%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL501+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 : n012.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 07:51:58 AM UTC 2026
% Result : Theorem 14.64s 8.62s
% Output : Refutation 14.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 71
% Syntax : Number of formulae : 171 ( 57 unt; 0 typ; 26 def)
% Number of atoms : 512 ( 73 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1671 ( 156 ~; 131 |; 48 &;1238 @)
% ( 26 <=>; 72 =>; 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 : 66 ( 63 usr; 59 con; 0-2 aty)
% Number of variables : 332 ( 0 ^; 306 !; 0 ?; 332 :)
% ( 0 !>; 0 ?*; 0 @-; 26 @+)
% Comments :
%------------------------------------------------------------------------------
thf(kn3_decl,type,
kn3: $o ).
thf(r3_decl,type,
r3: $o ).
thf(r4_decl,type,
r4: $o ).
thf(r2_decl,type,
r2: $o ).
thf(op_equiv_decl,type,
op_equiv: $o ).
thf(r5_decl,type,
r5: $o ).
thf(op_or_decl,type,
op_or: $o ).
thf(r1_decl,type,
r1: $o ).
thf(modus_ponens_decl,type,
modus_ponens: $o ).
thf(op_implies_or_decl,type,
op_implies_or: $o ).
thf(op_and_decl,type,
op_and: $o ).
thf(substitution_of_equivalents_decl,type,
substitution_of_equivalents: $o ).
thf(op_implies_and_decl,type,
op_implies_and: $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(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(not_decl,type,
not: $i > $i ).
thf(kn2_decl,type,
kn2: $o ).
thf(or_3_decl,type,
or_3: $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(and_3_decl,type,
and_3: $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(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(cn2_decl,type,
cn2: $o ).
thf(or_2_decl,type,
or_2: $o ).
thf(or_1_decl,type,
or_1: $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(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(sk25_decl,type,
sk25: $i ).
thf(sk26_decl,type,
sk26: $i ).
thf(sk29_decl,type,
sk29: $i ).
thf(sk30_decl,type,
sk30: $i ).
thf(sk33_decl,type,
sk33: $i ).
thf(sk36_decl,type,
sk36: $i ).
thf(sk37_decl,type,
sk37: $i ).
thf(sk41_decl,type,
sk41: $i ).
thf(sk42_decl,type,
sk42: $i ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk44_decl,type,
sk44: $i ).
thf(sk45_decl,type,
sk45: $i ).
thf(sk46_decl,type,
sk46: $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(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( sk5 @ ( A @ ( sk5 @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ and ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( A @ ( sk10 @ and ) @ ( A @ implies ) @ ( sk10 @ implies ) @ is_a_theorem ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ! [B: $i] : ( A @ ( B @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
~ ( sk18 @ ( A @ implies ) @ ( A @ ( sk18 @ equiv ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
~ ! [B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( sk20 @ ( A @ ( sk20 @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ equiv ) @ is_a_theorem )
=> ( A = B ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( @+[A: $i] :
~ ( ( A @ ( sk25 @ equiv ) @ is_a_theorem )
=> ( sk25 = A ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: $i] :
~ ( ( ( A @ ( sk29 @ implies ) @ is_a_theorem )
& ( sk29 @ is_a_theorem ) )
=> ( A @ is_a_theorem ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( @+[A: $i] :
~ ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( @+[A: $i] :
~ ! [B: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( @+[A: $i] :
~ ( sk36 @ ( A @ implies ) @ ( sk36 @ implies ) @ is_a_theorem ) ) ) ).
thf(sk41_def,definition,
( sk41
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( @+[A: $i] :
~ ( A @ ( sk41 @ not @ implies ) @ ( sk41 @ implies ) @ is_a_theorem ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ) ) ).
thf(sk44_def,definition,
( sk44
= ( @+[A: $i] :
~ ( A @ ( sk43 @ or ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ or ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( @+[A: $i] :
~ ( A @ ( sk45 @ or ) @ ( sk45 @ implies ) @ is_a_theorem ) ) ) ).
thf(23,axiom,
( kn1
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
thf(88,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)],[23]) ).
thf(16,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(61,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)],[16]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equiv ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) )
| ~ op_equiv ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ op_equiv
| ( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(51,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ) ),
inference(rewrite,[status(thm)],[63,51]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(11,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_modus_ponens) ).
thf(56,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(44,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(174,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)],[44]) ).
thf(7,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).
thf(52,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
( r2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
thf(84,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)],[22]) ).
thf(15,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).
thf(60,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,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(92,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)],[24]) ).
thf(25,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(96,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)],[25]) ).
thf(32,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(129,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,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(64,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)],[17]) ).
thf(65,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)],[64]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
| ~ and_2 ),
inference(cnfConj,[status(thm)],[65]) ).
