TSTP Solution File: LCL498+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:30:34 EDT 2023
% Result : Theorem 20.17s 4.34s
% Output : Refutation 20.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 93
% Syntax : Number of formulae : 188 ( 38 unt; 51 typ; 0 def)
% Number of atoms : 325 ( 57 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1410 ( 66 ~; 64 |; 28 &;1164 @)
% ( 25 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 47 con; 0-2 aty)
% Number of variables : 275 ( 0 ^; 275 !; 0 ?; 275 :)
% Comments :
%------------------------------------------------------------------------------
thf(cn3_type,type,
cn3: $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(r3_type,type,
r3: $o ).
thf(r4_type,type,
r4: $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(r1_type,type,
r1: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(r2_type,type,
r2: $o ).
thf(r5_type,type,
r5: $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(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(equivalence_3_type,type,
equivalence_3: $o ).
thf(equivalence_1_type,type,
equivalence_1: $o ).
thf(implies_1_type,type,
implies_1: $o ).
thf(cn1_type,type,
cn1: $o ).
thf(and_2_type,type,
and_2: $o ).
thf(cn2_type,type,
cn2: $o ).
thf(or_2_type,type,
or_2: $o ).
thf(kn3_type,type,
kn3: $o ).
thf(or_1_type,type,
or_1: $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(sk12_type,type,
sk12: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk30_type,type,
sk30: $i ).
thf(sk31_type,type,
sk31: $i ).
thf(sk35_type,type,
sk35: $i ).
thf(sk36_type,type,
sk36: $i ).
thf(sk39_type,type,
sk39: $i ).
thf(sk40_type,type,
sk40: $i ).
thf(sk44_type,type,
sk44: $i ).
thf(sk45_type,type,
sk45: $i ).
thf(18,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(68,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)],[18]) ).
thf(69,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk3 @ sk4 ) @ sk3 ) )
| kn2 ),
inference(cnf,[status(esa)],[68]) ).
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(60,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(61,plain,
! [B: $i,A: $i] :
( ~ op_and
| ( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_and ),
inference(lifteq,[status(thm)],[61]) ).
thf(13,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(57,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_or ),
inference(lifteq,[status(thm)],[58]) ).
thf(3,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
thf(45,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[59,45]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(4,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
thf(46,plain,
op_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( and @ A @ B )
= ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[62,170,46]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(9,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(51,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)],[9]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ op_equiv ),
inference(lifteq,[status(thm)],[52]) ).
thf(5,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_equiv) ).
thf(47,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ $true ),
inference(rewrite,[status(thm)],[53,47]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) ),
inference(simp,[status(thm)],[152]) ).
thf(172,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)],[153,69]) ).
thf(173,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)],[172]) ).
thf(190,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)],[185,185]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) @ A )
= ( not @ ( not @ ( and @ ( and @ B @ C ) @ ( not @ ( not @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( and @ ( not @ ( not @ H ) ) @ ( not @ ( not @ J ) ) )),bind(D,$thf( D ))]]) ).
thf(218,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)],[191]) ).
thf(40,axiom,
( r1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(136,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)],[40]) ).
thf(33,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(115,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)],[33]) ).
thf(188,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)],[185,185]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) )
= ( and @ A @ B ) ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( not @ ( not @ F ) )),bind(B,$thf( not @ ( not @ H ) )),bind(C,$thf( F )),bind(D,$thf( H ))]]) ).
thf(217,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)],[189]) ).
thf(12,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(56,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,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(142,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(38,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(130,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)],[38]) ).
thf(131,plain,
( ~ ( is_a_theorem @ ( implies @ sk44 @ ( or @ sk44 @ sk45 ) ) )
| or_1 ),
inference(cnf,[status(esa)],[130]) ).
thf(448,plain,
( ~ ( is_a_theorem @ ( implies @ sk44 @ ( not @ ( and @ ( not @ sk44 ) @ ( not @ sk45 ) ) ) ) )
| or_1 ),
inference(rewrite,[status(thm)],[131,170]) ).
thf(30,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(106,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)],[30]) ).
thf(35,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(121,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)],[35]) ).
thf(20,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(74,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)],[20]) ).
thf(25,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(89,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)],[25]) ).
thf(39,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(133,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)],[39]) ).
thf(26,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(92,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)],[26]) ).
thf(17,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(65,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)],[17]) ).
thf(31,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(109,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)],[31]) ).
thf(36,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(124,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)],[36]) ).
thf(21,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(77,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)],[21]) ).
thf(16,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
thf(64,plain,
r5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(80,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)],[22]) ).
thf(81,plain,
( ~ ( is_a_theorem @ ( implies @ sk12 @ ( and @ sk12 @ sk12 ) ) )
| kn1 ),
inference(cnf,[status(esa)],[80]) ).
thf(175,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)],[153,81]) ).
thf(176,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)],[175]) ).
thf(125,plain,
( ~ ( is_a_theorem @ ( implies @ sk40 @ ( or @ sk39 @ sk40 ) ) )
| or_2 ),
inference(cnf,[status(esa)],[124]) ).
thf(423,plain,
( ~ ( is_a_theorem @ ( implies @ sk40 @ ( not @ ( and @ ( not @ sk39 ) @ ( not @ sk40 ) ) ) ) )
| or_2 ),
inference(rewrite,[status(thm)],[125,170]) ).
thf(1,conjecture,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
thf(2,negated_conjecture,
~ cn3,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ cn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,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(118,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)],[34]) ).
thf(19,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(71,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)],[19]) ).
