TSTP Solution File: LCL944^8 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LCL944^8 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:08:45 EDT 2024
% Result : Theorem 65.77s 15.19s
% Output : Refutation 65.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 120
% Syntax : Number of formulae : 190 ( 10 unt; 47 typ; 5 def)
% Number of atoms : 1627 ( 5 equ; 0 cnn)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 3806 ( 2 ~; 0 |; 31 &;3147 @)
% ( 0 <=>; 626 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 13 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 2 con; 0-3 aty)
% Number of variables : 723 ( 165 ^ 556 !; 2 ?; 723 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_type,type,
mrel: mworld > mworld > $o ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mand_type,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_type,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(eiw_di_type,type,
eiw_di: $i > mworld > $o ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(r2_type,type,
r2: mworld > $o ).
thf(r3_type,type,
r3: mworld > $o ).
thf(r4_type,type,
r4: mworld > $o ).
thf(r5_type,type,
r5: mworld > $o ).
thf(equivalence_1_type,type,
equivalence_1: mworld > $o ).
thf(equivalence_2_type,type,
equivalence_2: mworld > $o ).
thf(cn2_type,type,
cn2: mworld > $o ).
thf(cn1_type,type,
cn1: mworld > $o ).
thf(cn3_type,type,
cn3: mworld > $o ).
thf(kn2_type,type,
kn2: mworld > $o ).
thf(kn1_type,type,
kn1: mworld > $o ).
thf(kn3_type,type,
kn3: mworld > $o ).
thf(equivalence_3_type,type,
equivalence_3: mworld > $o ).
thf(op_implies_or_type,type,
op_implies_or: mworld > $o ).
thf(op_and_type,type,
op_and: mworld > $o ).
thf(and_2_type,type,
and_2: mworld > $o ).
thf(and_3_type,type,
and_3: mworld > $o ).
thf(and_1_type,type,
and_1: mworld > $o ).
thf(implies_2_type,type,
implies_2: mworld > $o ).
thf(implies_3_type,type,
implies_3: mworld > $o ).
thf(op_implies_and_type,type,
op_implies_and: mworld > $o ).
thf(implies_1_type,type,
implies_1: mworld > $o ).
thf(substitution_of_equivalents_type,type,
substitution_of_equivalents: mworld > $o ).
thf(op_or_type,type,
op_or: mworld > $o ).
thf(modus_tollens_type,type,
modus_tollens: mworld > $o ).
thf(or_1_type,type,
or_1: mworld > $o ).
thf(or_2_type,type,
or_2: mworld > $o ).
thf(or_3_type,type,
or_3: mworld > $o ).
thf(op_equiv_type,type,
op_equiv: mworld > $o ).
thf(modus_ponens_type,type,
modus_ponens: mworld > $o ).
thf(r1_type,type,
r1: mworld > $o ).
thf(qmltpeq_type,type,
qmltpeq: $i > $i > mworld > $o ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > mworld > $o ).
thf(equiv_type,type,
equiv: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(51,axiom,
mlocal @ ( mbox @ implies_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
thf(448,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(371,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(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(327,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(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(410,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(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(138,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(54,axiom,
mlocal @ ( mbox @ op_implies_and ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(468,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_implies_and @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
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(352,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(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(120,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(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(269,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(35,axiom,
mlocal @ ( mbox @ or_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(340,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( or_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(153,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(404,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(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(288,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(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(389,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(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(570,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(37,axiom,
mlocal @ ( mbox @ and_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(344,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( and_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
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(157,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(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(211,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(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(485,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(39,axiom,
mlocal @ ( mbox @ op_and ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
thf(348,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_and @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(58,axiom,
mlocal @ ( mbox @ or_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(492,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( or_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(17,axiom,
mlocal @ ( mbox @ substitution_of_equivalents ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents_1) ).
thf(164,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( substitution_of_equivalents @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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(453,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(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(312,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(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(117,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(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(534,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(15,axiom,
mlocal @ ( mbox @ op_equiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(160,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_equiv @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
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(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(429,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(20,axiom,
mlocal @ ( mbox @ equivalence_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
thf(192,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( equivalence_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
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(407,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(64,axiom,
mlocal @ ( mbox @ modus_ponens ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
thf(554,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( modus_ponens @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
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(537,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(3,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(73,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(266,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(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(166,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(68,axiom,
mlocal @ ( mbox @ and_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
thf(573,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( and_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
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(181,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(40,axiom,
mlocal @ ( mbox @ op_equiv ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(350,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_equiv @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
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(230,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(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(567,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(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(245,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(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(509,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(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(98,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(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(303,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(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(494,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(13,axiom,
mlocal @ ( mbox @ implies_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
thf(155,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( implies_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(367,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(63,axiom,
mlocal @ ( mbox @ op_implies_or ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(552,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_implies_or @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
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(306,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(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(80,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(57,axiom,
mlocal @ ( mbox @ equivalence_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
thf(490,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( equivalence_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(16,axiom,
mlocal @ ( mbox @ modus_tollens ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
thf(162,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( modus_tollens @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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(374,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(22,axiom,
mlocal @ ( mbox @ equivalence_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(209,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( equivalence_2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
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(194,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(342,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( implies_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
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(123,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(34,axiom,
mlocal @ ( mbox @ op_or ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(338,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( op_or @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
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(470,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(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(450,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(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(556,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(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(75,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(38,axiom,
mlocal @ ( mbox @ and_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(346,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( and_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
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(575,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(43,axiom,
mlocal @ ( mbox @ or_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
thf(369,plain,
! [A: mworld] :
( ( mrel @ mactual @ A )
=> ( or_3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
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(83,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(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(309,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(4491,plain,
$false,
inference(e,[status(thm)],[448,371,327,410,138,468,352,120,269,340,153,404,288,389,570,344,157,211,485,348,492,164,453,312,117,534,160,70,429,192,407,554,537,73,266,166,573,181,350,230,567,245,509,98,303,494,155,367,552,306,80,490,162,374,209,194,342,123,338,470,450,556,75,346,575,369,83,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL944^8 : TPTP v8.2.0. Released v8.1.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 03:30:23 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.81/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.00 % [INFO] Parsing done (198ms).
% 1.42/1.01 % [INFO] Running in sequential loop mode.
% 2.12/1.26 % [INFO] eprover registered as external prover.
% 2.12/1.26 % [INFO] cvc4 registered as external prover.
% 2.12/1.26 % [INFO] Scanning for conjecture ...
% 2.46/1.38 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 2.77/1.46 % [INFO] Axiom selection finished. Selected 67 axioms (removed 0 axioms).
% 3.16/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 3.16/1.58 % [INFO] Type checking passed.
% 3.16/1.58 % [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 ...
% 65.77/15.18 % External prover 'e' found a proof!
% 65.77/15.18 % [INFO] Killing All external provers ...
% 65.77/15.18 % Time passed: 14740ms (effective reasoning time: 14172ms)
% 65.77/15.18 % 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)>
% 65.77/15.19 % 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
% 65.77/15.19 % No. of inferences in proof: 138
% 65.77/15.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14740 ms resp. 14172 ms w/o parsing
% 65.94/15.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 65.94/15.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------