%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL457+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 : n013.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 07:51:53 AM UTC 2026
% Result : Theorem 27.60s 6.72s
% Output : Refutation 27.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 61
% Syntax : Number of formulae : 165 ( 59 unt; 0 typ; 8 def)
% Number of atoms : 457 ( 61 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1468 ( 131 ~; 124 |; 38 &;1077 @)
% ( 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 : 48 ( 45 usr; 41 con; 0-2 aty)
% Number of variables : 315 ( 0 ^; 307 !; 0 ?; 315 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r4_decl,type,
r4: $o ).
thf(op_and_decl,type,
op_and: $o ).
thf(op_implies_and_decl,type,
op_implies_and: $o ).
thf(op_equiv_decl,type,
op_equiv: $o ).
thf(op_or_decl,type,
op_or: $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(equivalence_2_decl,type,
equivalence_2: $o ).
thf(or_2_decl,type,
or_2: $o ).
thf(implies_2_decl,type,
implies_2: $o ).
thf(substitution_of_equivalents_decl,type,
substitution_of_equivalents: $o ).
thf(implies_3_decl,type,
implies_3: $o ).
thf(modus_tollens_decl,type,
modus_tollens: $o ).
thf(or_3_decl,type,
or_3: $o ).
thf(modus_ponens_decl,type,
modus_ponens: $o ).
thf(equivalence_3_decl,type,
equivalence_3: $o ).
thf(op_implies_or_decl,type,
op_implies_or: $o ).
thf(or_1_decl,type,
or_1: $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(and_2_decl,type,
and_2: $o ).
thf(implies_1_decl,type,
implies_1: $o ).
thf(and_1_decl,type,
and_1: $o ).
thf(and_3_decl,type,
and_3: $o ).
thf(equivalence_1_decl,type,
equivalence_1: $o ).
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(kn2_decl,type,
kn2: $o ).
thf(r2_decl,type,
r2: $o ).
thf(kn1_decl,type,
kn1: $o ).
thf(r1_decl,type,
r1: $o ).
thf(r3_decl,type,
r3: $o ).
thf(cn3_decl,type,
cn3: $o ).
thf(cn1_decl,type,
cn1: $o ).
thf(cn2_decl,type,
cn2: $o ).
thf(kn3_decl,type,
kn3: $o ).
thf(r5_decl,type,
r5: $o ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk24_decl,type,
sk24: $i ).
thf(sk27_decl,type,
sk27: $i ).
thf(sk28_decl,type,
sk28: $i ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( sk3 @ ( A @ ( sk3 @ and ) @ implies ) @ is_a_theorem ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( A @ ( sk10 @ or ) @ ( A @ implies ) @ is_a_theorem ) ) ) ).
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(sk27_def,definition,
( sk27
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( @+[A: $i] :
~ ( ( ( A @ ( sk27 @ implies ) @ is_a_theorem )
& ( sk27 @ is_a_theorem ) )
=> ( A @ is_a_theorem ) ) ) ) ).
thf(51,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(185,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)],[51]) ).
thf(36,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(121,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)],[36]) ).
thf(47,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(169,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)],[47]) ).
thf(6,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
thf(59,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(80,plain,
and_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(39,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(133,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)],[39]) ).
thf(134,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)],[133]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents ),
inference(cnfConj,[status(thm)],[134]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ substitution_of_equivalents
| ( A = B ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(12,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(67,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ~ $true
| ( A = B ) ),
inference(rewrite,[status(thm)],[138,67]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equiv ) @ is_a_theorem )
| ( A = B ) ),
inference(simp,[status(thm)],[211]) ).
thf(41,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(144,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)],[41]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( modus_ponens
| ~ ( sk28 @ is_a_theorem ) )
& ( modus_ponens
| ( sk28 @ ( sk27 @ implies ) @ is_a_theorem ) )
& ( modus_ponens
| ( sk27 @ is_a_theorem ) )
& ( ( B @ is_a_theorem )
| ~ ( B @ ( A @ implies ) @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ modus_ponens ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,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)],[145]) ).
thf(201,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)],[146]) ).
