%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL508+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 07:51:59 AM UTC 2026
% Result : Theorem 53.31s 19.88s
% Output : Refutation 54.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 53
% Syntax : Number of formulae : 167 ( 53 unt; 0 typ; 10 def)
% Number of atoms : 521 ( 100 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2029 ( 172 ~; 163 |; 39 &;1557 @)
% ( 26 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 43 con; 0-2 aty)
% Number of variables : 442 ( 0 ^; 432 !; 0 ?; 442 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(and_3_decl,type,
and_3: $o ).
thf(op_or_decl,type,
op_or: $o ).
thf(kn2_decl,type,
kn2: $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(op_equiv_decl,type,
op_equiv: $o ).
thf(substitution_of_equivalents_decl,type,
substitution_of_equivalents: $o ).
thf(op_implies_and_decl,type,
op_implies_and: $o ).
thf(modus_ponens_decl,type,
modus_ponens: $o ).
thf(kn3_decl,type,
kn3: $o ).
thf(kn1_decl,type,
kn1: $o ).
thf(equiv_decl,type,
equiv: $i > $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(and_2_decl,type,
and_2: $o ).
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(modus_tollens_decl,type,
modus_tollens: $o ).
thf(r2_decl,type,
r2: $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(cn3_decl,type,
cn3: $o ).
thf(equivalence_1_decl,type,
equivalence_1: $o ).
thf(implies_1_decl,type,
implies_1: $o ).
thf(cn1_decl,type,
cn1: $o ).
thf(or_3_decl,type,
or_3: $o ).
thf(cn2_decl,type,
cn2: $o ).
thf(or_2_decl,type,
or_2: $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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk25_decl,type,
sk25: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( A @ ( A @ ( sk1 @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( A @ ( sk3 @ implies ) @ ( sk3 @ not @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( A @ ( sk7 @ or ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ( A @ ( sk20 @ equiv ) @ is_a_theorem )
=> ( sk20 = A ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( @+[A: $i] :
~ ( ( ( A @ ( sk24 @ implies ) @ is_a_theorem )
& ( sk24 @ is_a_theorem ) )
=> ( A @ is_a_theorem ) ) ) ) ).
thf(11,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
thf(56,plain,
kn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(174,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(147,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)],[36]) ).
thf(15,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
thf(60,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)],[15]) ).
thf(26,axiom,
( substitution_of_equivalents
<=> ! [A: $i,B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(103,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)],[26]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( substitution_of_equivalents
| ( sk20 != sk21 ) )
& ( substitution_of_equivalents
| ( sk21 @ ( sk20 @ equiv ) @ is_a_theorem ) )
& ( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ) ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(cnfConj,[status(thm)],[104]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents
| ( A = B ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(8,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(53,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ $true
| ( A = B ) ),
inference(rewrite,[status(thm)],[108,53]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ( A = B ) ),
inference(simp,[status(thm)],[204]) ).
thf(30,axiom,
( equivalence_3
<=> ! [A: $i,B: $i] : ( B @ ( A @ equiv ) @ ( A @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
thf(123,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)],[30]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',or_3) ).
thf(143,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)],[35]) ).
thf(37,axiom,
( or_2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
thf(151,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)],[37]) ).
thf(20,axiom,
( kn1
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(79,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)],[20]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',implies_3) ).
thf(83,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)],[21]) ).
thf(17,axiom,
( modus_tollens
<=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
thf(67,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)],[17]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( modus_tollens
| ~ ( sk4 @ ( sk3 @ implies ) @ ( sk3 @ not @ ( sk4 @ not @ implies ) @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ modus_tollens ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ modus_tollens ),
inference(cnfConj,[status(thm)],[68]) ).
