%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL562+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 07:52:06 AM UTC 2026
% Result : Theorem 25.61s 8.39s
% Output : Refutation 26.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 76
% Syntax : Number of formulae : 154 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 395 ( 24 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1401 ( 2 ~; 0 |; 58 &;1158 @)
% ( 49 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 68 usr; 59 con; 0-2 aty)
% Number of variables : 314 ( 0 ^; 314 !; 0 ?; 314 :)
% Comments :
%------------------------------------------------------------------------------
thf(equivalence_2_decl,type,
equivalence_2: $o ).
thf(axiom_m4_decl,type,
axiom_m4: $o ).
thf(op_or_decl,type,
op_or: $o ).
thf(op_strict_implies_decl,type,
op_strict_implies: $o ).
thf(axiom_m1_decl,type,
axiom_m1: $o ).
thf(axiom_m3_decl,type,
axiom_m3: $o ).
thf(op_strict_equiv_decl,type,
op_strict_equiv: $o ).
thf(op_implies_and_decl,type,
op_implies_and: $o ).
thf(op_possibly_decl,type,
op_possibly: $o ).
thf(axiom_m5_decl,type,
axiom_m5: $o ).
thf(axiom_m2_decl,type,
axiom_m2: $o ).
thf(strict_implies_decl,type,
strict_implies: $i > $i > $i ).
thf(necessarily_decl,type,
necessarily: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(substitution_strict_equiv_decl,type,
substitution_strict_equiv: $o ).
thf(op_equiv_decl,type,
op_equiv: $o ).
thf(substitution_of_equivalents_decl,type,
substitution_of_equivalents: $o ).
thf(axiom_m10_decl,type,
axiom_m10: $o ).
thf(possibly_decl,type,
possibly: $i > $i ).
thf(axiom_s2_decl,type,
axiom_s2: $o ).
thf(not_decl,type,
not: $i > $i ).
thf(axiom_s3_decl,type,
axiom_s3: $o ).
thf(modus_ponens_strict_implies_decl,type,
modus_ponens_strict_implies: $o ).
thf(op_necessarily_decl,type,
op_necessarily: $o ).
thf(adjunction_decl,type,
adjunction: $o ).
thf(strict_equiv_decl,type,
strict_equiv: $i > $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(axiom_m7_decl,type,
axiom_m7: $o ).
thf(op_and_decl,type,
op_and: $o ).
thf(equiv_decl,type,
equiv: $i > $i > $i ).
thf(axiom_M_decl,type,
axiom_M: $o ).
thf(and_2_decl,type,
and_2: $o ).
thf(axiom_K_decl,type,
axiom_K: $o ).
thf(axiom_4_decl,type,
axiom_4: $o ).
thf(axiom_5_decl,type,
axiom_5: $o ).
thf(modus_tollens_decl,type,
modus_tollens: $o ).
thf(kn2_decl,type,
kn2: $o ).
thf(axiom_m9_decl,type,
axiom_m9: $o ).
thf(or_3_decl,type,
or_3: $o ).
thf(and_3_decl,type,
and_3: $o ).
thf(axiom_m6_decl,type,
axiom_m6: $o ).
thf(cn2_decl,type,
cn2: $o ).
thf(necessitation_decl,type,
necessitation: $o ).
thf(kn3_decl,type,
kn3: $o ).
thf(axiom_s4_decl,type,
axiom_s4: $o ).
thf(r4_decl,type,
r4: $o ).
thf(axiom_m8_decl,type,
axiom_m8: $o ).
thf(r2_decl,type,
r2: $o ).
thf(kn1_decl,type,
kn1: $o ).
thf(implies_3_decl,type,
implies_3: $o ).
thf(axiom_B_decl,type,
axiom_B: $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(modus_ponens_decl,type,
modus_ponens: $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(axiom_s1_decl,type,
axiom_s1: $o ).
thf(or_2_decl,type,
or_2: $o ).
thf(or_1_decl,type,
or_1: $o ).
thf(r5_decl,type,
r5: $o ).
thf(66,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(282,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(27,axiom,
( op_necessarily
=> ! [A: $i] :
( ( A @ necessarily )
= ( A @ not @ possibly @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_necessarily) ).
thf(127,plain,
( op_necessarily
=> ! [A: $i] :
( ( A @ necessarily )
= ( A @ not @ possibly @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(32,axiom,
( axiom_m3
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( B @ and ) @ ( A @ and ) @ ( C @ ( B @ ( A @ and ) @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m3) ).
