( sk162 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ F @ ( sk161 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ mactual @ V )
| ~ ( sk159 @ V )
| ~ ( mrel @ V @ U )
| ~ ( eiw_di @ T @ U )
| ~ ( mrel @ U @ S )
| ~ ( eiw_di @ R @ S )
| ~ ( mrel @ S @ Q )
| ~ ( is_a_theorem @ ( implies @ T @ R ) @ ( sk162 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ Q @ ( sk161 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ mactual @ P )
| ~ ( sk159 @ P )
| ~ ( mrel @ P @ O )
| ~ ( eiw_di @ R @ O )
| ~ ( mrel @ O @ N )
| ~ ( eiw_di @ M @ N )
| ~ ( mrel @ N @ L )
| ~ ( is_a_theorem @ ( implies @ R @ M ) @ ( sk162 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ L @ K )
| ( is_a_theorem @ M @ K ) ),
inference(simp,[status(thm)],[709]) ).
thf(1866,plain,
! [ZR: mworld,ZQ: mworld,ZP: $i,ZO: mworld,ZN: $i,ZM: mworld,ZL: mworld,ZK: mworld,ZJ: mworld,ZI: $i,ZH: mworld,ZG: mworld,ZF: mworld,ZE: mworld,ZD: $i,ZC: mworld,ZB: mworld,ZA: mworld,Z: mworld,Y: $i,X: mworld,W: mworld,V: mworld,U: mworld,T: $i,S: mworld,R: $i,Q: mworld,P: mworld,O: mworld,N: mworld,M: $i,L: mworld,K: mworld,J: mworld,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ H @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ H @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ H ) @ ( sk162 @ E @ H @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ mactual @ J )
| ~ ( sk159 @ J )
| ~ ( mrel @ J @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( eiw_di @ T @ G )
| ~ ( mrel @ G @ F )
| ~ ( is_a_theorem @ ( implies @ H @ T ) @ ( sk162 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ F @ ( sk161 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ mactual @ V )
| ~ ( sk159 @ V )
| ~ ( mrel @ V @ U )
| ~ ( eiw_di @ T @ U )
| ~ ( mrel @ U @ S )
| ~ ( eiw_di @ R @ S )
| ~ ( mrel @ S @ Q )
| ~ ( is_a_theorem @ ( implies @ T @ R ) @ ( sk162 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ Q @ ( sk161 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ mactual @ P )
| ~ ( sk159 @ P )
| ~ ( mrel @ P @ O )
| ~ ( eiw_di @ R @ O )
| ~ ( mrel @ O @ N )
| ~ ( eiw_di @ M @ N )
| ~ ( mrel @ N @ L )
| ~ ( is_a_theorem @ ( implies @ R @ M ) @ ( sk162 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ L @ K )
| ~ ( mrel @ mactual @ W )
| ~ ( sk159 @ W )
| ~ ( mrel @ W @ X )
| ~ ( eiw_di @ Y @ X )
| ~ ( mrel @ X @ Z )
| ~ ( eiw_di @ ZD @ Z )
| ~ ( mrel @ Z @ ZA )
| ~ $true