thf(28,axiom,
( modus_ponens
<=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
thf(114,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)],[28]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( modus_ponens
| ~ ( sk25 @ is_a_theorem ) )
& ( modus_ponens
| ( sk25 @ ( sk24 @ implies ) @ is_a_theorem ) )
& ( modus_ponens
| ( sk24 @ is_a_theorem ) )
& ( ( B @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ modus_ponens ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ modus_ponens ),
inference(cnfConj,[status(thm)],[115]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ modus_ponens ),
inference(eqfactor_ordered,[status(thm)],[116]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ~ modus_ponens
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[182]) ).
thf(10,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).
thf(55,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ~ $true
| ( B @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[183,55]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= ( A @ is_a_theorem ) )
| ~ ( A @ is_a_theorem )
| ( B @ is_a_theorem ) ),
inference(simp,[status(thm)],[198]) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( D @ ( C @ implies ) ) )
| ( ( B @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[205,199]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( F @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[211]) ).
thf(896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( E @ ( D @ implies ) ) )
| ( ( C @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ( E @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[205,241]) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( G @ ( F @ implies ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ ( A @ ( D @ ( C @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[897]) ).
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/sandbox/benchmark/theBenchmark.p',r5) ).
thf(170,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(29,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(120,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(7,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(52,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
( r3
<=> ! [A: $i,B: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
thf(110,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)],[27]) ).
thf(3,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).
thf(46,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(57,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
( r2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(75,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)],[19]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( r2
| ~ ( sk8 @ ( sk7 @ or ) @ ( sk8 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem )
| ~ r2 ) ),
inference(cnf,[status(esa)],[75]) ).
thf(78,plain,
( r2
| ~ ( sk8 @ ( sk7 @ or ) @ ( sk8 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[76]) ).
thf(6,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(49,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) )
| ~ op_or ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(rewrite,[status(thm)],[51,46]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ),
inference(simp,[status(thm)],[185]) ).
thf(187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ and ) @ not )
!= ( D @ not ) )
| ( ( B @ ( A @ or ) @ ( C @ not @ and ) @ not )
= ( D @ ( C @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,186]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( A @ not @ and ) @ not )
= ( C @ not @ ( B @ not @ and ) @ ( A @ or ) ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ not @ ( G @ not @ and ) ))]]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( A @ not @ and ) @ not )
= ( C @ not @ ( B @ not @ and ) @ ( A @ or ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ not @ ( B @ not @ and ) @ ( A @ or ) )
!= ( E @ ( D @ or ) ) )
| ( ( C @ ( B @ or ) @ ( A @ not @ and ) @ not )
= ( E @ not @ ( D @ not @ and ) @ not ) ) ),
inference(paramod_ordered,[status(thm)],[191,186]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( A @ not @ and ) @ not )
= ( C @ not @ ( B @ not @ and ) @ not @ ( A @ not @ and ) @ not ) ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( A )),bind(E,$thf( I @ not @ ( H @ not @ and ) ))]]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( A @ not @ and ) @ not )
= ( C @ not @ ( B @ not @ and ) @ not @ ( A @ not @ and ) @ not ) ),
inference(simp,[status(thm)],[329]) ).
thf(70,plain,
( modus_tollens
| ~ ( sk4 @ ( sk3 @ implies ) @ ( sk3 @ not @ ( sk4 @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ and ) @ not )
!= ( C @ not ) )
| ( ( D @ not @ ( B @ ( A @ or ) @ and ) @ not )
= ( D @ ( C @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,186]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( C @ ( B @ or ) @ and ) @ not )
= ( A @ ( C @ not @ ( B @ not @ and ) @ or ) ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ not @ ( G @ not @ and ) )),bind(D,$thf( D ))]]) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( C @ ( B @ or ) @ and ) @ not )
= ( A @ ( C @ not @ ( B @ not @ and ) @ or ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) )
| ~ op_equiv ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ) ),
inference(rewrite,[status(thm)],[62,52]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ),
inference(simp,[status(thm)],[251]) ).
thf(16,axiom,
( and_2
<=> ! [A: $i,B: $i] : ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
thf(63,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)],[16]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( and_2
| ~ ( sk2 @ ( sk2 @ ( sk1 @ and ) @ implies ) @ is_a_theorem ) )
& ( ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
| ~ and_2 ) ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
| ~ and_2 ),
inference(cnfConj,[status(thm)],[64]) ).
