%------------------------------------------------------------------------------
% File : Leo-III---1.7.19
% Problem : LCL470+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 : Wed Oct 1 12:41:11 PM UTC 2025
% Result : Theorem 24.27s 6.55s
% Output : Refutation 24.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 113 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 38 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1096 ( 24 ~; 20 |; 29 &; 929 @)
% ( 26 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 35 con; 0-2 aty)
% Number of variables : 235 ( 0 ^; 235 !; 0 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
thf(or_2_type,type,
or_2: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(substitution_of_equivalents_type,type,
substitution_of_equivalents: $o ).
thf(cn3_type,type,
cn3: $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(modus_ponens_type,type,
modus_ponens: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
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(r1_type,type,
r1: $o ).
thf(r3_type,type,
r3: $o ).
thf(op_implies_or_type,type,
op_implies_or: $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(kn3_type,type,
kn3: $o ).
thf(or_1_type,type,
or_1: $o ).
thf(r4_type,type,
r4: $o ).
thf(op_and_type,type,
op_and: $o ).
thf(r5_type,type,
r5: $o ).
thf(sk54_type,type,
sk54: $i ).
thf(sk55_type,type,
sk55: $i ).
thf(12,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_modus_ponens) ).
thf(56,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
thf(52,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)],[10]) ).
thf(29,axiom,
( modus_ponens
<=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
thf(106,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)],[29]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',or_3) ).
thf(70,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)],[18]) ).
thf(27,axiom,
( substitution_of_equivalents
<=> ! [A: $i,B: $i] :
( ( is_a_theorem @ ( equiv @ A @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(97,plain,
( ( substitution_of_equivalents
=> ! [A: $i,B: $i] :
( ( is_a_theorem @ ( equiv @ A @ B ) )
=> ( A = B ) ) )
& ( ! [A: $i,B: $i] :
( ( is_a_theorem @ ( equiv @ A @ B ) )
=> ( A = B ) )
=> substitution_of_equivalents ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(141,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)],[40]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ op_equiv ),
inference(lifteq,[status(thm)],[53]) ).
thf(5,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(47,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) )
| ~ $true ),
inference(rewrite,[status(thm)],[54,47]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equiv @ A @ B ) ),
inference(simp,[status(thm)],[186]) ).
thf(15,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
thf(61,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ op_implies_and
| ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) )
| ~ op_implies_and ),
inference(lifteq,[status(thm)],[62]) ).
thf(4,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(46,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[63,46]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[748]) ).
thf(753,plain,
! [B: $i,A: $i] :
( ( and @ ( not @ ( and @ A @ ( not @ B ) ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) )
= ( equiv @ A @ B ) ),
inference(rewrite,[status(thm)],[187,749]) ).
thf(36,axiom,
( and_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
thf(129,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)],[36]) ).
thf(19,axiom,
( and_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
thf(73,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)],[19]) ).
thf(1,conjecture,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(2,negated_conjecture,
~ or_2,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ or_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
thf(76,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)],[20]) ).
thf(30,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
thf(111,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
( or_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
thf(138,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)],[39]) ).
thf(43,axiom,
( or_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
thf(150,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)],[43]) ).
thf(151,plain,
( ~ ( is_a_theorem @ ( implies @ sk55 @ ( or @ sk54 @ sk55 ) ) )
| or_2 ),
inference(cnf,[status(esa)],[150]) ).
thf(13,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',luka_op_or) ).
thf(45,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[59,45]) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(512,plain,
( ~ ( is_a_theorem @ ( implies @ sk55 @ ( not @ ( and @ ( not @ sk54 ) @ ( not @ sk55 ) ) ) ) )
| $false ),
inference(rewrite,[status(thm)],[151,433,44]) ).
thf(513,plain,
~ ( is_a_theorem @ ( implies @ sk55 @ ( not @ ( and @ ( not @ sk54 ) @ ( not @ sk55 ) ) ) ) ),
inference(simp,[status(thm)],[512]) ).
thf(760,plain,
~ ( is_a_theorem @ ( not @ ( and @ sk55 @ ( not @ ( not @ ( and @ ( not @ sk54 ) @ ( not @ sk55 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[513,749]) ).
thf(24,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
thf(88,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)],[24]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[97]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ substitution_of_equivalents
| ~ ( is_a_theorem @ ( equiv @ A @ B ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(8,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(50,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ $true
| ~ ( is_a_theorem @ ( equiv @ A @ B ) ) ),
inference(rewrite,[status(thm)],[102,50]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( is_a_theorem @ ( equiv @ A @ B ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(33,axiom,
( equivalence_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).
thf(120,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)],[33]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(147,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)],[42]) ).
thf(37,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2) ).
thf(132,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)],[37]) ).
thf(23,axiom,
( equivalence_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2) ).
thf(85,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)],[23]) ).
thf(14,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn2) ).
thf(60,plain,
cn2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(32,axiom,
( cn3
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
thf(117,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)],[32]) ).
thf(16,axiom,
( modus_tollens
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).
