%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL470+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:51:55 AM UTC 2026
% Result : Theorem 39.52s 10.01s
% Output : Refutation 40.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 46
% Syntax : Number of formulae : 119 ( 38 unt; 0 typ; 4 def)
% Number of atoms : 277 ( 46 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1148 ( 33 ~; 26 |; 32 &; 961 @)
% ( 26 <=>; 70 =>; 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 : 44 ( 41 usr; 37 con; 0-2 aty)
% Number of variables : 245 ( 0 ^; 241 !; 0 ?; 245 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(or_2_decl,type,
or_2: $o ).
thf(op_or_decl,type,
op_or: $o ).
thf(op_implies_and_decl,type,
op_implies_and: $o ).
thf(op_equiv_decl,type,
op_equiv: $o ).
thf(substitution_of_equivalents_decl,type,
substitution_of_equivalents: $o ).
thf(cn3_decl,type,
cn3: $o ).
thf(equiv_decl,type,
equiv: $i > $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(cn1_decl,type,
cn1: $o ).
thf(modus_ponens_decl,type,
modus_ponens: $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(cn2_decl,type,
cn2: $o ).
thf(modus_tollens_decl,type,
modus_tollens: $o ).
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(kn2_decl,type,
kn2: $o ).
thf(or_3_decl,type,
or_3: $o ).
thf(and_3_decl,type,
and_3: $o ).
thf(r2_decl,type,
r2: $o ).
thf(kn1_decl,type,
kn1: $o ).
thf(implies_3_decl,type,
implies_3: $o ).
thf(equivalence_2_decl,type,
equivalence_2: $o ).
thf(and_1_decl,type,
and_1: $o ).
thf(implies_2_decl,type,
implies_2: $o ).
thf(r1_decl,type,
r1: $o ).
thf(r3_decl,type,
r3: $o ).
thf(op_implies_or_decl,type,
op_implies_or: $o ).
thf(equivalence_3_decl,type,
equivalence_3: $o ).
thf(equivalence_1_decl,type,
equivalence_1: $o ).
thf(implies_1_decl,type,
implies_1: $o ).
thf(and_2_decl,type,
and_2: $o ).
thf(kn3_decl,type,
kn3: $o ).
thf(or_1_decl,type,
or_1: $o ).
thf(r4_decl,type,
r4: $o ).
thf(op_and_decl,type,
op_and: $o ).
thf(r5_decl,type,
r5: $o ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk54_decl,type,
sk54: $i ).
thf(sk55_decl,type,
sk55: $i ).
thf(sk23_def,definition,
( sk23
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( @+[A: $i] :
~ ( ( A @ ( sk23 @ equiv ) @ is_a_theorem )
=> ( sk23 = A ) ) ) ) ).
thf(sk54_def,definition,
( sk54
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ) ) ).
thf(sk55_def,definition,
( sk55
= ( @+[A: $i] :
~ ( A @ ( sk54 @ or ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(22,axiom,
( implies_3
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
=> implies_3 )
& ( implies_3
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
( r3
<=> ! [A: $i,B: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).
thf(115,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ is_a_theorem )
=> r3 )
& ( r3
=> ! [A: $i,B: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
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(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(38,axiom,
( kn3
<=> ! [A: $i,B: $i,C: $i] : ( A @ ( C @ and ) @ not @ ( C @ ( B @ and ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn3) ).
thf(156,plain,
( ( ! [A: $i,B: $i,C: $i] : ( A @ ( C @ and ) @ not @ ( C @ ( B @ and ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
=> kn3 )
& ( kn3
=> ! [A: $i,B: $i,C: $i] : ( A @ ( C @ and ) @ not @ ( C @ ( B @ and ) @ not @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
thf(96,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
=> and_1 )
& ( and_1
=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
( equivalence_3
<=> ! [A: $i,B: $i] : ( B @ ( A @ equiv ) @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
thf(128,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ equiv ) @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
=> equivalence_3 )
& ( equivalence_3
=> ! [A: $i,B: $i] : ( B @ ( A @ equiv ) @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
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(19,axiom,
( and_3
<=> ! [A: $i,B: $i] : ( B @ ( A @ and ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
thf(76,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ and ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
=> and_3 )
& ( and_3
=> ! [A: $i,B: $i] : ( B @ ( A @ and ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
( r2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
thf(80,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem )
=> r2 )
& ( r2
=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
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(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(26,axiom,
( r1
<=> ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
thf(104,plain,
( ( ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem )
=> r1 )
& ( r1
=> ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
( modus_ponens
<=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) )
=> modus_ponens )
& ( modus_ponens
=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(33,axiom,
( equivalence_1
<=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).