thf(138,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( B @ and ) @ ( A @ and ) @ ( C @ ( B @ ( A @ and ) @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m3 )
& ( axiom_m3
=> ! [A: $i,B: $i,C: $i] : ( C @ ( B @ and ) @ ( A @ and ) @ ( C @ ( B @ ( A @ and ) @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(12,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
thf(88,plain,
axiom_m2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
( axiom_s3
<=> ! [A: $i,B: $i] : ( A @ possibly @ not @ ( B @ possibly @ not @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s3) ).
thf(115,plain,
( ( ! [A: $i,B: $i] : ( A @ possibly @ not @ ( B @ possibly @ not @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem )
=> axiom_s3 )
& ( axiom_s3
=> ! [A: $i,B: $i] : ( A @ possibly @ not @ ( B @ possibly @ not @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(52,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(217,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)],[52]) ).
thf(65,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(276,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)],[65]) ).
thf(25,axiom,
( axiom_m4
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
thf(120,plain,
( ( ! [A: $i] : ( A @ ( A @ and ) @ ( A @ strict_implies ) @ is_a_theorem )
=> axiom_m4 )
& ( axiom_m4
=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(59,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(247,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)],[59]) ).
thf(33,axiom,
( axiom_m7
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m7) ).
thf(142,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_m7 )
& ( axiom_m7
=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(36,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(153,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)],[36]) ).
thf(71,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(301,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)],[71]) ).
thf(75,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(320,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)],[75]) ).
thf(44,axiom,
( axiom_m9
<=> ! [A: $i] : ( A @ possibly @ ( A @ possibly @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m9) ).
thf(184,plain,
( ( ! [A: $i] : ( A @ possibly @ ( A @ possibly @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_m9 )
& ( axiom_m9
=> ! [A: $i] : ( A @ possibly @ ( A @ possibly @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(47,axiom,
( axiom_m6
<=> ! [A: $i] : ( A @ possibly @ ( A @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m6) ).
thf(196,plain,
( ( ! [A: $i] : ( A @ possibly @ ( A @ strict_implies ) @ is_a_theorem )
=> axiom_m6 )
& ( axiom_m6
=> ! [A: $i] : ( A @ possibly @ ( A @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(15,axiom,
( axiom_m5
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ strict_implies ) @ ( C @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5) ).
thf(93,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ strict_implies ) @ ( C @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m5 )
& ( axiom_m5
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ strict_implies ) @ ( C @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(68,axiom,
( cn3
<=> ! [A: $i] : ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(289,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)],[68]) ).
thf(1,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(2,negated_conjecture,
~ equivalence_2,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(78,plain,
~ equivalence_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,axiom,
( axiom_K
<=> ! [A: $i,B: $i] : ( B @ necessarily @ ( A @ necessarily @ implies ) @ ( B @ ( A @ implies ) @ necessarily @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_K) ).
thf(164,plain,
( ( ! [A: $i,B: $i] : ( B @ necessarily @ ( A @ necessarily @ implies ) @ ( B @ ( A @ implies ) @ necessarily @ implies ) @ is_a_theorem )
=> axiom_K )
& ( axiom_K
=> ! [A: $i,B: $i] : ( B @ necessarily @ ( A @ necessarily @ implies ) @ ( B @ ( A @ implies ) @ necessarily @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(8,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
thf(84,plain,
op_strict_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,axiom,
( axiom_m8
<=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m8) ).
thf(221,plain,
( ( ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem )
=> axiom_m8 )
& ( axiom_m8
=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(69,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(293,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)],[69]) ).
thf(13,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(89,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(56,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(233,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)],[56]) ).
thf(64,axiom,
( modus_ponens_strict_implies
<=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ strict_implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ( ( B @ ( A @ strict_implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) )
=> modus_ponens_strict_implies )
& ( modus_ponens_strict_implies
=> ! [A: $i,B: $i] :
( ( ( B @ ( A @ strict_implies ) @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(9,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(85,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,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(160,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)],[38]) ).
thf(70,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(297,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)],[70]) ).
thf(46,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(192,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)],[46]) ).
thf(31,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
thf(137,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55,axiom,
( kn1
<=> ! [A: $i] : ( A @ ( A @ and ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(229,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)],[55]) ).
thf(16,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
thf(97,plain,
substitution_strict_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(76,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(324,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)],[76]) ).
thf(67,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(285,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)],[67]) ).