| ~ ( is_a_theorem @ ( implies @ Y @ ZD ) @ ( sk162 @ ZA @ ZD @ Z @ Y @ X @ W ) )
| ~ ( mrel @ ZA @ ( sk161 @ ZB @ ZP @ ZC @ ZD @ ZE @ ZF ) )
| ~ ( mrel @ mactual @ ZF )
| ~ ( sk159 @ ZF )
| ~ ( mrel @ ZF @ ZE )
| ~ ( eiw_di @ ZD @ ZE )
| ~ ( mrel @ ZE @ ZC )
| ~ ( eiw_di @ ZP @ ZC )
| ~ ( mrel @ ZC @ ZB )
| ~ ( is_a_theorem @ ( implies @ ZD @ ZP ) @ ( sk162 @ ZB @ ZP @ ZC @ ZD @ ZE @ ZF ) )
| ~ ( mrel @ ZB @ ( sk161 @ ZM @ ZN @ ZO @ ZP @ ZQ @ ZR ) )
| ~ ( mrel @ mactual @ ZR )
| ~ ( sk159 @ ZR )
| ~ ( mrel @ ZR @ ZQ )
| ~ ( eiw_di @ ZP @ ZQ )
| ~ ( mrel @ ZQ @ ZO )
| ~ ( eiw_di @ ZN @ ZO )
| ~ ( mrel @ ZO @ ZM )
| ~ ( is_a_theorem @ ( implies @ ZP @ ZN ) @ ( sk162 @ ZM @ ZN @ ZO @ ZP @ ZQ @ ZR ) )
| ~ ( mrel @ ZM @ ( sk161 @ ZH @ ZI @ ZJ @ ZN @ ZK @ ZL ) )
| ~ ( mrel @ mactual @ ZL )
| ~ ( sk159 @ ZL )
| ~ ( mrel @ ZL @ ZK )
| ~ ( eiw_di @ ZN @ ZK )
| ~ ( mrel @ ZK @ ZJ )
| ~ ( eiw_di @ ZI @ ZJ )
| ~ ( mrel @ ZJ @ ZH )
| ~ ( is_a_theorem @ ( implies @ ZN @ ZI ) @ ( sk162 @ ZH @ ZI @ ZJ @ ZN @ ZK @ ZL ) )
| ~ ( mrel @ ZH @ ZG )
| ( is_a_theorem @ ZI @ ZG )
| ( ( is_a_theorem @ M @ K )
!= ( is_a_theorem @ Y @ ( sk161 @ ZA @ ZD @ Z @ Y @ X @ W ) ) ) ),
inference(paramod_ordered,[status(thm)],[871,871]) ).
thf(1867,plain,
! [ZR: mworld,ZQ: mworld,ZP: $i,ZO: mworld,ZN: $i,ZM: mworld,ZL: mworld,ZK: mworld,ZJ: mworld,ZI: $i,ZH: mworld,ZG: mworld,ZF: mworld,ZE: mworld,ZD: $i,ZC: mworld,ZB: mworld,ZA: mworld,Z: mworld,Y: $i,X: mworld,W: mworld,V: mworld,U: mworld,T: $i,S: mworld,R: $i,Q: mworld,P: mworld,O: mworld,N: mworld,M: $i,L: mworld,K: mworld,J: mworld,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ H @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ H @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ H ) @ ( sk162 @ E @ H @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ mactual @ J )
| ~ ( sk159 @ J )
| ~ ( mrel @ J @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( eiw_di @ T @ G )
| ~ ( mrel @ G @ F )
| ~ ( is_a_theorem @ ( implies @ H @ T ) @ ( sk162 @ F @ T @ G @ H @ I @ J ) )
| ~ ( mrel @ F @ ( sk161 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ mactual @ V )
| ~ ( sk159 @ V )
| ~ ( mrel @ V @ U )
| ~ ( eiw_di @ T @ U )
| ~ ( mrel @ U @ S )
| ~ ( eiw_di @ R @ S )
| ~ ( mrel @ S @ Q )
| ~ ( is_a_theorem @ ( implies @ T @ R ) @ ( sk162 @ Q @ R @ S @ T @ U @ V ) )
| ~ ( mrel @ Q @ ( sk161 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ mactual @ P )