thf(441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ not @ ( B @ not @ and ) @ or ) )
!= ( E @ ( D @ or ) ) )
| ( ( A @ not @ ( C @ ( B @ or ) @ and ) @ not )
= ( E @ not @ ( D @ not @ and ) @ not ) ) ),
inference(paramod_ordered,[status(thm)],[192,186]) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( C @ ( B @ or ) @ and ) @ not )
= ( A @ not @ ( C @ not @ ( B @ not @ and ) @ not @ and ) @ not ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( I @ not @ ( H @ not @ and ) )),bind(E,$thf( A ))]]) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ not @ ( C @ ( B @ or ) @ and ) @ not )
= ( A @ not @ ( C @ not @ ( B @ not @ and ) @ not @ and ) @ not ) ),
inference(simp,[status(thm)],[442]) ).
thf(927,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( F @ ( E @ implies ) @ equiv ) ) )
| ( ( D @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ is_a_theorem )
| ( F @ is_a_theorem )
| ~ ( D @ ( C @ equiv ) @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[205,909]) ).
thf(928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ( E @ is_a_theorem )
| ~ ( B @ ( C @ equiv ) @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( E @ ( D @ implies ) @ equiv ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( H @ ( J @ ( I @ implies ) @ equiv ) )),bind(B,$thf( B )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( J ))]]) ).
thf(948,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ( E @ is_a_theorem )
| ~ ( B @ ( C @ equiv ) @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( A @ ( C @ ( E @ ( D @ implies ) @ equiv ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[928]) ).
thf(2019,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( E @ ( G @ ( F @ implies ) @ equiv ) ) )
| ( ( D @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ~ ( F @ is_a_theorem )
| ( G @ is_a_theorem )
| ~ ( D @ ( E @ equiv ) @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[205,948]) ).
thf(2020,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ is_a_theorem )
| ( F @ is_a_theorem )
| ~ ( C @ ( D @ equiv ) @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ ( A @ ( D @ ( F @ ( E @ implies ) @ equiv ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2019:[bind(A,$thf( I @ ( K @ ( J @ implies ) @ equiv ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( J )),bind(G,$thf( K ))]]) ).
thf(2100,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ is_a_theorem )
!= ( E @ is_a_theorem ) )
| ~ ( E @ is_a_theorem )
| ( F @ is_a_theorem )
| ~ ( C @ ( D @ equiv ) @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ ( A @ ( D @ ( F @ ( E @ implies ) @ equiv ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2020]) ).
thf(1,conjecture,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(2,negated_conjecture,
~ and_3,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(45,plain,
~ and_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( E @ ( D @ or ) ) )
| ( ( C @ not @ ( B @ not @ ( A @ not @ and ) @ not @ and ) @ not )
= ( C @ ( E @ not @ ( D @ not @ and ) @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,192]) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ not @ ( A @ not @ and ) @ not @ and ) @ not )
= ( C @ ( B @ not @ ( A @ not @ and ) @ or ) ) ),
inference(pattern_uni,[status(thm)],[443:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(1560,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ and ) @ not )
!= ( D @ not @ ( C @ not @ and ) @ not ) )
| ( ( E @ not @ ( B @ ( A @ or ) @ and ) @ not )
= ( E @ ( D @ not @ ( C @ not @ and ) @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,444]) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ ( A @ or ) @ and ) @ not )
= ( C @ ( B @ not @ ( A @ not @ and ) @ or ) ) ),
inference(pattern_uni,[status(thm)],[1560:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( B @ ( A @ or ) @ and ) @ not )
= ( C @ ( B @ not @ ( A @ not @ and ) @ or ) ) ),
inference(simp,[status(thm)],[1561]) ).