thf(29,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(112,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)],[29]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( substitution_of_equivalents
| ( sk25 != sk26 ) )
& ( substitution_of_equivalents
| ( sk26 @ ( sk25 @ equiv ) @ is_a_theorem ) )
& ( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ) ),
inference(cnf,[status(esa)],[112]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(cnfConj,[status(thm)],[113]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents
| ( A = B ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(31,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(123,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)],[31]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( modus_ponens
| ~ ( sk30 @ is_a_theorem ) )
& ( modus_ponens
| ( sk30 @ ( sk29 @ implies ) @ is_a_theorem ) )
& ( modus_ponens
| ( sk29 @ is_a_theorem ) )
& ( ( B @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ modus_ponens ) ),
inference(cnf,[status(esa)],[123]) ).
thf(125,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)],[124]) ).
thf(185,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)],[125]) ).
thf(186,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)],[185]) ).
thf(193,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)],[186,56]) ).
thf(194,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)],[193]) ).
thf(205,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 )
| ~ substitution_of_equivalents ),
inference(paramod_ordered,[status(thm)],[117,194]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( F @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(212,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 )
| ~ substitution_of_equivalents ),
inference(simp,[status(thm)],[206]) ).
thf(14,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(59,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(238,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 )
| ~ $true ),
inference(rewrite,[status(thm)],[212,59]) ).
thf(239,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)],[238]) ).
thf(277,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ equiv ) @ is_a_theorem ) )
| ( ( C @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ( E @ is_a_theorem )
| ~ $true
| ~ and_2 ),
inference(paramod_ordered,[status(thm)],[66,239]) ).
thf(278,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
!= ( C @ ( E @ ( D @ implies ) @ equiv ) @ is_a_theorem ) )
| ( ( C @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ( E @ is_a_theorem )
| ~ and_2 ),
inference(simp,[status(thm)],[277]) ).
thf(293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ and ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ equiv ) ) )
| ( ( C @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ~ ( D @ is_a_theorem )
| ~ and_2
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[278]) ).
thf(327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ( ( B @ ( B @ ( A @ and ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ equiv ) ) )
| ~ ( D @ is_a_theorem )
| ~ and_2
| ( E @ is_a_theorem ) ),
inference(bool_ext,[status(thm)],[293]) ).
thf(343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ is_a_theorem )
| ( ( B @ ( B @ ( A @ and ) @ implies ) )
!= ( C @ ( E @ ( D @ implies ) @ equiv ) ) )
| ~ ( D @ is_a_theorem )
| ~ and_2
| ( E @ is_a_theorem ) ),
inference(simp,[status(thm)],[327]) ).
thf(20,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(76,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)],[20]) ).
thf(3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
thf(48,plain,
r3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).
thf(72,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)],[19]) ).
thf(38,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)],[38]) ).
thf(12,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(57,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,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(144,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)],[36]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( implies_1
| ~ ( sk36 @ ( sk37 @ implies ) @ ( sk36 @ implies ) @ is_a_theorem ) )
& ( ( A @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ implies_1 ) ),
inference(cnf,[status(esa)],[144]) ).
thf(147,plain,
( implies_1
| ~ ( sk36 @ ( sk37 @ implies ) @ ( sk36 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[145]) ).
thf(33,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(132,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)],[33]) ).
thf(40,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(160,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,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(68,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)],[18]) ).
thf(69,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)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( A @ not @ ( B @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ modus_tollens ),
inference(cnfConj,[status(thm)],[69]) ).
thf(39,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(156,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)],[39]) ).
thf(8,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).
thf(53,plain,
r5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,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(163,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)],[41]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( or_1
| ~ ( sk46 @ ( sk45 @ or ) @ ( sk45 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ or ) @ ( A @ implies ) @ is_a_theorem )
| ~ or_1 ) ),
inference(cnf,[status(esa)],[163]) ).
thf(166,plain,
( or_1
| ~ ( sk46 @ ( sk45 @ or ) @ ( sk45 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[164]) ).
thf(37,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(148,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)],[37]) ).
thf(9,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).
thf(54,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
thf(49,plain,
r4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,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(181,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)],[46]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( or_2
| ~ ( sk44 @ ( sk43 @ or ) @ ( sk44 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem )
| ~ or_2 ) ),
inference(cnf,[status(esa)],[156]) ).
thf(159,plain,
( or_2
| ~ ( sk44 @ ( sk43 @ or ) @ ( sk44 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[157]) ).
thf(26,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(100,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)],[26]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( and_1
| ~ ( sk20 @ ( sk21 @ ( sk20 @ and ) @ implies ) @ is_a_theorem ) )
& ( ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
| ~ and_1 ) ),
inference(cnf,[status(esa)],[100]) ).
thf(103,plain,
( and_1
| ~ ( sk20 @ ( sk21 @ ( sk20 @ and ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[101]) ).
thf(35,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(140,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)],[35]) ).
thf(89,plain,
! [A: $i] :
( ( kn1
| ~ ( sk14 @ ( sk14 @ and ) @ ( sk14 @ implies ) @ is_a_theorem ) )
& ( ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem )
| ~ kn1 ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
( kn1
| ~ ( sk14 @ ( sk14 @ and ) @ ( sk14 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( cn2
| ~ ( sk42 @ ( sk41 @ not @ implies ) @ ( sk41 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ cn2 ) ),
inference(cnf,[status(esa)],[152]) ).
thf(155,plain,
( cn2
| ~ ( sk42 @ ( sk41 @ not @ implies ) @ ( sk41 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[153]) ).