| ~ ( sk159 @ P )
| ~ ( mrel @ P @ O )
| ~ ( eiw_di @ R @ O )
| ~ ( mrel @ O @ N )
| ~ ( eiw_di @ M @ N )
| ~ ( mrel @ N @ L )
| ~ ( is_a_theorem @ ( implies @ R @ M ) @ ( sk162 @ L @ M @ N @ R @ O @ P ) )
| ~ ( mrel @ L @ K )
| ~ ( mrel @ mactual @ W )
| ~ ( sk159 @ W )
| ~ ( mrel @ W @ X )
| ~ ( eiw_di @ Y @ X )
| ~ ( mrel @ X @ Z )
| ~ ( eiw_di @ ZD @ Z )
| ~ ( mrel @ Z @ ZA )
| ~ ( is_a_theorem @ ( implies @ Y @ ZD ) @ ( sk162 @ ZA @ ZD @ Z @ Y @ X @ W ) )
| ~ ( mrel @ ZA @ ( sk161 @ ZB @ ZP @ ZC @ ZD @ ZE @ ZF ) )
| ~ ( mrel @ mactual @ ZF )
| ~ ( sk159 @ ZF )
| ~ ( mrel @ ZF @ ZE )
| ~ ( eiw_di @ ZD @ ZE )
| ~ ( mrel @ ZE @ ZC )
| ~ ( eiw_di @ ZP @ ZC )
| ~ ( mrel @ ZC @ ZB )
| ~ ( is_a_theorem @ ( implies @ ZD @ ZP ) @ ( sk162 @ ZB @ ZP @ ZC @ ZD @ ZE @ ZF ) )
| ~ ( mrel @ ZB @ ( sk161 @ ZM @ ZN @ ZO @ ZP @ ZQ @ ZR ) )
| ~ ( mrel @ mactual @ ZR )
| ~ ( sk159 @ ZR )
| ~ ( mrel @ ZR @ ZQ )
| ~ ( eiw_di @ ZP @ ZQ )
| ~ ( mrel @ ZQ @ ZO )
| ~ ( eiw_di @ ZN @ ZO )
| ~ ( mrel @ ZO @ ZM )
| ~ ( is_a_theorem @ ( implies @ ZP @ ZN ) @ ( sk162 @ ZM @ ZN @ ZO @ ZP @ ZQ @ ZR ) )
| ~ ( mrel @ ZM @ ( sk161 @ ZH @ ZI @ ZJ @ ZN @ ZK @ ZL ) )
| ~ ( mrel @ mactual @ ZL )
| ~ ( sk159 @ ZL )
| ~ ( mrel @ ZL @ ZK )
| ~ ( eiw_di @ ZN @ ZK )
| ~ ( mrel @ ZK @ ZJ )
| ~ ( eiw_di @ ZI @ ZJ )
| ~ ( mrel @ ZJ @ ZH )
| ~ ( is_a_theorem @ ( implies @ ZN @ ZI ) @ ( sk162 @ ZH @ ZI @ ZJ @ ZN @ ZK @ ZL ) )
| ~ ( mrel @ ZH @ ZG )
| ( is_a_theorem @ ZI @ ZG )
| ( ( is_a_theorem @ M @ K )
!= ( is_a_theorem @ Y @ ( sk161 @ ZA @ ZD @ Z @ Y @ X @ W ) ) ) ),
inference(simp,[status(thm)],[1866]) ).
thf(1868,plain,
! [ZP: mworld,ZO: mworld,ZN: $i,ZM: mworld,ZL: $i,ZK: mworld,ZJ: mworld,ZI: mworld,ZH: $i,ZG: mworld,ZF: $i,ZE: mworld,ZD: mworld,ZC: mworld,ZB: mworld,ZA: $i,Z: mworld,Y: mworld,X: mworld,W: mworld,V: mworld,U: mworld,T: mworld,S: mworld,R: $i,Q: mworld,P: $i,O: mworld,N: mworld,M: mworld,L: mworld,K: mworld,J: mworld,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ H @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ H @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ H ) @ ( sk162 @ E @ H @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ F @ R @ G @ H @ I @ J ) )
| ~ ( mrel @ mactual @ J )
| ~ ( sk159 @ J )
| ~ ( mrel @ J @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( eiw_di @ R @ G )
| ~ ( mrel @ G @ F )