thf(330,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( E @ ( D @ or ) ) )
| ( ( B @ not @ ( A @ not @ and ) @ not @ ( C @ not @ and ) @ not )
= ( E @ not @ ( D @ not @ and ) @ ( C @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,191]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ not @ ( A @ not @ and ) @ not @ ( C @ not @ and ) @ not )
= ( B @ not @ ( A @ not @ and ) @ ( C @ or ) ) ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(578,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ and ) @ ( C @ or ) )
!= ( F @ not @ ( E @ not @ and ) @ ( D @ or ) ) )
| ( ( B @ not @ ( A @ not @ and ) @ not @ ( C @ not @ and ) @ not )
= ( F @ ( E @ or ) @ ( D @ not @ and ) @ not ) ) ),
inference(paramod_ordered,[status(thm)],[331,191]) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ not @ ( A @ not @ and ) @ not @ ( C @ not @ and ) @ not )
= ( B @ ( A @ or ) @ ( C @ not @ and ) @ not ) ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(14,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_equiv) ).
thf(59,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(71,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)],[18]) ).
thf(39,axiom,
( or_1
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
thf(159,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(9,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
thf(54,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2116,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( F @ ( H @ ( G @ implies ) @ equiv ) ) )
| ( ( E @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ~ ( G @ is_a_theorem )
| ( H @ is_a_theorem )
| ~ ( E @ ( F @ equiv ) @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ ( D @ ( C @ equiv ) @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[205,2100]) ).
thf(2117,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ~ ( F @ is_a_theorem )
| ( G @ is_a_theorem )
| ~ ( D @ ( E @ equiv ) @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ ( A @ ( E @ ( G @ ( F @ implies ) @ equiv ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[2116:[bind(A,$thf( J @ ( L @ ( K @ implies ) @ equiv ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( J )),bind(G,$thf( K )),bind(H,$thf( L ))]]) ).
thf(2220,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ is_a_theorem )
!= ( F @ is_a_theorem ) )
| ~ ( F @ is_a_theorem )
| ( G @ is_a_theorem )
| ~ ( D @ ( E @ equiv ) @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ ( A @ ( E @ ( G @ ( F @ implies ) @ equiv ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[2117]) ).
thf(3594,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( I @ ( H @ implies ) ) )
| ( ( F @ is_a_theorem )
!= ( H @ is_a_theorem ) )
| ~ ( H @ is_a_theorem )
| ( I @ is_a_theorem )
| ~ ( F @ ( G @ equiv ) @ is_a_theorem )
| ~ ( E @ is_a_theorem )
| ~ ( E @ ( D @ equiv ) @ is_a_theorem )
| ~ ( D @ ( C @ equiv ) @ is_a_theorem )
| ~ ( C @ ( G @ ( B @ equiv ) @ equiv ) @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[205,2220]) ).
thf(3595,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ~ ( G @ is_a_theorem )
| ( H @ is_a_theorem )
| ~ ( E @ ( F @ equiv ) @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ ( D @ ( C @ equiv ) @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( F @ ( A @ equiv ) @ equiv ) @ is_a_theorem )
| ~ ( A @ ( H @ ( G @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[3594:[bind(A,$thf( K @ ( J @ implies ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( J )),bind(I,$thf( K ))]]) ).
thf(3747,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ is_a_theorem )
!= ( G @ is_a_theorem ) )
| ~ ( G @ is_a_theorem )
| ( H @ is_a_theorem )
| ~ ( E @ ( F @ equiv ) @ is_a_theorem )
| ~ ( D @ is_a_theorem )
| ~ ( D @ ( C @ equiv ) @ is_a_theorem )
| ~ ( C @ ( B @ equiv ) @ is_a_theorem )
| ~ ( B @ ( F @ ( A @ equiv ) @ equiv ) @ is_a_theorem )
| ~ ( A @ ( H @ ( G @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[3595]) ).
thf(23,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
thf(91,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)],[23]) ).
thf(66,plain,
( and_2
| ~ ( sk2 @ ( sk2 @ ( sk1 @ and ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[64]) ).