thf(37,axiom,
( axiom_M
<=> ! [A: $i] : ( A @ ( A @ necessarily @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
thf(156,plain,
( ( ! [A: $i] : ( A @ ( A @ necessarily @ implies ) @ is_a_theorem )
=> axiom_M )
& ( axiom_M
=> ! [A: $i] : ( A @ ( A @ necessarily @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(45,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(188,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)],[45]) ).
thf(77,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(328,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)],[77]) ).
thf(26,axiom,
( op_possibly
=> ! [A: $i] :
( ( A @ possibly )
= ( A @ not @ necessarily @ not ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_possibly) ).
thf(124,plain,
( op_possibly
=> ! [A: $i] :
( ( A @ possibly )
= ( A @ not @ necessarily @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
( r2
<=> ! [A: $i,B: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(225,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)],[54]) ).
thf(30,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(134,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( B @ ( A @ or ) )
= ( B @ not @ ( A @ not @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(57,axiom,
( axiom_B
<=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_B) ).
thf(237,plain,
( ( ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ implies ) @ is_a_theorem )
=> axiom_B )
& ( axiom_B
=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(63,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(266,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)],[63]) ).
thf(43,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(180,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)],[43]) ).
thf(35,axiom,
( axiom_m2
<=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
thf(149,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m2 )
& ( axiom_m2
=> ! [A: $i,B: $i] : ( A @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,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(176,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)],[42]) ).
thf(49,axiom,
( necessitation
<=> ! [A: $i] :
( ( A @ is_a_theorem )
=> ( A @ necessarily @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
thf(204,plain,
( ( ! [A: $i] :
( ( A @ is_a_theorem )
=> ( A @ necessarily @ is_a_theorem ) )
=> necessitation )
& ( necessitation
=> ! [A: $i] :
( ( A @ is_a_theorem )
=> ( A @ necessarily @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(62,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(259,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)],[62]) ).
thf(74,axiom,
( substitution_strict_equiv
<=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) @ is_a_theorem )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) @ is_a_theorem )
=> ( A = B ) )
=> substitution_strict_equiv )
& ( substitution_strict_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) @ is_a_theorem )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(10,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
thf(86,plain,
op_possibly,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
( axiom_5
<=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(172,plain,
( ( ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ implies ) @ is_a_theorem )
=> axiom_5 )
& ( axiom_5
=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
thf(81,plain,
op_strict_implies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(98,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(51,axiom,
( axiom_s4
<=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s4) ).
thf(213,plain,
( ( ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ strict_implies ) @ is_a_theorem )
=> axiom_s4 )
& ( axiom_s4
=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(60,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(251,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)],[60]) ).
thf(21,axiom,
( axiom_s2
<=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ and ) @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s2) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ and ) @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_s2 )
& ( axiom_s2
=> ! [A: $i,B: $i] : ( B @ possibly @ ( A @ possibly @ and ) @ ( B @ ( A @ and ) @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
thf(130,plain,
adjunction,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(58,axiom,
( adjunction
<=> ! [A: $i,B: $i] :
( ( ( B @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ ( A @ and ) @ is_a_theorem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ( ( B @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ ( A @ and ) @ is_a_theorem ) )
=> adjunction )
& ( adjunction
=> ! [A: $i,B: $i] :
( ( ( B @ is_a_theorem )
& ( A @ is_a_theorem ) )
=> ( B @ ( A @ and ) @ is_a_theorem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(4,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
thf(80,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,axiom,
( r1
<=> ! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(255,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)],[61]) ).
thf(50,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(209,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)],[50]) ).
thf(22,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(112,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ implies ) )
= ( B @ not @ ( A @ and ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(18,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
thf(99,plain,
substitution_of_equivalents,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
thf(87,plain,
axiom_m5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
( axiom_m10
<=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m10) ).
thf(104,plain,
( ( ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ strict_implies ) @ is_a_theorem )
=> axiom_m10 )
& ( axiom_m10
=> ! [A: $i] : ( A @ possibly @ necessarily @ ( A @ possibly @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
thf(119,plain,
modus_ponens_strict_implies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
thf(82,plain,
axiom_m1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
( axiom_4
<=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(168,plain,
( ( ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ implies ) @ is_a_theorem )
=> axiom_4 )
& ( axiom_4
=> ! [A: $i] : ( A @ necessarily @ necessarily @ ( A @ necessarily @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(34,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(146,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(72,axiom,
( axiom_s1
<=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ necessarily @ ( C @ ( B @ implies ) @ necessarily @ ( B @ ( A @ implies ) @ necessarily @ and ) @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s1) ).
