TSTP Solution File: LCL456+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 11:30:29 EDT 2023
% Result : Theorem 4.64s 2.12s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 87
% Syntax : Number of formulae : 140 ( 44 unt; 36 typ; 0 def)
% Number of atoms : 220 ( 10 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 751 ( 2 ~; 0 |; 28 &; 633 @)
% ( 25 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 31 con; 0-2 aty)
% Number of variables : 179 ( 0 ^; 179 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(r3_type,type,
r3: $o ).
thf(op_and_type,type,
op_and: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(op_or_type,type,
op_or: $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(equivalence_2_type,type,
equivalence_2: $o ).
thf(or_2_type,type,
or_2: $o ).
thf(implies_2_type,type,
implies_2: $o ).
thf(modus_tollens_type,type,
modus_tollens: $o ).
thf(or_3_type,type,
or_3: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(equivalence_3_type,type,
equivalence_3: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(or_1_type,type,
or_1: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(and_2_type,type,
and_2: $o ).
thf(implies_3_type,type,
implies_3: $o ).
thf(implies_1_type,type,
implies_1: $o ).
thf(and_1_type,type,
and_1: $o ).
thf(and_3_type,type,
and_3: $o ).
thf(equivalence_1_type,type,
equivalence_1: $o ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(kn2_type,type,
kn2: $o ).
thf(r2_type,type,
r2: $o ).
thf(kn1_type,type,
kn1: $o ).
thf(cn3_type,type,
cn3: $o ).
thf(cn1_type,type,
cn1: $o ).
thf(cn2_type,type,
cn2: $o ).
thf(kn3_type,type,
kn3: $o ).
thf(r4_type,type,
r4: $o ).
thf(r1_type,type,
r1: $o ).
thf(r5_type,type,
r5: $o ).
thf(5,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(56,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
thf(2,negated_conjecture,
~ r3,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(53,plain,
~ r3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(77,plain,
and_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,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(59,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)],[8]) ).
thf(14,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
thf(67,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(46,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(143,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)],[46]) ).
thf(33,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(104,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)],[33]) ).
thf(4,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(55,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(47,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(146,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)],[47]) ).
thf(16,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(69,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(101,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)],[32]) ).
thf(35,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(110,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)],[35]) ).
thf(40,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(125,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)],[40]) ).
thf(49,axiom,
( r1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(152,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)],[49]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(57,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(78,plain,
and_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(89,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)],[28]) ).
thf(37,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(116,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(19,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
thf(74,plain,
and_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(51,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(160,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)],[51]) ).
thf(17,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(70,plain,
or_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(137,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)],[44]) ).
thf(29,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(92,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)],[29]) ).
thf(12,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
thf(65,plain,
modus_tollens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,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(134,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)],[43]) ).
thf(41,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(128,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)],[41]) ).
thf(11,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
thf(64,plain,
implies_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(48,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(149,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)],[48]) ).
thf(18,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(71,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
thf(54,plain,
op_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,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(86,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)],[27]) ).
thf(36,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(113,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)],[36]) ).
thf(21,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
thf(76,plain,
implies_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(98,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)],[31]) ).
thf(45,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(140,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)],[45]) ).
thf(13,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
thf(66,plain,
or_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,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(155,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)],[50]) ).
thf(10,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(63,plain,
or_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,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(95,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)],[30]) ).
thf(20,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
thf(75,plain,
implies_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
thf(82,plain,
equivalence_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(38,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(119,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)],[38]) ).
thf(7,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(58,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,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(107,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)],[34]) ).
thf(24,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(79,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(42,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(131,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)],[42]) ).
thf(52,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(163,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)],[52]) ).
thf(15,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
thf(68,plain,
equivalence_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(62,plain,
equivalence_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
( cn3
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(122,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)],[39]) ).
thf(26,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(83,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(169,plain,
$false,
inference(cvc4,[status(thm)],[56,53,77,59,67,143,104,55,146,69,101,110,125,152,57,78,89,116,74,160,70,137,92,65,134,128,64,149,71,54,86,113,76,98,140,66,155,63,95,75,82,119,58,107,79,131,163,68,62,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 16:09:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/0.98 % [INFO] Parsing done (136ms).
% 1.37/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.20 % [INFO] eprover registered as external prover.
% 1.70/1.20 % [INFO] cvc4 registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.89/1.26 % [INFO] Found a conjecture and 52 axioms. Running axiom selection ...
% 1.99/1.31 % [INFO] Axiom selection finished. Selected 50 axioms (removed 2 axioms).
% 2.27/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.36 % [INFO] Type checking passed.
% 2.27/1.37 % [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 ...
% 4.64/2.12 % External prover 'cvc4' found a proof!
% 4.64/2.12 % [INFO] Killing All external provers ...
% 4.64/2.12 % Time passed: 1609ms (effective reasoning time: 1124ms)
% 4.64/2.12 % 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)>
% 4.64/2.12 % Axioms used in derivation (50): or_3, and_1, cn1, op_equiv, kn2, hilbert_implies_1, kn1, op_and, hilbert_and_2, op_implies_and, cn3, hilbert_and_1, principia_op_and, equivalence_2, cn2, hilbert_and_3, hilbert_op_implies_and, equivalence_3, modus_tollens, hilbert_or_1, r5, kn3, hilbert_or_2, hilbert_implies_2, and_3, or_1, principia_op_equiv, r4, modus_ponens, hilbert_modus_tollens, hilbert_op_or, hilbert_equivalence_2, r1, implies_3, hilbert_equivalence_3, hilbert_modus_ponens, hilbert_implies_3, r2, equivalence_1, or_2, hilbert_equivalence_1, hilbert_or_3, implies_1, r3, and_2, op_or, op_implies_or, hilbert_op_equiv, implies_2, principia_op_implies_or
% 4.64/2.12 % No. of inferences in proof: 104
% 4.64/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1609 ms resp. 1124 ms w/o parsing
% 4.83/2.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.83/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------