thf(64,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)],[16]) ).
thf(41,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).
thf(144,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(7,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(49,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
( r3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).
thf(103,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)],[28]) ).
thf(25,axiom,
( implies_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
thf(91,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)],[25]) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( and @ ( not @ ( and @ C @ ( not @ D ) ) ) @ ( not @ ( equiv @ A @ B ) ) )
= ( equiv @ C @ D ) )
| ( ( and @ ( not @ ( and @ A @ ( not @ B ) ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) )
!= ( and @ D @ ( not @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[753,753]) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( and @ ( not @ ( and @ ( and @ A @ ( not @ B ) ) @ ( not @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ) ) @ ( not @ ( equiv @ B @ A ) ) )
= ( equiv @ ( and @ A @ ( not @ B ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[853:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( and @ I @ ( not @ K ) )),bind(D,$thf( not @ ( and @ K @ ( not @ I ) ) ))]]) ).
thf(868,plain,
! [B: $i,A: $i] :
( ( and @ ( not @ ( and @ ( and @ A @ ( not @ B ) ) @ ( not @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ) ) @ ( not @ ( equiv @ B @ A ) ) )
= ( equiv @ ( and @ A @ ( not @ B ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ),
inference(simp,[status(thm)],[854]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',kn3) ).
thf(135,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)],[38]) ).
thf(34,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
thf(123,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)],[34]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_op_equiv) ).
thf(48,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
thf(67,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)],[17]) ).
thf(11,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn1) ).
thf(55,plain,
cn1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
( equivalence_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
thf(114,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)],[31]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',implies_3) ).
thf(82,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)],[22]) ).
thf(9,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
thf(51,plain,
cn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( and @ ( not @ ( equiv @ A @ B ) ) @ ( not @ ( and @ D @ ( not @ C ) ) ) )
= ( equiv @ C @ D ) )
| ( ( and @ ( not @ ( and @ A @ ( not @ B ) ) ) @ ( not @ ( and @ B @ ( not @ A ) ) ) )
!= ( and @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[753,753]) ).
thf(852,plain,
! [B: $i,A: $i] :
( ( and @ ( not @ ( equiv @ B @ A ) ) @ ( not @ ( and @ ( and @ A @ ( not @ B ) ) @ ( not @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ) ) )
= ( equiv @ ( not @ ( and @ B @ ( not @ A ) ) ) @ ( and @ A @ ( not @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[851:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( not @ ( and @ K @ ( not @ I ) ) )),bind(D,$thf( and @ I @ ( not @ K ) ))]]) ).
thf(867,plain,
! [B: $i,A: $i] :
( ( and @ ( not @ ( equiv @ B @ A ) ) @ ( not @ ( and @ ( and @ A @ ( not @ B ) ) @ ( not @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ) ) )
= ( equiv @ ( not @ ( and @ B @ ( not @ A ) ) ) @ ( and @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[852]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',cn1) ).
thf(126,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)],[35]) ).
thf(21,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
thf(79,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)],[21]) ).
thf(26,axiom,
( r1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
thf(94,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)],[26]) ).
thf(3598,plain,
$false,
inference(e,[status(thm)],[56,52,106,70,97,141,753,129,73,44,76,47,111,138,760,88,170,120,46,57,147,61,132,85,60,117,45,64,144,49,103,91,868,135,749,123,48,150,50,67,55,114,433,82,51,867,126,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL470+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Sep 30 13:36:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.05/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.09 % [INFO] Parsing done (148ms).
% 1.49/1.10 % [INFO] Running in sequential loop mode.
% 1.79/1.31 % [INFO] eprover registered as external prover.
% 1.79/1.32 % [INFO] Scanning for conjecture ...
% 2.01/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.18/1.42 % [INFO] Axiom selection finished. Selected 41 axioms (removed 1 axioms).
% 2.18/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.48/1.48 % [INFO] Type checking passed.
% 2.48/1.48 % [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 ...
% 24.27/6.54 % External prover 'e' found a proof!
% 24.27/6.54 % [INFO] Killing All external provers ...
% 24.27/6.54 % Time passed: 6019ms (effective reasoning time: 5444ms)
% 24.27/6.54 % 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)>
% 24.27/6.55 % Axioms used in derivation (41): or_3, and_1, equivalence_2, luka_op_or, cn1, op_equiv, kn1, implies_3, op_implies_and, cn3, luka_cn3, substitution_of_equivalents, luka_cn2, kn2, cn2, hilbert_op_implies_and, equivalence_3, modus_tollens, luka_cn1, op_and, luka_modus_ponens, r5, or_1, kn3, luka_op_equiv, and_3, use_substitution_of_equivalents, r4, modus_ponens, hilbert_op_or, r1, r2, equivalence_1, or_2, implies_1, r3, and_2, op_or, op_implies_or, hilbert_op_equiv, implies_2
% 24.27/6.55 % No. of inferences in proof: 113
% 24.27/6.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6019 ms resp. 5444 ms w/o parsing
% 24.27/6.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.27/6.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------