TSTP Solution File: LCL475+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL475+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Fri May 19 11:30:31 EDT 2023
% Result : Theorem 122.24s 30.21s
% Output : Refutation 122.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 100
% Syntax : Number of formulae : 231 ( 47 unt; 60 typ; 0 def)
% Number of atoms : 390 ( 86 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2113 ( 109 ~; 91 |; 28 &;1797 @)
% ( 25 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 56 con; 0-2 aty)
% Number of variables : 336 ( 0 ^; 336 !; 0 ?; 336 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_type,type,
r1: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(op_and_type,type,
op_and: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(equiv_type,type,
equiv: $i > $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(cn1_type,type,
cn1: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(cn3_type,type,
cn3: $o ).
thf(cn2_type,type,
cn2: $o ).
thf(modus_tollens_type,type,
modus_tollens: $o ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(kn2_type,type,
kn2: $o ).
thf(or_3_type,type,
or_3: $o ).
thf(and_3_type,type,
and_3: $o ).
thf(r2_type,type,
r2: $o ).
thf(kn1_type,type,
kn1: $o ).
thf(implies_3_type,type,
implies_3: $o ).
thf(equivalence_2_type,type,
equivalence_2: $o ).
thf(and_1_type,type,
and_1: $o ).
thf(implies_2_type,type,
implies_2: $o ).
thf(r3_type,type,
r3: $o ).
thf(equivalence_3_type,type,
equivalence_3: $o ).
thf(equivalence_1_type,type,
equivalence_1: $o ).
thf(implies_1_type,type,
implies_1: $o ).
thf(and_2_type,type,
and_2: $o ).
thf(or_2_type,type,
or_2: $o ).
thf(kn3_type,type,
kn3: $o ).
thf(or_1_type,type,
or_1: $o ).
thf(r4_type,type,
r4: $o ).
thf(r5_type,type,
r5: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk17_type,type,
sk17: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk22_type,type,
sk22: $i ).
thf(sk23_type,type,
sk23: $i ).
thf(sk31_type,type,
sk31: $i ).
thf(sk32_type,type,
sk32: $i ).
thf(sk36_type,type,
sk36: $i ).
thf(sk37_type,type,
sk37: $i ).
thf(sk40_type,type,
sk40: $i ).
thf(sk41_type,type,
sk41: $i ).
thf(sk45_type,type,
sk45: $i ).
thf(sk46_type,type,
sk46: $i ).
thf(sk53_type,type,
sk53: $i ).
thf(12,axiom,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
thf(56,plain,
cn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_modus_ponens) ).
thf(52,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
( and_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
thf(70,plain,
( ( and_3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) )
=> and_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(76,plain,
( ( kn1
=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) )
=> kn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,plain,
( ~ ( is_a_theorem @ ( implies @ sk12 @ ( and @ sk12 @ sk12 ) ) )
| kn1 ),
inference(cnf,[status(esa)],[76]) ).
thf(37,axiom,
( or_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
thf(129,plain,
( ( or_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) )
=> or_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(3,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
thf(43,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(99,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
( cn1
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
thf(114,plain,
( ( cn1
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
=> cn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(40,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(138,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24,axiom,
( implies_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
thf(88,plain,
( ( implies_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) )
=> implies_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(73,plain,
( ( r2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> r2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(74,plain,
( ~ ( is_a_theorem @ ( implies @ sk11 @ ( or @ sk10 @ sk11 ) ) )
| r2 ),
inference(cnf,[status(esa)],[73]) ).
thf(11,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(53,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_or ),
inference(lifteq,[status(thm)],[54]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[55,43]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
( ~ ( is_a_theorem @ ( implies @ sk11 @ ( not @ ( and @ ( not @ sk10 ) @ ( not @ sk11 ) ) ) ) )
| r2 ),
inference(rewrite,[status(thm)],[74,169]) ).
thf(34,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(120,plain,
( ( cn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) )
=> cn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
thf(47,plain,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ op_equiv ),
inference(lifteq,[status(thm)],[48]) ).
thf(5,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_equiv) ).
thf(45,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ $true ),
inference(rewrite,[status(thm)],[49,45]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) ),
inference(simp,[status(thm)],[148]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ sk12 @ ( equiv @ A @ B ) ) )
| kn1
| ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
!= ( and @ sk12 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[149,77]) ).