thf(136,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem )
=> equivalence_1 )
& ( equivalence_1
=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(10,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
thf(52,plain,
( op_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
thf(125,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(27,axiom,
( substitution_of_equivalents
<=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) )
=> substitution_of_equivalents )
& ( substitution_of_equivalents
=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( substitution_of_equivalents
| ( sk23 != sk24 ) )
& ( substitution_of_equivalents
| ( sk24 @ ( sk23 @ equiv ) @ is_a_theorem ) )
& ( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ) ),
inference(cnf,[status(esa)],[108]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(cnfConj,[status(thm)],[109]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents
| ( A = B ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ $true
| ( A = B ) ),
inference(rewrite,[status(thm)],[113,50]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ( A = B ) ),
inference(simp,[status(thm)],[195]) ).
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(37,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2) ).
thf(152,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
=> cn2 )
& ( cn2
=> ! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
thf(57,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
( r4
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(164,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ is_a_theorem )
=> r4 )
& ( r4
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
( kn1
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
thf(84,plain,
( ( ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem )
=> kn1 )
& ( kn1
=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
thf(61,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
( cn3
<=> ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
thf(132,plain,
( ( ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
=> cn3 )
& ( cn3
=> ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) )
| ~ op_equiv ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ 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(212,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ) ),
inference(rewrite,[status(thm)],[54,47]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) )
| ~ op_implies_and ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ op_implies_and
| ( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(774,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(rewrite,[status(thm)],[63,46]) ).
thf(775,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ),
inference(simp,[status(thm)],[774]) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ and ) @ not @ ( B @ not @ ( A @ and ) @ not @ and ) )
= ( B @ ( A @ equiv ) ) ),
inference(rewrite,[status(thm)],[213,775]) ).
thf(39,axiom,
( or_1
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
thf(160,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( A @ implies ) @ is_a_theorem )
=> or_1 )
& ( or_1
=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
( equivalence_2
<=> ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2) ).
thf(92,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem )
=> equivalence_2 )
& ( equivalence_2
=> ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( B @ and ) @ not @ ( B @ not @ ( A @ and ) @ not @ and ) )
!= ( D @ not @ ( C @ and ) ) )
| ( ( C @ not @ ( D @ and ) @ not @ ( B @ ( A @ equiv ) @ not @ and ) )
= ( D @ ( C @ equiv ) ) ) ),
inference(paramod_ordered,[status(thm)],[778,778]) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ and ) @ not @ not @ ( B @ not @ ( A @ and ) @ and ) @ not @ ( A @ ( B @ equiv ) @ not @ and ) )
= ( B @ not @ ( A @ and ) @ ( A @ not @ ( B @ and ) @ not @ equiv ) ) ),
inference(pattern_uni,[status(thm)],[875:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( I @ not @ ( K @ and ) @ not )),bind(D,$thf( K @ not @ ( I @ and ) ))]]) ).
thf(889,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ and ) @ not @ not @ ( B @ not @ ( A @ and ) @ and ) @ not @ ( A @ ( B @ equiv ) @ not @ and ) )
= ( B @ not @ ( A @ and ) @ ( A @ not @ ( B @ and ) @ not @ equiv ) ) ),
inference(simp,[status(thm)],[876]) ).
thf(36,axiom,
( and_2
<=> ! [A: $i,B: $i] : ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
thf(148,plain,
( ( ! [A: $i,B: $i] : ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
=> and_2 )
& ( and_2
=> ! [A: $i,B: $i] : ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
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(16,axiom,
( modus_tollens
<=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).
thf(64,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
=> modus_tollens )
& ( modus_tollens
=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,axiom,
( cn1
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn1) ).
thf(144,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
=> cn1 )
& ( cn1
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
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(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( B @ and ) @ not @ ( B @ not @ ( A @ and ) @ not @ and ) )
!= ( C @ not @ ( D @ and ) ) )
| ( ( B @ ( A @ equiv ) @ not @ ( D @ not @ ( C @ and ) @ not @ and ) )
= ( D @ ( C @ equiv ) ) ) ),
inference(paramod_ordered,[status(thm)],[778,778]) ).