| ~ ( is_a_theorem @ ( implies @ H @ R ) @ ( sk162 @ F @ R @ G @ H @ I @ J ) )
| ~ ( mrel @ F @ ( sk161 @ O @ P @ Q @ R @ S @ T ) )
| ~ ( mrel @ mactual @ T )
| ~ ( sk159 @ T )
| ~ ( mrel @ T @ S )
| ~ ( eiw_di @ R @ S )
| ~ ( mrel @ S @ Q )
| ~ ( eiw_di @ P @ Q )
| ~ ( mrel @ Q @ O )
| ~ ( is_a_theorem @ ( implies @ R @ P ) @ ( sk162 @ O @ P @ Q @ R @ S @ T ) )
| ~ ( mrel @ O @ ( sk161 @ K @ ZN @ L @ P @ M @ N ) )
| ~ ( mrel @ mactual @ N )
| ~ ( sk159 @ N )
| ~ ( mrel @ N @ M )
| ~ ( eiw_di @ P @ M )
| ~ ( mrel @ M @ L )
| ~ ( eiw_di @ ZN @ L )
| ~ ( mrel @ L @ K )
| ~ ( is_a_theorem @ ( implies @ P @ ZN ) @ ( sk162 @ K @ ZN @ L @ P @ M @ N ) )
| ~ ( mrel @ K @ ( sk161 @ ZK @ ZL @ ZM @ ZN @ ZO @ ZP ) )
| ~ ( mrel @ mactual @ ZP )
| ~ ( sk159 @ ZP )
| ~ ( mrel @ ZP @ ZO )
| ~ ( eiw_di @ ZN @ ZO )
| ~ ( mrel @ ZO @ ZM )
| ~ ( eiw_di @ ZL @ ZM )
| ~ ( mrel @ ZM @ ZK )
| ~ ( is_a_theorem @ ( implies @ ZN @ ZL ) @ ( sk162 @ ZK @ ZL @ ZM @ ZN @ ZO @ ZP ) )
| ~ ( mrel @ ZK @ ( sk161 @ U @ ZH @ V @ ZL @ W @ X ) )
| ~ ( mrel @ mactual @ X )
| ~ ( sk159 @ X )
| ~ ( mrel @ X @ W )
| ~ ( eiw_di @ ZL @ W )
| ~ ( mrel @ W @ V )
| ~ ( eiw_di @ ZH @ V )
| ~ ( mrel @ V @ U )
| ~ ( is_a_theorem @ ( implies @ ZL @ ZH ) @ ( sk162 @ U @ ZH @ V @ ZL @ W @ X ) )
| ~ ( mrel @ U @ ( sk161 @ ZE @ ZF @ ZG @ ZH @ ZI @ ZJ ) )
| ~ ( mrel @ mactual @ ZJ )
| ~ ( sk159 @ ZJ )
| ~ ( mrel @ ZJ @ ZI )
| ~ ( eiw_di @ ZH @ ZI )
| ~ ( mrel @ ZI @ ZG )
| ~ ( eiw_di @ ZF @ ZG )
| ~ ( mrel @ ZG @ ZE )
| ~ ( is_a_theorem @ ( implies @ ZH @ ZF ) @ ( sk162 @ ZE @ ZF @ ZG @ ZH @ ZI @ ZJ ) )
| ~ ( mrel @ ZE @ ( sk161 @ Z @ ZA @ ZB @ ZF @ ZC @ ZD ) )
| ~ ( mrel @ mactual @ ZD )
| ~ ( sk159 @ ZD )
| ~ ( mrel @ ZD @ ZC )
| ~ ( eiw_di @ ZF @ ZC )
| ~ ( mrel @ ZC @ ZB )
| ~ ( eiw_di @ ZA @ ZB )
| ~ ( mrel @ ZB @ Z )
| ~ ( is_a_theorem @ ( implies @ ZF @ ZA ) @ ( sk162 @ Z @ ZA @ ZB @ ZF @ ZC @ ZD ) )
| ~ ( mrel @ Z @ Y )
| ( is_a_theorem @ ZA @ Y ) ),
inference(pattern_uni,[status(thm)],[1867:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( sk161 @ ZS @ ZT @ ZU @ ZV @ ZW @ ZX )),bind(L,$thf( L )),bind(M,$thf( ZV )),bind(N,$thf( N )),bind(O,$thf( O )),bind(P,$thf( P )),bind(Q,$thf( Q )),bind(R,$thf( R )),bind(S,$thf( S )),bind(T,$thf( T )),bind(U,$thf( U )),bind(V,$thf( V )),bind(W,$thf( ZX )),bind(X,$thf( ZW )),bind(Y,$thf( ZV )),bind(Z,$thf( ZU )),bind(ZA,$thf( ZS )),bind(ZB,$thf( ZB )),bind(ZC,$thf( ZC )),bind(ZD,$thf( ZT ))]]) ).