thf(174,plain,
! [B: $i,A: $i] :
( kn1
| ~ ( is_a_theorem @ ( implies @ sk12 @ ( equiv @ A @ B ) ) )
| ( ( implies @ A @ B )
!= sk12 )
| ( ( implies @ B @ A )
!= sk12 ) ),
inference(simp,[status(thm)],[173]) ).
thf(130,plain,
( ~ ( is_a_theorem @ ( implies @ sk45 @ ( or @ sk45 @ sk46 ) ) )
| or_1 ),
inference(cnf,[status(esa)],[129]) ).
thf(185,plain,
( ~ ( is_a_theorem @ ( implies @ sk45 @ ( not @ ( and @ ( not @ sk45 ) @ ( not @ sk46 ) ) ) ) )
| or_1 ),
inference(rewrite,[status(thm)],[130,169]) ).
thf(1,conjecture,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
thf(2,negated_conjecture,
~ r1,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ r1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
thf(58,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ op_and
| ( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_and ),
inference(lifteq,[status(thm)],[59]) ).
thf(4,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
thf(44,plain,
op_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( ( and @ A @ B )
= ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[60,169,44]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(46,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
thf(57,plain,
cn2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
( modus_tollens
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
thf(61,plain,
( ( modus_tollens
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
=> modus_tollens ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
( r4
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(132,plain,
( ( r4
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
=> r4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( and @ ( not @ ( and @ A @ B ) ) @ ( not @ ( not @ D ) ) ) ) )
= ( and @ C @ D ) )
| ( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) )
!= ( not @ C ) ) ),
inference(paramod_ordered,[status(thm)],[189,189]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( not @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) @ A )
= ( not @ ( not @ ( and @ ( not @ ( and @ B @ C ) ) @ ( not @ ( not @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( not @ ( and @ ( not @ ( not @ I ) ) @ ( not @ ( not @ K ) ) ) )),bind(D,$thf( D ))]]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( not @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) @ A )
= ( not @ ( not @ ( and @ ( not @ ( and @ B @ C ) ) @ ( not @ ( not @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(16,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(64,plain,
( ( kn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> kn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ kn2
| ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(41,axiom,
( r1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(141,plain,
( ( r1
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) )
=> r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(142,plain,
( ~ ( is_a_theorem @ ( implies @ ( or @ sk53 @ sk53 ) @ sk53 ) )
| r1 ),
inference(cnf,[status(esa)],[141]) ).
thf(493,plain,
( ~ ( is_a_theorem @ ( implies @ ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) @ sk53 ) )
| $false ),
inference(rewrite,[status(thm)],[142,169,42]) ).
thf(494,plain,
~ ( is_a_theorem @ ( implies @ ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) @ sk53 ) ),
inference(simp,[status(thm)],[493]) ).
thf(3409,plain,
! [B: $i,A: $i] :
( ~ kn2
| ( ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
!= ( is_a_theorem @ ( implies @ ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) @ sk53 ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,494]) ).
thf(3435,plain,
! [B: $i,A: $i] :
( ~ kn2
| ( ( implies @ ( and @ A @ B ) @ A )
!= ( implies @ ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) @ sk53 ) ) ),
inference(simp,[status(thm)],[3409]) ).
thf(4465,plain,
! [B: $i,A: $i] :
( ~ kn2
| ( ( and @ A @ B )
!= ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) )
| ( A != sk53 ) ),
inference(simp,[status(thm)],[3435]) ).
thf(4604,plain,
! [A: $i] :
( ~ kn2
| ( ( and @ sk53 @ A )
!= ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) ) ),
inference(simp,[status(thm)],[4465]) ).
thf(33,axiom,
( and_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
thf(117,plain,
( ( and_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) )
=> and_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(23,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
thf(85,plain,
( ( and_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> and_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) ) )
= ( and @ C @ D ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ ( not @ C ) ) @ ( not @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,189]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( not @ ( not @ F ) )),bind(B,$thf( not @ ( not @ H ) )),bind(C,$thf( F )),bind(D,$thf( H ))]]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(simp,[status(thm)],[207]) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) )
= ( and @ C @ D ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ ( not @ C ) ) @ ( not @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,189]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( not @ ( not @ F ) )),bind(B,$thf( not @ ( not @ H ) )),bind(C,$thf( F )),bind(D,$thf( H ))]]) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(simp,[status(thm)],[297]) ).