thf(305,plain,
( ( ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ necessarily @ ( C @ ( B @ implies ) @ necessarily @ ( B @ ( A @ implies ) @ necessarily @ and ) @ implies ) @ is_a_theorem )
=> axiom_s1 )
& ( axiom_s1
=> ! [A: $i,B: $i,C: $i] : ( C @ ( A @ implies ) @ necessarily @ ( C @ ( B @ implies ) @ necessarily @ ( B @ ( A @ implies ) @ necessarily @ and ) @ implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(3,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
thf(79,plain,
axiom_m4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
( op_strict_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) )
= ( A @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
thf(131,plain,
( op_strict_equiv
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_equiv ) )
= ( A @ ( B @ strict_implies ) @ ( B @ ( A @ strict_implies ) @ and ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(48,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(200,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)],[48]) ).
thf(14,axiom,
( op_strict_implies
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_implies ) )
= ( B @ ( A @ implies ) @ necessarily ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
thf(90,plain,
( op_strict_implies
=> ! [A: $i,B: $i] :
( ( B @ ( A @ strict_implies ) )
= ( B @ ( A @ implies ) @ necessarily ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
axiom_m3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m3) ).
thf(83,plain,
axiom_m3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(73,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(309,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)],[73]) ).
thf(19,axiom,
( axiom_m1
<=> ! [A: $i,B: $i] : ( A @ ( B @ and ) @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
thf(100,plain,
( ( ! [A: $i,B: $i] : ( A @ ( B @ and ) @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem )
=> axiom_m1 )
& ( axiom_m1
=> ! [A: $i,B: $i] : ( A @ ( B @ and ) @ ( B @ ( A @ and ) @ strict_implies ) @ is_a_theorem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(637,plain,
$false,
inference(e,[status(thm)],[282,127,138,88,115,217,276,120,247,142,153,301,320,184,196,93,289,78,164,84,221,293,89,233,270,85,160,297,192,137,229,97,324,285,156,188,328,124,225,134,237,266,180,149,176,204,259,313,86,172,81,98,213,251,108,130,241,80,255,209,112,99,87,104,119,82,168,146,305,79,131,200,90,83,309,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL562+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
% 0.15/0.40 % Computer : n013.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 22:44:55 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.91/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.23 % [INFO] Parsing done (253ms).
% 1.57/1.25 % [INFO] Running in sequential loop mode.
% 2.52/1.65 % [INFO] eprover registered as external prover.
% 2.52/1.66 % [INFO] Scanning for conjecture ...
% 2.79/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 76 axioms. Running axiom selection ...
% 2.79/1.77 % [INFO] Axiom selection finished. Selected 75 axioms (removed 1 axioms).
% 3.10/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 3.10/1.86 % [INFO] Type checking passed.
% 3.10/1.86 % [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 ...
% 25.61/8.39 % External prover 'e' found a proof!
% 25.61/8.39 % [INFO] Killing All external provers ...
% 25.61/8.39 % Time passed: 7843ms (effective reasoning time: 7136ms)
% 25.61/8.39 % 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)>
% 25.61/8.39 % Axioms used in derivation (75): op_equiv, kn2, s1_0_axiom_m5, s1_0_axiom_m2, kn1, op_necessarily, op_possibly, modus_ponens_strict_implies, s1_0_modus_ponens_strict_implies, s1_0_op_strict_equiv, or_3, axiom_m9, axiom_s3, s1_0_axiom_m1, axiom_m3, and_1, axiom_K, adjunction, s1_0_substitution_strict_equiv, equivalence_2, axiom_m6, cn1, cn2, hilbert_op_implies_and, equivalence_3, axiom_s2, modus_tollens, s1_0_op_or, s1_0_adjunction, s1_0_op_strict_implies, op_and, axiom_m2, r5, or_1, kn3, axiom_B, and_3, s1_0_op_equiv, axiom_m5, use_substitution_of_equivalents, r4, modus_ponens, hilbert_op_or, axiom_M, axiom_m7, r1, axiom_s1, s1_0_axiom_m3, implies_3, axiom_m1, op_implies_and, op_strict_equiv, axiom_5, s1_0_op_possibly, cn3, r2, axiom_m4, equivalence_1, or_2, axiom_s4, axiom_m8, implies_1, r3, axiom_m10, and_2, substitution_of_equivalents, s1_0_axiom_m4, op_or, op_implies_or, hilbert_op_equiv, necessitation, axiom_4, op_strict_implies, substitution_strict_equiv, implies_2
% 25.61/8.39 % No. of inferences in proof: 154
% 25.61/8.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7843 ms resp. 7136 ms w/o parsing
% 26.08/8.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.08/8.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------