thf(202,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)],[201]) ).
thf(215,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 )
| ~ modus_ponens
| ( D @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[212,202]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( A )),bind(B,$thf( F @ ( E @ implies ) )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[216]) ).
thf(16,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
thf(71,plain,
modus_ponens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ~ $true
| ( C @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[251,71]) ).
thf(342,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)],[341]) ).
thf(1,conjecture,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
thf(2,negated_conjecture,
~ r4,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(55,plain,
~ r4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( D @ ( C @ implies ) ) )
| ( D @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ modus_ponens
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[212,146]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( F @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[238]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ $true
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[248,71]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[261]) ).
thf(22,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
thf(79,plain,
implies_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
thf(68,plain,
implies_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
thf(69,plain,
modus_tollens,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,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(101,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)],[31]) ).
thf(3,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
thf(56,plain,
op_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,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(153,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)],[43]) ).
thf(37,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(125,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)],[37]) ).
thf(44,axiom,
( cn3
<=> ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(157,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)],[44]) ).
thf(52,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(189,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)],[52]) ).
thf(29,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(93,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)],[29]) ).
thf(4,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)],[4]) ).
thf(21,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
thf(78,plain,
and_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(32,axiom,
( r2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(105,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)],[32]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( r2
| ~ ( sk11 @ ( sk10 @ or ) @ ( sk11 @ implies ) @ is_a_theorem ) )
& ( ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem )
| ~ r2 ) ),
inference(cnf,[status(esa)],[105]) ).
thf(108,plain,
( r2
| ~ ( sk11 @ ( sk10 @ or ) @ ( sk11 @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[106]) ).
thf(20,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(75,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) )
| ~ op_or ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(7,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(60,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(rewrite,[status(thm)],[77,60]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ),
inference(simp,[status(thm)],[301]) ).
thf(397,plain,
( r2
| ~ ( sk11 @ not @ ( sk10 @ not @ and ) @ not @ ( sk11 @ implies ) @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[108,302]) ).
thf(8,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(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)],[8]) ).
thf(19,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(74,plain,
or_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
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(5,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(58,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ) ),
inference(rewrite,[status(thm)],[63,58]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equiv ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(28,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(89,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)],[28]) ).
thf(26,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
thf(85,plain,
equivalence_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,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(117,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)],[35]) ).
thf(15,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
thf(70,plain,
or_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(46,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(165,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)],[46]) ).
thf(54,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(197,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)],[54]) ).
thf(10,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(65,plain,
or_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,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(97,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)],[30]) ).
thf(33,axiom,
( kn1
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(109,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)],[33]) ).
thf(53,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(193,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)],[53]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( kn2
| ~ ( sk3 @ ( sk4 @ ( sk3 @ and ) @ implies ) @ is_a_theorem ) )
& ( ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem )
| ~ kn2 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(96,plain,
( kn2
| ~ ( sk3 @ ( sk4 @ ( sk3 @ and ) @ implies ) @ is_a_theorem ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(48,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(173,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)],[48]) ).
thf(38,axiom,
( r1
<=> ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(129,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)],[38]) ).
thf(18,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(73,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,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(161,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)],[45]) ).
thf(9,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(64,plain,
equivalence_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,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(181,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)],[50]) ).
thf(27,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(86,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,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(113,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)],[34]) ).
thf(24,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(81,plain,
and_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,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(140,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)],[40]) ).
thf(25,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(82,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) )
| ~ op_and ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ op_and
| ( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ and ) )
= ( B @ not @ not @ ( A @ not @ not @ and ) @ not @ not ) ) ),
inference(rewrite,[status(thm)],[84,56,302]) ).