thf(28,axiom,
( equivalence_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
thf(102,plain,
( ( equivalence_3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) )
=> equivalence_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) )
= ( and @ C @ D ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ ( not @ ( not @ ( not @ C ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,240]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( not @ ( not @ ( not @ ( not @ H ) ) ) )),bind(B,$thf( not @ ( not @ ( not @ ( not @ L ) ) ) )),bind(C,$thf( H )),bind(D,$thf( L ))]]) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(simp,[status(thm)],[278]) ).
thf(65,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk3 @ sk4 ) @ sk3 ) )
| kn2 ),
inference(cnf,[status(esa)],[64]) ).
thf(26,axiom,
( modus_ponens
<=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
thf(94,plain,
( ( modus_ponens
=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) )
& ( ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) )
=> modus_ponens ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ modus_ponens
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ( is_a_theorem @ B ) ),
inference(cnf,[status(esa)],[94]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ modus_ponens
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[98]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ modus_ponens
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ $true
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(rewrite,[status(thm)],[145,52]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(498,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) ) @ sk53 ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,494]) ).
thf(499,plain,
~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ sk53 ) ) ) @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) @ sk53 ) ),
inference(pattern_uni,[status(thm)],[498:[bind(A,$thf( not @ sk53 )),bind(B,$thf( not @ sk53 ))]]) ).
thf(507,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) @ sk53 ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,494]) ).
thf(508,plain,
~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) ) ) ) ) @ sk53 ) ),
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( not @ sk53 )),bind(B,$thf( not @ sk53 ))]]) ).
thf(29,axiom,
( cn3
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(105,plain,
( ( cn3
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) )
=> cn3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( and @ ( and @ A @ B ) @ ( not @ ( not @ D ) ) ) ) )
= ( and @ C @ D ) )
| ( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) )
!= ( not @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,189]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) @ A )
= ( not @ ( not @ ( and @ ( and @ B @ C ) @ ( not @ ( not @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( and @ ( not @ ( not @ H ) ) @ ( not @ ( not @ J ) ) )),bind(D,$thf( D ))]]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) @ A )
= ( not @ ( not @ ( and @ ( and @ B @ C ) @ ( not @ ( not @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(86,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk18 @ sk19 ) @ sk18 ) )
| and_1 ),
inference(cnf,[status(esa)],[85]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk18 ) )
| and_1
| ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
!= ( and @ sk18 @ sk19 ) ) ),
inference(paramod_ordered,[status(thm)],[149,86]) ).
thf(176,plain,
! [B: $i,A: $i] :
( and_1
| ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk18 ) )
| ( ( implies @ A @ B )
!= sk18 )
| ( ( implies @ B @ A )
!= sk19 ) ),
inference(simp,[status(thm)],[175]) ).
thf(118,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk36 @ sk37 ) @ sk37 ) )
| and_2 ),
inference(cnf,[status(esa)],[117]) ).
thf(71,plain,
( ~ ( is_a_theorem @ ( implies @ sk8 @ ( implies @ sk9 @ ( and @ sk8 @ sk9 ) ) ) )
| and_3 ),
inference(cnf,[status(esa)],[70]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk37 ) )
| and_2
| ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
!= ( and @ sk36 @ sk37 ) ) ),
inference(paramod_ordered,[status(thm)],[149,118]) ).
thf(181,plain,
! [B: $i,A: $i] :
( and_2
| ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk37 ) )
| ( ( implies @ A @ B )
!= sk36 )
| ( ( implies @ B @ A )
!= sk37 ) ),
inference(simp,[status(thm)],[180]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) )
= ( equiv @ C @ D ) )
| ( ( and @ A @ B )
!= ( and @ ( implies @ C @ D ) @ ( implies @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,149]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ ( implies @ B @ A ) ) ) @ ( not @ ( not @ ( implies @ A @ B ) ) ) ) ) )
= ( equiv @ B @ A ) ),
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( implies @ H @ G )),bind(B,$thf( implies @ G @ H )),bind(C,$thf( H )),bind(D,$thf( G ))]]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ ( implies @ B @ A ) ) ) @ ( not @ ( not @ ( implies @ A @ B ) ) ) ) ) )
= ( equiv @ B @ A ) ),
inference(simp,[status(thm)],[218]) ).