thf(10,axiom,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
thf(54,plain,
r1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
thf(49,plain,
r3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(90,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk18 @ sk19 ) @ sk18 ) )
| and_1 ),
inference(cnf,[status(esa)],[89]) ).
thf(180,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)],[153,90]) ).
thf(181,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)],[180]) ).
thf(24,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(86,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)],[24]) ).
thf(28,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(98,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)],[28]) ).
thf(102,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)],[98]) ).
thf(148,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)],[102]) ).
thf(149,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)],[148]) ).
thf(11,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
thf(55,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(158,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)],[149,55]) ).
thf(159,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)],[158]) ).
thf(32,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(112,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)],[32]) ).
thf(113,plain,
( ~ ( is_a_theorem @ ( implies @ sk30 @ ( implies @ sk31 @ sk30 ) ) )
| implies_1 ),
inference(cnf,[status(esa)],[112]) ).
thf(29,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(103,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(66,plain,
( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sk2 ) @ ( not @ sk1 ) ) @ ( implies @ sk1 @ sk2 ) ) )
| modus_tollens ),
inference(cnf,[status(esa)],[65]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ( is_a_theorem @ B ) ),
inference(rewrite,[status(thm)],[102,55]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ( is_a_theorem @ B ) ),
inference(simp,[status(thm)],[154]) ).
thf(43,axiom,
( cn3
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(145,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)],[43]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(48,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
thf(63,plain,
r2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,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(95,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)],[27]) ).
thf(8,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
thf(50,plain,
r4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,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(127,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)],[37]) ).
thf(41,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(139,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)],[41]) ).
thf(119,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk35 @ sk36 ) @ sk36 ) )
| and_2 ),
inference(cnf,[status(esa)],[118]) ).
thf(197,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)],[185,185]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( and @ B @ C ) ) ) )
= ( and @ A @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( not @ C ) ) ) ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( and @ ( not @ ( not @ H ) ) @ ( not @ ( not @ J ) ) ))]]) ).
thf(214,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)],[198]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk36 ) )
| and_2
| ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
!= ( and @ sk35 @ sk36 ) ) ),
inference(paramod_ordered,[status(thm)],[153,119]) ).
thf(183,plain,
! [B: $i,A: $i] :
( and_2
| ~ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ sk36 ) )
| ( ( implies @ A @ B )
!= sk35 )
| ( ( implies @ B @ A )
!= sk36 ) ),
inference(simp,[status(thm)],[182]) ).
thf(23,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(83,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)],[23]) ).
thf(203,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)],[185,153]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( and @ ( not @ ( not @ ( implies @ B @ A ) ) ) @ ( not @ ( not @ ( implies @ A @ B ) ) ) ) ) )
= ( equiv @ B @ A ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( implies @ H @ G )),bind(B,$thf( implies @ G @ H )),bind(C,$thf( H )),bind(D,$thf( G ))]]) ).
thf(215,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)],[204]) ).
thf(231,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)],[217,185]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( not @ ( not @ ( not @ ( not @ ( and @ ( not @ ( not @ ( not @ ( not @ A ) ) ) ) @ ( not @ ( not @ ( not @ ( not @ B ) ) ) ) ) ) ) ) )
= ( not @ ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ ( not @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(2061,plain,
$false,
inference(e,[status(thm)],[69,185,60,173,218,136,170,115,217,56,142,153,46,448,57,106,121,74,89,133,92,65,109,124,77,45,64,176,423,44,118,71,54,49,181,86,159,113,81,98,103,66,155,130,80,112,145,48,63,95,50,127,55,139,119,214,51,183,47,68,90,83,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 16:23:20 EDT 2023
% 0.15/0.29 % CPUTime :
% 0.62/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.97/0.81 % [INFO] Parsing done (127ms).
% 0.97/0.81 % [INFO] Running in sequential loop mode.
% 1.28/1.01 % [INFO] eprover registered as external prover.
% 1.28/1.01 % [INFO] cvc4 registered as external prover.
% 1.45/1.02 % [INFO] Scanning for conjecture ...
% 1.45/1.06 % [INFO] Found a conjecture and 44 axioms. Running axiom selection ...
% 1.62/1.11 % [INFO] Axiom selection finished. Selected 41 axioms (removed 3 axioms).
% 1.62/1.16 % [INFO] Problem is first-order (TPTP FOF).
% 1.62/1.16 % [INFO] Type checking passed.
% 1.62/1.16 % [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 ...
% 20.17/4.34 % External prover 'e' found a proof!
% 20.17/4.34 % [INFO] Killing All external provers ...
% 20.17/4.34 % Time passed: 3945ms (effective reasoning time: 3520ms)
% 20.17/4.34 % 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)>
% 20.17/4.34 % Axioms used in derivation (41): or_3, and_1, luka_op_or, cn1, op_equiv, cn2, kn1, op_and, r5, principia_r5, r1, implies_3, principia_r4, op_implies_and, cn3, principia_r2, principia_op_and, principia_r3, equivalence_2, principia_modus_ponens, kn2, equivalence_3, modus_tollens, kn3, luka_op_equiv, and_3, or_1, principia_op_equiv, r4, modus_ponens, r2, equivalence_1, or_2, implies_1, r3, and_2, principia_r1, op_or, op_implies_or, implies_2, principia_op_implies_or
% 20.17/4.34 % No. of inferences in proof: 137
% 20.17/4.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3945 ms resp. 3520 ms w/o parsing
% 20.17/4.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.17/4.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------