TSTP Solution File: LCL558+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:30:42 EDT 2023
% Result : Theorem 5.92s 2.30s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 141
% Syntax : Number of formulae : 217 ( 36 unt; 67 typ; 0 def)
% Number of atoms : 384 ( 21 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1385 ( 2 ~; 0 |; 57 &;1149 @)
% ( 48 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 67 usr; 58 con; 0-2 aty)
% Number of variables : 308 ( 0 ^; 308 !; 0 ?; 308 :)
% Comments :
%------------------------------------------------------------------------------
thf(or_1_type,type,
or_1: $o ).
thf(axiom_m4_type,type,
axiom_m4: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(op_strict_implies_type,type,
op_strict_implies: $o ).
thf(axiom_m1_type,type,
axiom_m1: $o ).
thf(axiom_m3_type,type,
axiom_m3: $o ).
thf(op_strict_equiv_type,type,
op_strict_equiv: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(op_possibly_type,type,
op_possibly: $o ).
thf(axiom_m5_type,type,
axiom_m5: $o ).
thf(axiom_m2_type,type,
axiom_m2: $o ).
thf(strict_implies_type,type,
strict_implies: $i > $i > $i ).
thf(necessarily_type,type,
necessarily: $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(and_type,type,
and: $i > $i > $i ).
thf(substitution_strict_equiv_type,type,
substitution_strict_equiv: $o ).
thf(axiom_m10_type,type,
axiom_m10: $o ).
thf(possibly_type,type,
possibly: $i > $i ).
thf(axiom_s2_type,type,
axiom_s2: $o ).
thf(not_type,type,
not: $i > $i ).
thf(axiom_s3_type,type,
axiom_s3: $o ).
thf(equiv_type,type,
equiv: $i > $i > $i ).
thf(modus_ponens_strict_implies_type,type,
modus_ponens_strict_implies: $o ).
thf(op_necessarily_type,type,
op_necessarily: $o ).
thf(adjunction_type,type,
adjunction: $o ).
thf(strict_equiv_type,type,
strict_equiv: $i > $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(axiom_m7_type,type,
axiom_m7: $o ).
thf(axiom_M_type,type,
axiom_M: $o ).
thf(and_2_type,type,
and_2: $o ).
thf(axiom_K_type,type,
axiom_K: $o ).
thf(axiom_4_type,type,
axiom_4: $o ).
thf(axiom_5_type,type,
axiom_5: $o ).
thf(modus_tollens_type,type,
modus_tollens: $o ).
thf(kn2_type,type,
kn2: $o ).
thf(axiom_m9_type,type,
axiom_m9: $o ).
thf(or_3_type,type,
or_3: $o ).
thf(and_3_type,type,
and_3: $o ).
thf(axiom_m6_type,type,
axiom_m6: $o ).
thf(cn2_type,type,
cn2: $o ).
thf(necessitation_type,type,
necessitation: $o ).
thf(kn3_type,type,
kn3: $o ).
thf(axiom_s4_type,type,
axiom_s4: $o ).
thf(r4_type,type,
r4: $o ).
thf(axiom_m8_type,type,
axiom_m8: $o ).
thf(r2_type,type,
r2: $o ).
thf(kn1_type,type,
kn1: $o ).
thf(implies_3_type,type,
implies_3: $o ).
thf(axiom_B_type,type,
axiom_B: $o ).
thf(equivalence_2_type,type,
equivalence_2: $o ).
thf(and_1_type,type,
and_1: $o ).
thf(implies_2_type,type,
implies_2: $o ).
thf(r3_type,type,
r3: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(equivalence_3_type,type,
equivalence_3: $o ).
thf(cn3_type,type,
cn3: $o ).
thf(equivalence_1_type,type,
equivalence_1: $o ).
thf(implies_1_type,type,
implies_1: $o ).
thf(cn1_type,type,
cn1: $o ).
thf(axiom_s1_type,type,
axiom_s1: $o ).
thf(or_2_type,type,
or_2: $o ).
thf(r1_type,type,
r1: $o ).
thf(op_and_type,type,
op_and: $o ).
thf(r5_type,type,
r5: $o ).
thf(39,axiom,
( axiom_5
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( possibly @ A ) @ ( necessarily @ ( possibly @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(153,plain,
( ( axiom_5
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( possibly @ A ) @ ( necessarily @ ( possibly @ A ) ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( possibly @ A ) @ ( necessarily @ ( possibly @ A ) ) ) )
=> axiom_5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
( cn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(174,plain,
( ( cn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) )
=> cn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(11,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(85,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,axiom,
( or_3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_3) ).