thf(25,axiom,
( r3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
thf(91,plain,
( ( r3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
=> r3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,axiom,
( equivalence_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
thf(108,plain,
( ( equivalence_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) )
=> equivalence_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
( r5
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(135,plain,
( ( r5
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) )
=> r5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( and @ ( not @ ( not @ C ) ) @ ( and @ A @ B ) ) ) )
= ( and @ C @ D ) )
| ( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) )
!= ( not @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,189]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( and @ B @ C ) ) ) )
= ( and @ A @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( and @ ( not @ ( not @ H ) ) @ ( not @ ( not @ J ) ) ))]]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( and @ B @ C ) ) ) )
= ( and @ A @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk3 ) )
| kn2
| ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
!= ( and @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[149,65]) ).
thf(167,plain,
! [B: $i,A: $i] :
( kn2
| ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk3 ) )
| ( ( implies @ A @ B )
!= sk3 )
| ( ( implies @ B @ A )
!= sk4 ) ),
inference(simp,[status(thm)],[166]) ).
thf(31,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
thf(111,plain,
( ( implies_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
=> implies_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(112,plain,
( ~ ( is_a_theorem @ ( implies @ sk31 @ ( implies @ sk32 @ sk31 ) ) )
| implies_1 ),
inference(cnf,[status(esa)],[111]) ).
thf(35,axiom,
( or_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
thf(123,plain,
( ( or_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> or_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ modus_tollens
| ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) )
= ( not @ ( not @ ( and @ ( not @ ( not @ C ) ) @ ( not @ ( not @ D ) ) ) ) ) )
| ( ( and @ A @ B )
!= ( and @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[240,189]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) )
= ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1725,plain,
! [B: $i,A: $i] :
( ~ modus_tollens
| ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
!= ( is_a_theorem @ ( implies @ ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) @ sk53 ) ) ) ),
inference(paramod_ordered,[status(thm)],[63,494]) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ~ modus_tollens
| ( ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) )
!= ( implies @ ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) @ sk53 ) ) ),
inference(simp,[status(thm)],[1725]) ).
thf(8,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
thf(50,plain,
cn1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
( or_3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_3) ).
thf(67,plain,
( ( or_3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) )
=> or_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(124,plain,
( ~ ( is_a_theorem @ ( implies @ sk41 @ ( or @ sk40 @ sk41 ) ) )
| or_2 ),
inference(cnf,[status(esa)],[123]) ).
thf(182,plain,
( ~ ( is_a_theorem @ ( implies @ sk41 @ ( not @ ( and @ ( not @ sk40 ) @ ( not @ sk41 ) ) ) ) )
| or_2 ),
inference(rewrite,[status(thm)],[124,169]) ).
thf(642,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ sk53 ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,508]) ).
thf(643,plain,
~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ sk53 ) ),
inference(pattern_uni,[status(thm)],[642:[bind(A,$thf( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) )),bind(B,$thf( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ))]]) ).
thf(2462,plain,
! [B: $i,A: $i] :
( ~ modus_tollens
| ( ( implies @ ( not @ B ) @ ( not @ A ) )
!= ( not @ ( and @ ( not @ sk53 ) @ ( not @ sk53 ) ) ) )
| ( ( implies @ A @ B )
!= sk53 ) ),
inference(simp,[status(thm)],[1753]) ).
thf(22,axiom,
( equivalence_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
thf(82,plain,
( ( equivalence_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) )
=> equivalence_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ( is_a_theorem @ B ) ),
inference(rewrite,[status(thm)],[98,52]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ( is_a_theorem @ B ) ),
inference(simp,[status(thm)],[150]) ).
thf(9,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(51,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(92,plain,
( ~ ( is_a_theorem @ ( implies @ ( or @ sk22 @ sk23 ) @ ( or @ sk23 @ sk22 ) ) )
| r3 ),
inference(cnf,[status(esa)],[91]) ).