thf(441,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ not @ ( A @ not @ not @ and ) @ not @ not ) ),
inference(simp,[status(thm)],[440]) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ and ) )
!= ( D @ not @ not @ ( C @ not @ not @ and ) ) )
| ( ( B @ not @ not @ ( A @ not @ not @ and ) @ not @ not @ not @ not )
= ( D @ ( C @ and ) ) ) ),
inference(paramod_ordered,[status(thm)],[441,441]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( B @ not @ not @ not @ not @ ( A @ not @ not @ not @ not @ and ) @ not @ not @ not @ not )
= ( B @ ( A @ and ) ) ),
inference(pattern_uni,[status(thm)],[486:[bind(A,$thf( F @ not @ not )),bind(B,$thf( H @ not @ not )),bind(C,$thf( F )),bind(D,$thf( H ))]]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( B @ not @ not @ not @ not @ ( A @ not @ not @ not @ not @ and ) @ not @ not @ not @ not )
= ( B @ ( A @ and ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(11,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
thf(66,plain,
implies_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( D @ ( C @ implies ) ) )
| ( D @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( C @ is_a_theorem )
| ~ modus_ponens
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[212,146]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( A )),bind(B,$thf( F @ ( E @ implies ) )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[240]) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ $true
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[249,71]) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ is_a_theorem )
| ~ ( C @ ( B @ implies ) @ ( A @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[281]) ).
thf(42,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(150,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(49,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(177,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)],[49]) ).
thf(17,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
thf(72,plain,
equivalence_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(213,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 )
| ~ modus_ponens
| ( D @ is_a_theorem )
| ~ ( B @ ( A @ equiv ) @ is_a_theorem ) ),
inference(paramod_ordered,[status(thm)],[212,202]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ( C @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( F @ ( E @ implies ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ~ modus_ponens
| ( C @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[214]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ~ ( B @ is_a_theorem )
| ~ $true
| ( C @ is_a_theorem )
| ~ ( A @ ( C @ ( B @ implies ) @ equiv ) @ is_a_theorem ) ),
inference(rewrite,[status(thm)],[250,71]) ).
thf(314,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)],[313]) ).
thf(4282,plain,
$false,
inference(e,[status(thm)],[185,121,169,59,80,342,55,262,79,68,69,101,56,153,125,157,189,93,57,78,397,61,74,206,89,133,85,60,117,302,70,165,197,65,97,109,193,212,96,173,129,73,105,161,64,71,144,181,86,113,81,140,520,66,282,150,67,177,441,72,314,75,58,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL457+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 22:35:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.85/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.19 % [INFO] Parsing done (223ms).
% 1.52/1.21 % [INFO] Running in sequential loop mode.
% 2.01/1.60 % [INFO] eprover registered as external prover.
% 2.20/1.60 % [INFO] Scanning for conjecture ...
% 2.20/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 52 axioms. Running axiom selection ...
% 2.37/1.76 % [INFO] Axiom selection finished. Selected 52 axioms (removed 0 axioms).
% 2.55/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.55/1.85 % [INFO] Type checking passed.
% 2.55/1.86 % [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 ...
% 27.60/6.72 % External prover 'e' found a proof!
% 27.60/6.72 % [INFO] Killing All external provers ...
% 27.60/6.72 % Time passed: 6185ms (effective reasoning time: 5508ms)
% 27.60/6.72 % 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)>
% 27.60/6.72 % Axioms used in derivation (52): or_3, and_1, cn1, op_equiv, kn2, hilbert_implies_1, kn1, op_and, hilbert_and_2, op_implies_and, cn3, hilbert_and_1, substitution_of_equivalents, principia_op_and, equivalence_2, cn2, hilbert_and_3, hilbert_op_implies_and, equivalence_3, modus_tollens, hilbert_or_1, r5, kn3, hilbert_or_2, hilbert_implies_2, and_3, or_1, principia_op_equiv, use_substitution_of_equivalents, r4, modus_ponens, hilbert_modus_tollens, hilbert_op_or, hilbert_equivalence_2, r1, implies_3, hilbert_equivalence_3, hilbert_modus_ponens, hilbert_implies_3, r2, equivalence_1, or_2, hilbert_equivalence_1, hilbert_or_3, implies_1, r3, and_2, op_or, op_implies_or, hilbert_op_equiv, implies_2, principia_op_implies_or
% 27.60/6.72 % No. of inferences in proof: 157
% 27.60/6.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6185 ms resp. 5508 ms w/o parsing
% 27.60/6.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.60/6.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------