thf(2203,plain,
! [ZP: mworld,ZO: mworld,ZN: $i,ZM: mworld,ZL: $i,ZK: mworld,ZJ: mworld,ZI: mworld,ZH: $i,ZG: mworld,ZF: $i,ZE: mworld,ZD: mworld,ZC: mworld,ZB: mworld,ZA: $i,Z: mworld,Y: mworld,X: mworld,W: mworld,V: mworld,U: mworld,T: mworld,S: mworld,R: $i,Q: mworld,P: $i,O: mworld,N: mworld,M: mworld,L: mworld,K: mworld,J: mworld,I: mworld,H: $i,G: mworld,F: mworld,E: mworld,D: mworld,C: $i,B: mworld,A: mworld] :
( ~ ( mrel @ mactual @ A )
| ~ ( sk159 @ A )
| ~ ( mrel @ A @ B )
| ~ ( eiw_di @ C @ B )
| ~ ( mrel @ B @ D )
| ~ ( eiw_di @ H @ D )
| ~ ( mrel @ D @ E )
| ~ ( is_a_theorem @ C @ ( sk161 @ E @ H @ D @ C @ B @ A ) )
| ~ ( is_a_theorem @ ( implies @ C @ H ) @ ( sk162 @ E @ H @ D @ C @ B @ A ) )
| ~ ( mrel @ E @ ( sk161 @ F @ R @ G @ H @ I @ J ) )
| ~ ( mrel @ mactual @ J )
| ~ ( sk159 @ J )
| ~ ( mrel @ J @ I )
| ~ ( eiw_di @ H @ I )
| ~ ( mrel @ I @ G )
| ~ ( eiw_di @ R @ G )
| ~ ( mrel @ G @ F )
| ~ ( is_a_theorem @ ( implies @ H @ R ) @ ( sk162 @ F @ R @ G @ H @ I @ J ) )
| ~ ( mrel @ F @ ( sk161 @ O @ P @ Q @ R @ S @ T ) )
| ~ ( mrel @ mactual @ T )
| ~ ( sk159 @ T )
| ~ ( mrel @ T @ S )
| ~ ( eiw_di @ R @ S )
| ~ ( mrel @ S @ Q )
| ~ ( eiw_di @ P @ Q )
| ~ ( mrel @ Q @ O )
| ~ ( is_a_theorem @ ( implies @ R @ P ) @ ( sk162 @ O @ P @ Q @ R @ S @ T ) )
| ~ ( mrel @ O @ ( sk161 @ K @ ZN @ L @ P @ M @ N ) )
| ~ ( mrel @ mactual @ N )
| ~ ( sk159 @ N )
| ~ ( mrel @ N @ M )
| ~ ( eiw_di @ P @ M )
| ~ ( mrel @ M @ L )
| ~ ( eiw_di @ ZN @ L )
| ~ ( mrel @ L @ K )
| ~ ( is_a_theorem @ ( implies @ P @ ZN ) @ ( sk162 @ K @ ZN @ L @ P @ M @ N ) )
| ~ ( mrel @ K @ ( sk161 @ ZK @ ZL @ ZM @ ZN @ ZO @ ZP ) )
| ~ ( mrel @ mactual @ ZP )
| ~ ( sk159 @ ZP )
| ~ ( mrel @ ZP @ ZO )
| ~ ( eiw_di @ ZN @ ZO )
| ~ ( mrel @ ZO @ ZM )
| ~ ( eiw_di @ ZL @ ZM )
| ~ ( mrel @ ZM @ ZK )
| ~ ( is_a_theorem @ ( implies @ ZN @ ZL ) @ ( sk162 @ ZK @ ZL @ ZM @ ZN @ ZO @ ZP ) )
| ~ ( mrel @ ZK @ ( sk161 @ U @ ZH @ V @ ZL @ W @ X ) )
| ~ ( mrel @ mactual @ X )
| ~ ( sk159 @ X )
| ~ ( mrel @ X @ W )
| ~ ( eiw_di @ ZL @ W )
| ~ ( mrel @ W @ V )
| ~ ( eiw_di @ ZH @ V )
| ~ ( mrel @ V @ U )
| ~ ( is_a_theorem @ ( implies @ ZL @ ZH ) @ ( sk162 @ U @ ZH @ V @ ZL @ W @ X ) )
| ~ ( mrel @ U @ ( sk161 @ ZE @ ZF @ ZG @ ZH @ ZI @ ZJ ) )
| ~ ( mrel @ mactual @ ZJ )
| ~ ( sk159 @ ZJ )
| ~ ( mrel @ ZJ @ ZI )
| ~ ( eiw_di @ ZH @ ZI )
| ~ ( mrel @ ZI @ ZG )
| ~ ( eiw_di @ ZF @ ZG )
| ~ ( mrel @ ZG @ ZE )
| ~ ( is_a_theorem @ ( implies @ ZH @ ZF ) @ ( sk162 @ ZE @ ZF @ ZG @ ZH @ ZI @ ZJ ) )
| ~ ( mrel @ ZE @ ( sk161 @ Z @ ZA @ ZB @ ZF @ ZC @ ZD ) )
| ~ ( mrel @ mactual @ ZD )
| ~ ( sk159 @ ZD )
| ~ ( mrel @ ZD @ ZC )
| ~ ( eiw_di @ ZF @ ZC )
| ~ ( mrel @ ZC @ ZB )
| ~ ( eiw_di @ ZA @ ZB )
| ~ ( mrel @ ZB @ Z )
| ~ ( is_a_theorem @ ( implies @ ZF @ ZA ) @ ( sk162 @ Z @ ZA @ ZB @ ZF @ ZC @ ZD ) )
| ~ ( mrel @ Z @ Y )
| ( is_a_theorem @ ZA @ Y ) ),
inference(simp,[status(thm)],[1868]) ).