thf(878,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equiv ) @ not @ ( A @ not @ ( B @ and ) @ not @ not @ ( B @ not @ ( A @ and ) @ and ) @ not @ and ) )
= ( A @ not @ ( B @ and ) @ not @ ( B @ not @ ( A @ and ) @ equiv ) ) ),
inference(pattern_uni,[status(thm)],[877:[bind(A,$thf( K )),bind(B,$thf( I )),bind(C,$thf( K @ not @ ( I @ and ) )),bind(D,$thf( I @ not @ ( K @ and ) @ not ))]]) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equiv ) @ not @ ( A @ not @ ( B @ and ) @ not @ not @ ( B @ not @ ( A @ and ) @ and ) @ not @ and ) )
= ( A @ not @ ( B @ and ) @ not @ ( B @ not @ ( A @ and ) @ equiv ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(34,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
thf(140,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
=> implies_1 )
& ( implies_1
=> ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,axiom,
( or_3
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ or ) @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
thf(72,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ or ) @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem )
=> or_3 )
& ( or_3
=> ! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ or ) @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(43,axiom,
( or_2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
thf(175,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem )
=> or_2 )
& ( or_2
=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
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(42,axiom,
( r5
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ or ) @ ( B @ ( A @ or ) @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(171,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ or ) @ ( B @ ( A @ or ) @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem )
=> r5 )
& ( r5
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ or ) @ ( B @ ( A @ or ) @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( or_2
| ~ ( sk55 @ ( sk54 @ or ) @ ( sk55 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem )
| ~ or_2 ) ),
inference(cnf,[status(esa)],[175]) ).
thf(178,plain,
( or_2
| ~ ( sk55 @ ( sk54 @ or ) @ ( sk55 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[176]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) )
| ~ op_or ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(458,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(rewrite,[status(thm)],[59,45]) ).
thf(459,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ),
inference(simp,[status(thm)],[458]) ).
thf(538,plain,
( $false
| ~ ( sk55 @ not @ ( sk54 @ not @ and ) @ not @ ( sk55 @ implies ) @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[178,459,44]) ).
thf(539,plain,
~ ( sk55 @ not @ ( sk54 @ not @ and ) @ not @ ( sk55 @ implies ) @ is_a_theorem ),
inference(simp,[status(thm)],[538]) ).
thf(786,plain,
~ ( sk55 @ not @ ( sk54 @ not @ and ) @ not @ not @ ( sk55 @ and ) @ not @ is_a_theorem ),
inference(rewrite,[status(thm)],[539,775]) ).
thf(41,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).
thf(168,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
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(17,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
thf(68,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
=> kn2 )
& ( kn2
=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,axiom,
( implies_2
<=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
thf(100,plain,
( ( ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem )
=> implies_2 )
& ( implies_2
=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4254,plain,
$false,
inference(e,[status(thm)],[88,115,56,60,156,96,128,44,76,80,48,50,104,119,136,52,125,196,46,152,57,164,84,61,132,778,160,92,889,148,45,64,144,49,890,140,108,72,175,55,171,786,168,51,459,47,68,775,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL470+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n008.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 22:37:39 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.21 % [INFO] Parsing done (218ms).
% 1.48/1.23 % [INFO] Running in sequential loop mode.
% 2.20/1.63 % [INFO] eprover registered as external prover.
% 2.20/1.64 % [INFO] Scanning for conjecture ...
% 2.42/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.59/1.81 % [INFO] Axiom selection finished. Selected 41 axioms (removed 1 axioms).
% 2.59/1.89 % [INFO] Problem is first-order (TPTP FOF).
% 2.86/1.90 % [INFO] Type checking passed.
% 2.86/1.91 % [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 ...
% 39.52/10.01 % External prover 'e' found a proof!
% 39.52/10.01 % [INFO] Killing All external provers ...
% 39.52/10.01 % Time passed: 9453ms (effective reasoning time: 8775ms)
% 39.52/10.01 % 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)>
% 39.52/10.01 % 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
% 39.52/10.01 % No. of inferences in proof: 115
% 39.52/10.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9453 ms resp. 8775 ms w/o parsing
% 40.15/10.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.15/10.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------