thf(3264,plain,
( ~ ( is_a_theorem @ ( implies @ ( not @ ( and @ ( not @ sk22 ) @ ( not @ sk23 ) ) ) @ ( not @ ( and @ ( not @ sk23 ) @ ( not @ sk22 ) ) ) ) )
| r3 ),
inference(rewrite,[status(thm)],[92,169]) ).
thf(563,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ) @ sk53 ) )
| ( ( and @ A @ B )
!= ( and @ ( not @ ( not @ ( not @ sk53 ) ) ) @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,499]) ).
thf(564,plain,
~ ( is_a_theorem @ ( implies @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ ( not @ sk53 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ sk53 ) ),
inference(pattern_uni,[status(thm)],[563:[bind(A,$thf( not @ ( not @ ( not @ sk53 ) ) )),bind(B,$thf( not @ ( not @ ( not @ sk53 ) ) ))]]) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( not @ ( not @ ( and @ ( not @ ( not @ C ) ) @ ( not @ ( and @ A @ B ) ) ) ) )
= ( and @ C @ D ) )
| ( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) )
!= ( not @ D ) ) ),
inference(paramod_ordered,[status(thm)],[189,189]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( and @ B @ C ) ) ) ) )
= ( and @ A @ ( not @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( C )),bind(D,$thf( not @ ( and @ ( not @ ( not @ I ) ) @ ( not @ ( not @ K ) ) ) ))]]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( and @ B @ C ) ) ) ) )
= ( and @ A @ ( not @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(36,axiom,
( kn3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
thf(126,plain,
( ( kn3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) )
=> kn3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
( implies_3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
thf(79,plain,
( ( implies_3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
=> implies_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(62,plain,
( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sk2 ) @ ( not @ sk1 ) ) @ ( implies @ sk1 @ sk2 ) ) )
| modus_tollens ),
inference(cnf,[status(esa)],[61]) ).
thf(83,plain,
( ~ ( is_a_theorem @ ( implies @ ( equiv @ sk16 @ sk17 ) @ ( implies @ sk17 @ sk16 ) ) )
| equivalence_2 ),
inference(cnf,[status(esa)],[82]) ).
thf(7599,plain,
$false,
inference(e,[status(thm)],[56,52,70,77,129,43,99,114,138,88,170,120,174,185,42,189,46,57,61,132,243,3435,4604,117,85,366,102,361,65,156,53,169,141,499,73,508,105,244,45,64,149,176,44,118,71,181,86,76,245,494,91,66,240,108,135,241,167,112,123,63,295,1753,50,67,182,643,58,2462,82,151,51,3264,564,242,126,79,94,47,62,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL475+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n026.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu May 18 16:28:36 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/1.03 % [INFO] Parsing done (156ms).
% 1.11/1.04 % [INFO] Running in sequential loop mode.
% 1.76/1.27 % [INFO] eprover registered as external prover.
% 1.76/1.27 % [INFO] cvc4 registered as external prover.
% 1.76/1.27 % [INFO] Scanning for conjecture ...
% 1.96/1.33 % [INFO] Found a conjecture and 42 axioms. Running axiom selection ...
% 2.10/1.38 % [INFO] Axiom selection finished. Selected 39 axioms (removed 3 axioms).
% 2.10/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.44 % [INFO] Type checking passed.
% 2.10/1.44 % [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 ...
% 122.24/30.20 % External prover 'e' found a proof!
% 122.24/30.20 % [INFO] Killing All external provers ...
% 122.24/30.21 % Time passed: 29681ms (effective reasoning time: 29160ms)
% 122.24/30.21 % 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)>
% 122.24/30.21 % Axioms used in derivation (39): or_3, and_1, luka_op_or, cn1, op_equiv, cn2, kn1, r1, implies_3, op_implies_and, cn3, luka_cn3, principia_op_and, equivalence_2, luka_cn2, kn2, equivalence_3, modus_tollens, luka_cn1, op_and, luka_modus_ponens, r5, kn3, luka_op_equiv, and_3, or_1, principia_op_equiv, r4, modus_ponens, r2, equivalence_1, or_2, implies_1, r3, and_2, op_or, op_implies_or, implies_2, principia_op_implies_or
% 122.24/30.21 % No. of inferences in proof: 171
% 122.24/30.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29681 ms resp. 29160 ms w/o parsing
% 122.34/30.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 122.34/30.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------