thf(59,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ equivalence_1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ equivalence_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1_0) ).
thf(530,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( equivalence_1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( equivalence_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(69,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ kn3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox @ kn3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn3_0) ).
thf(618,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( kn3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( not @ ( and @ E @ G ) ) @ ( not @ ( and @ G @ C ) ) ) ) @ H ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( not @ ( and @ E @ G ) ) @ ( not @ ( and @ G @ C ) ) ) ) @ H ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( kn3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(14,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 @ ( equiv @ A @ C ) @ ( equiv @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_substitution_1) ).
thf(166,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( equiv @ B @ F ) @ ( equiv @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ or_1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ or_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1_0) ).
thf(176,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( or_1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( or @ C @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( or @ C @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( or_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ or_3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ) ) ) ) ) ) )
@ ( mbox @ or_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3_0) ).
thf(286,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( or_3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ G ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ! [G: $i] :
( ( eiw_di @ G @ F )
=> ! [H: mworld] :
( ( mrel @ F @ H )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ G ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ G ) ) ) @ H ) ) ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( or_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(20,axiom,
mlocal @ ( mbox @ equivalence_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
thf(204,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( equivalence_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(61,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 @ ( or @ A @ C ) @ ( or @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_substitution_1) ).
thf(572,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( or @ B @ F ) @ ( or @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(33,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ r1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ) ) )
@ ( mbox @ r1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1_0) ).
thf(350,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( is_a_theorem @ ( implies @ ( or @ C @ C ) @ C ) @ D ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( is_a_theorem @ ( implies @ ( or @ C @ C ) @ C ) @ D ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ equivalence_3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ) ) ) ) )
@ ( mbox @ equivalence_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3_0) ).
thf(86,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( equivalence_3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ C ) @ ( equiv @ C @ E ) ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ C ) @ ( equiv @ C @ E ) ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( equivalence_3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
mlocal @ ( mbox @ modus_tollens ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
thf(172,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( modus_tollens @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(68,axiom,
mlocal @ ( mbox @ and_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
thf(616,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( and_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(72,plain,
mrel @ mactual @ sk1,
inference(cnfConj,[status(thm)],[71]) ).
thf(1374,plain,
! [A: mworld] :
( ~ $true
| ( implies_3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[72,165]) ).
thf(1375,plain,
! [A: mworld] :
( ( implies_3 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[1374]) ).
thf(1376,plain,
implies_3 @ sk1,
inference(pattern_uni,[status(thm)],[1375:[bind(A,$thf( sk1 ))]]) ).
thf(34,axiom,
mlocal @ ( mbox @ op_or ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(362,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_or @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(64,axiom,
mlocal @ ( mbox @ modus_ponens ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
thf(594,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( modus_ponens @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(520,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [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)],[56]) ).
thf(31,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 @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_substitution_2) ).
thf(330,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( implies @ F @ B ) @ ( implies @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(10,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ r3 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ) ) ) ) )
@ ( mbox @ r3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_0) ).
thf(130,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r3 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( or @ C @ E ) @ ( or @ E @ C ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( or @ C @ E ) @ ( or @ E @ C ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( r3 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(925,plain,
! [A: mworld] :
( ~ $true
| ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[72,560]) ).
thf(926,plain,
! [A: mworld] :
( ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A )
| ( ( mrel @ mactual @ sk1 )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
( ( mrel @ sk1 @ ( sk160 @ sk1 ) )
| ( sk159 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( sk1 ))]]) ).
thf(989,plain,
! [A: mworld] :
( ( sk159 @ sk1 )
| ~ $true
| ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A )
| ( ( mrel @ sk1 @ ( sk160 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(paramod_ordered,[status(thm)],[927,560]) ).
thf(990,plain,
! [A: mworld] :
( ( sk159 @ sk1 )
| ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A )
| ( ( mrel @ sk1 @ ( sk160 @ sk1 ) )
!= ( mrel @ mactual @ A ) ) ),
inference(simp,[status(thm)],[989]) ).