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/sandbox/benchmark/theBenchmark.p',kn3) ).
thf(155,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(33,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
thf(135,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)],[33]) ).
thf(41,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
thf(167,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(5,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
thf(48,plain,
kn2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
( implies_2
<=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ implies ) @ ( A @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
thf(95,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)],[24]) ).
thf(44,axiom,
( and_3
<=> ! [A: $i,B: $i] : ( B @ ( A @ and ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
thf(177,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)],[44]) ).
thf(31,axiom,
( cn3
<=> ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(127,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)],[31]) ).
thf(25,axiom,
( r1
<=> ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(99,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)],[25]) ).
thf(22,axiom,
( equivalence_2
<=> ! [A: $i,B: $i] : ( A @ ( B @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
thf(87,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)],[22]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cn1) ).
thf(139,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)],[34]) ).
thf(13,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
thf(58,plain,
kn1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ not @ and ) @ not )
!= ( D @ not @ ( C @ not @ and ) @ not ) )
| ( ( B @ ( A @ or ) @ ( E @ not @ and ) @ not )
= ( D @ not @ ( C @ not @ and ) @ ( E @ or ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,331]) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( C @ not @ and ) @ not )
= ( B @ not @ ( A @ not @ and ) @ ( C @ or ) ) ),
inference(pattern_uni,[status(thm)],[620:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( C @ not @ and ) @ not )
= ( B @ not @ ( A @ not @ and ) @ ( C @ or ) ) ),
inference(simp,[status(thm)],[621]) ).
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/sandbox/benchmark/theBenchmark.p',r4) ).
thf(163,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(32,axiom,
( equivalence_1
<=> ! [A: $i,B: $i] : ( B @ ( A @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
thf(131,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)],[32]) ).
thf(4,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(47,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14489,plain,
$false,
inference(e,[status(thm)],[56,174,147,60,205,123,143,151,79,83,69,909,170,120,52,110,46,57,78,349,70,192,252,65,493,2100,948,53,45,444,191,1615,579,59,71,49,159,54,2220,3747,103,91,66,155,135,241,167,48,63,95,67,199,177,331,127,99,87,186,139,55,114,75,58,684,163,131,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL508+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.45 % Computer : n015.cluster.edu
% 0.11/0.45 % Model : x86_64 x86_64
% 0.11/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.45 % Memory : 8046.5625MB
% 0.11/0.45 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Fri Sep 25 22:44:13 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.45 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.01/1.33 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.61 % [INFO] Parsing done (272ms).
% 1.51/1.62 % [INFO] Running in sequential loop mode.
% 2.06/2.11 % [INFO] eprover registered as external prover.
% 2.06/2.12 % [INFO] Scanning for conjecture ...
% 2.26/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.37/2.35 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 2.51/2.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.51/2.48 % [INFO] Type checking passed.
% 2.51/2.48 % [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 ...
% 53.31/19.87 % External prover 'e' found a proof!
% 53.31/19.87 % [INFO] Killing All external provers ...
% 53.31/19.87 % Time passed: 19177ms (effective reasoning time: 18248ms)
% 53.31/19.87 % 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)>
% 53.31/19.88 % Axioms used in derivation (42): or_3, and_1, equivalence_2, op_equiv, rosser_kn2, kn1, r5, rosser_modus_ponens, implies_3, op_implies_and, cn3, rosser_kn3, cn1, rosser_op_or, kn2, rosser_op_implies_and, cn2, hilbert_op_implies_and, equivalence_3, modus_tollens, rosser_kn1, op_and, or_1, kn3, and_3, use_substitution_of_equivalents, r4, modus_ponens, hilbert_op_or, r1, r2, equivalence_1, or_2, implies_1, r3, and_2, substitution_of_equivalents, rosser_op_equiv, op_or, op_implies_or, hilbert_op_equiv, implies_2
% 53.31/19.88 % No. of inferences in proof: 157
% 53.31/19.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19177 ms resp. 18248 ms w/o parsing
% 54.04/20.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.04/20.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------