thf(28,axiom,
( r1
<=> ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
thf(108,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)],[28]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( D @ ( C @ implies ) ) )
| ( ( A @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ~ ( C @ is_a_theorem )
| ( D @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(paramod_ordered,[status(thm)],[117,194]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( A )),bind(B,$thf( F @ ( E @ implies ) )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(simp,[status(thm)],[208]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem )
| ~ $true ),
inference(rewrite,[status(thm)],[209,59]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[222]) ).
thf(21,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(80,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)],[21]) ).
thf(42,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(167,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)],[42]) ).
thf(5,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
thf(50,plain,
r2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(67,plain,
( and_2
| ~ ( sk2 @ ( sk2 @ ( sk1 @ and ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( equivalence_2
| ~ ( sk18 @ ( sk19 @ implies ) @ ( sk19 @ ( sk18 @ equiv ) @ implies ) @ is_a_theorem ) )
& ( ( A @ ( B @ implies ) @ ( B @ ( A @ equiv ) @ implies ) @ is_a_theorem )
| ~ equivalence_2 ) ),
inference(cnf,[status(esa)],[96]) ).
thf(99,plain,
( equivalence_2
| ~ ( sk18 @ ( sk19 @ implies ) @ ( sk19 @ ( sk18 @ equiv ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[97]) ).
thf(27,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(104,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)],[27]) ).
thf(10,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
thf(55,plain,
r1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,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(171,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(34,axiom,
( cn3
<=> ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
thf(136,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)],[34]) ).
thf(137,plain,
! [A: $i] :
( ( cn3
| ~ ( sk33 @ ( sk33 @ ( sk33 @ not @ implies ) @ implies ) @ is_a_theorem ) )
& ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
| ~ cn3 ) ),
inference(cnf,[status(esa)],[136]) ).
thf(139,plain,
( cn3
| ~ ( sk33 @ ( sk33 @ ( sk33 @ not @ implies ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[137]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( kn2
| ~ ( sk5 @ ( sk6 @ ( sk5 @ and ) @ implies ) @ is_a_theorem ) )
& ( ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
| ~ kn2 ) ),
inference(cnf,[status(esa)],[72]) ).
thf(75,plain,
( kn2
| ~ ( sk5 @ ( sk6 @ ( sk5 @ and ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(30,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(119,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)],[30]) ).
thf(13,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
thf(58,plain,
op_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
thf(2,negated_conjecture,
~ kn3,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ kn3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,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(178,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( and_3
| ~ ( sk11 @ ( sk10 @ and ) @ ( sk11 @ implies ) @ ( sk10 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ and ) @ ( B @ implies ) @ ( A @ implies ) @ is_a_theorem )
| ~ and_3 ) ),
inference(cnf,[status(esa)],[80]) ).
thf(83,plain,
( and_3
| ~ ( sk11 @ ( sk10 @ and ) @ ( sk11 @ implies ) @ ( sk10 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(2839,plain,
$false,
inference(e,[status(thm)],[88,217,56,174,52,84,60,92,96,129,343,59,76,48,72,51,152,57,147,61,293,132,160,70,156,53,166,148,64,54,144,49,181,159,103,140,91,66,155,108,223,80,167,112,123,194,50,67,99,104,55,171,139,75,119,58,239,136,47,163,68,178,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL501+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % 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
% 0.12/5.37 % Computer : n012.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Fri Sep 25 22:40:11 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 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
% 0.14/5.65 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/5.75 % [INFO] Parsing done (101ms).
% 0.14/5.76 % [INFO] Running in sequential loop mode.
% 0.14/5.94 % [INFO] eprover registered as external prover.
% 0.14/5.94 % [INFO] Scanning for conjecture ...
% 0.14/5.98 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 1.29/6.02 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 1.29/6.06 % [INFO] Problem is first-order (TPTP FOF).
% 1.29/6.06 % [INFO] Type checking passed.
% 1.29/6.07 % [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 ...
% 14.64/8.62 % External prover 'e' found a proof!
% 14.64/8.62 % [INFO] Killing All external provers ...
% 14.64/8.62 % Time passed: 3161ms (effective reasoning time: 2854ms)
% 14.64/8.62 % 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)>
% 14.64/8.62 % Axioms used in derivation (44): or_3, and_1, op_equiv, cn2, kn1, op_and, r5, principia_r5, r1, implies_3, principia_r4, op_implies_and, cn3, principia_r2, principia_op_and, principia_r3, equivalence_2, cn1, rosser_op_or, principia_modus_ponens, kn2, rosser_op_implies_and, equivalence_3, modus_tollens, kn3, and_3, or_1, principia_op_equiv, use_substitution_of_equivalents, r4, modus_ponens, r2, equivalence_1, or_2, implies_1, r3, and_2, substitution_of_equivalents, rosser_op_equiv, principia_r1, op_or, op_implies_or, implies_2, principia_op_implies_or
% 14.64/8.62 % No. of inferences in proof: 145
% 14.64/8.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3161 ms resp. 2854 ms w/o parsing
% 14.64/8.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.64/8.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------