thf(1006,plain,
! [A: mworld] :
( ( sk159 @ sk1 )
| ( mrel @ A @ ( sk160 @ A ) )
| ( sk159 @ A )
| ( sk1 != mactual )
| ( ( sk160 @ sk1 )
!= A ) ),
inference(simp,[status(thm)],[990]) ).
thf(1015,plain,
( ( sk159 @ sk1 )
| ( mrel @ ( sk160 @ sk1 ) @ ( sk160 @ ( sk160 @ sk1 ) ) )
| ( sk159 @ ( sk160 @ sk1 ) )
| ( sk1 != mactual ) ),
inference(simp,[status(thm)],[1006]) ).
thf(66,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_substitution_1) ).
thf(608,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ( ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ B @ D @ F ) )
=> ! [F: mworld] :
( ( mrel @ E @ F )
=> ( qmltpeq @ ( not @ B ) @ ( not @ D ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(43,axiom,
mlocal @ ( mbox @ or_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
thf(394,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( or_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(28,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ modus_tollens )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ modus_tollens ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens_0) ).
thf(306,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( modus_tollens @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( implies @ ( not @ E ) @ ( not @ C ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( implies @ ( not @ E ) @ ( not @ C ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( modus_tollens @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(40,axiom,
mlocal @ ( mbox @ op_equiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(374,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_equiv @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(38,axiom,
mlocal @ ( mbox @ and_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(370,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( and_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(54,axiom,
mlocal @ ( mbox @ op_implies_and ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(502,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_implies_and @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(62,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ and_2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ) ) ) ) )
@ ( mbox @ and_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2_0) ).
thf(576,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( and_2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ E ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ E ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( and_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(67,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 @ ( equiv @ C @ A ) @ ( equiv @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_substitution_2) ).
thf(612,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( equiv @ F @ B ) @ ( equiv @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(52,axiom,
( mlocal
@ ( mbox
@ ( mimplies @ ( mbox @ op_implies_or )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( implies @ A @ B ) @ ( or @ ( not @ A ) @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or_0) ).
thf(482,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( op_implies_or @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( qmltpeq @ ( implies @ C @ E ) @ ( or @ ( not @ C ) @ E ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(37,axiom,
mlocal @ ( mbox @ and_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(368,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( and_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(75,plain,
! [A: mworld] : ( eiw_di @ ( sk2 @ A ) @ A ),
inference(cnf,[status(esa)],[74]) ).
thf(5,axiom,
( mlocal
@ ( mbox
@ ( mimplies @ ( mbox @ op_implies_and )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( implies @ A @ B ) @ ( not @ ( and @ A @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and_0) ).
thf(82,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( op_implies_and @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( qmltpeq @ ( implies @ C @ E ) @ ( not @ ( and @ C @ ( not @ E ) ) ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,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 @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_substitution_2) ).
thf(432,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( or @ F @ B ) @ ( or @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(11,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ kn2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) )
@ ( mbox @ kn2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2_0) ).
thf(146,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( kn2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( kn2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,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 @ ( and @ C @ A ) @ ( and @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_substitution_2) ).
thf(326,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( and @ F @ B ) @ ( and @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,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 @ ( and @ A @ C ) @ ( and @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_substitution_1) ).
thf(126,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( and @ B @ F ) @ ( and @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ or_2 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) )
@ ( mbox @ or_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2_0) ).
thf(400,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( or_2 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( or_2 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(65,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ kn1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ) ) )
@ ( mbox @ kn1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1_0) ).
thf(596,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( kn1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( is_a_theorem @ ( implies @ C @ ( and @ C @ C ) ) @ D ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( is_a_theorem @ ( implies @ C @ ( and @ C @ C ) ) @ D ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( kn1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(58,axiom,
mlocal @ ( mbox @ or_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(528,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( or_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(29,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 @ ( implies @ A @ C ) @ ( implies @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_substitution_1) ).
thf(322,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ! [B: $i] :
( ( eiw_di @ B @ A )
=> ! [C: mworld] :
( ( mrel @ A @ C )
=> ! [D: $i] :
( ( eiw_di @ D @ C )
=> ! [E: mworld] :
( ( mrel @ C @ E )
=> ! [F: $i] :
( ( eiw_di @ F @ E )
=> ! [G: mworld] :
( ( mrel @ E @ G )
=> ( ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ B @ D @ H ) )
=> ! [H: mworld] :
( ( mrel @ G @ H )
=> ( qmltpeq @ ( implies @ B @ F ) @ ( implies @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies @ ( mbox @ implies_1 )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ) ) ) ) )
@ ( mbox @ implies_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1_0) ).
thf(486,plain,
( ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( implies_1 @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( implies @ E @ C ) ) @ F ) ) ) ) ) ) ) )
& ! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( is_a_theorem @ ( implies @ C @ ( implies @ E @ C ) ) @ F ) ) ) ) ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ( implies_1 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(8,axiom,
( mlocal
@ ( mbox
@ ( mimplies @ ( mbox @ op_or )
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( or @ A @ B ) @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or_0) ).
thf(122,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( ! [B: mworld] :
( ( mrel @ A @ B )
=> ( op_or @ B ) )
=> ! [B: mworld] :
( ( mrel @ A @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ! [E: $i] :
( ( eiw_di @ E @ D )
=> ! [F: mworld] :
( ( mrel @ D @ F )
=> ( qmltpeq @ ( or @ C @ E ) @ ( not @ ( and @ ( not @ C ) @ ( not @ E ) ) ) @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
mlocal @ ( mbox @ equivalence_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(222,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( equivalence_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
mlocal @ ( mbox @ op_implies_or ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(592,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_implies_or @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(35,axiom,
mlocal @ ( mbox @ or_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(364,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( or_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12841,plain,
$false,
inference(e,[status(thm)],[930,224,526,282,170,440,174,436,372,504,460,1379,416,78,164,376,480,396,74,206,546,366,102,334,260,392,70,192,165,73,244,2203,530,618,166,176,694,286,204,572,350,86,172,616,1376,362,76,594,520,330,130,1015,608,394,306,162,927,374,370,502,576,72,612,482,368,75,549,82,432,146,326,126,400,596,528,163,871,322,486,122,560,222,592,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL944^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n017.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 10:41:52 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.08/1.14 % [INFO] Parsing done (353ms).
% 2.08/1.16 % [INFO] Running in sequential loop mode.
% 2.73/1.54 % [INFO] eprover registered as external prover.
% 2.73/1.55 % [INFO] Scanning for conjecture ...
% 3.18/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 3.45/1.83 % [INFO] Axiom selection finished. Selected 67 axioms (removed 0 axioms).
% 3.78/1.95 % [INFO] Problem is higher-order (TPTP THF).
% 3.78/1.96 % [INFO] Type checking passed.
% 3.78/1.97 % [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 ...
% 148.21/78.89 % External prover 'e' found a proof!
% 148.21/78.89 % [INFO] Killing All external provers ...
% 148.21/78.89 % Time passed: 78539ms (effective reasoning time: 77732ms)
% 148.21/78.89 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 148.35/78.90 % Axioms used in derivation (67): implies_2_0, equiv_substitution_1, principia_op_and, equivalence_2_0, kn1_0, implies_3_0, op_and_0, substitution_of_equivalents_1, r3_0, equiv_substitution_2, or_substitution_2, implies_substitution_2, r4_0, op_equiv_0, op_implies_or_0, hilbert_implies_1, hilbert_and_3, hilbert_op_implies_and, op_implies_and_0, substitution_of_equivalents_0, mrel_reflexive, and_substitution_2, or_1_0, cn3_0, and_3_0, cn2_0, modus_ponens_0, hilbert_or_1, kn2_0, principia_op_equiv, reflexivity, modus_tollens_0, hilbert_or_2, hilbert_implies_2, equivalence_3_0, or_2_0, hilbert_and_2, not_substitution_1, hilbert_modus_tollens, hilbert_op_or, implies_1_0, hilbert_equivalence_2, hilbert_equivalence_3, cn1_0, eiw_di_nonempty, hilbert_modus_ponens, hilbert_implies_3, is_a_theorem_substitution_1, and_substitution_1, hilbert_and_1, and_2_0, op_or_0, hilbert_equivalence_1, hilbert_or_3, and_1_0, transitivity, r1_0, r2_0, or_substitution_1, r5_0, implies_substitution_1, kn3_0, equivalence_1_0, hilbert_op_equiv, or_3_0, symmetry, principia_op_implies_or
% 148.35/78.90 % No. of inferences in proof: 177
% 148.35/78.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 78539 ms resp. 77732 ms w/o parsing
% 149.24/79.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 149.24/79.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------