thf(165,plain,
( ( or_3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) )
=> or_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(19,axiom,
( axiom_m1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ A @ B ) @ ( and @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
thf(97,plain,
( ( axiom_m1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ A @ B ) @ ( and @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ A @ B ) @ ( and @ B @ A ) ) )
=> axiom_m1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(129,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
( axiom_4
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ A ) @ ( necessarily @ ( necessarily @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(150,plain,
( ( axiom_4
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ A ) @ ( necessarily @ ( necessarily @ A ) ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ A ) @ ( necessarily @ ( necessarily @ A ) ) ) )
=> axiom_4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,axiom,
( axiom_m6
<=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ A @ ( possibly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m6) ).
thf(171,plain,
( ( axiom_m6
=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ A @ ( possibly @ A ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( strict_implies @ A @ ( possibly @ A ) ) )
=> axiom_m6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(34,axiom,
( axiom_m2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
thf(138,plain,
( ( axiom_m2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ A @ B ) @ A ) )
=> axiom_m2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(14,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)],[14]) ).
thf(25,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
thf(115,plain,
modus_ponens_strict_implies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(68,axiom,
( cn1
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
thf(247,plain,
( ( cn1
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
=> cn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(55,axiom,
( axiom_B
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( necessarily @ ( possibly @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_B) ).
thf(202,plain,
( ( axiom_B
=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( necessarily @ ( possibly @ A ) ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( necessarily @ ( possibly @ A ) ) ) )
=> axiom_B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(49,axiom,
( axiom_s4
<=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ A ) @ ( necessarily @ ( necessarily @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s4) ).
thf(184,plain,
( ( axiom_s4
=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ A ) @ ( necessarily @ ( necessarily @ A ) ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ A ) @ ( necessarily @ ( necessarily @ A ) ) ) )
=> axiom_s4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction) ).
thf(125,plain,
adjunction,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
( kn1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(196,plain,
( ( kn1
=> ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) )
=> kn1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(17,axiom,
( axiom_m5
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ A @ B ) @ ( strict_implies @ B @ C ) ) @ ( strict_implies @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5) ).
thf(93,plain,
( ( axiom_m5
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ A @ B ) @ ( strict_implies @ B @ C ) ) @ ( strict_implies @ A @ C ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ A @ B ) @ ( strict_implies @ B @ C ) ) @ ( strict_implies @ A @ C ) ) )
=> axiom_m5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
thf(78,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
( implies_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
thf(216,plain,
( ( implies_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) )
=> implies_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(70,axiom,
( or_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
thf(253,plain,
( ( or_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> or_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(22,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(106,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(65,axiom,
( cn3
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(238,plain,
( ( cn3
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) )
=> cn3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(10,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(84,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
( axiom_K
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ A @ B ) ) @ ( implies @ ( necessarily @ A ) @ ( necessarily @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_K) ).
thf(147,plain,
( ( axiom_K
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ A @ B ) ) @ ( implies @ ( necessarily @ A ) @ ( necessarily @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ A @ B ) ) @ ( implies @ ( necessarily @ A ) @ ( necessarily @ B ) ) ) )
=> axiom_K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
( axiom_m3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ A @ B ) @ C ) @ ( and @ A @ ( and @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m3) ).
thf(132,plain,
( ( axiom_m3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ A @ B ) @ C ) @ ( and @ A @ ( and @ B @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ A @ B ) @ C ) @ ( and @ A @ ( and @ B @ C ) ) ) )
=> axiom_m3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(15,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)],[15]) ).
thf(26,axiom,
( axiom_m4
<=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ A @ ( and @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
thf(116,plain,
( ( axiom_m4
=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ A @ ( and @ A @ A ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( strict_implies @ A @ ( and @ A @ A ) ) )
=> axiom_m4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(73,axiom,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
thf(265,plain,
( op_and
=> ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(40,axiom,
( modus_tollens
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
thf(156,plain,
( ( modus_tollens
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) )
=> modus_tollens ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(35,axiom,
( axiom_M
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
thf(141,plain,
( ( axiom_M
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ A ) @ A ) )
=> axiom_M ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
thf(77,plain,
axiom_m4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(52,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(193,plain,
( ( r2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> r2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(18,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
thf(96,plain,
substitution_strict_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
( axiom_s3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ A @ B ) @ ( strict_implies @ ( not @ ( possibly @ B ) ) @ ( not @ ( possibly @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s3) ).
thf(109,plain,
( ( axiom_s3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ A @ B ) @ ( strict_implies @ ( not @ ( possibly @ B ) ) @ ( not @ ( possibly @ A ) ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ A @ B ) @ ( strict_implies @ ( not @ ( possibly @ B ) ) @ ( not @ ( possibly @ A ) ) ) ) )
=> axiom_s3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(71,axiom,
( substitution_strict_equiv
<=> ! [A: $i,B: $i] :
( ( is_a_theorem @ ( strict_equiv @ A @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
thf(256,plain,
( ( substitution_strict_equiv
=> ! [A: $i,B: $i] :
( ( is_a_theorem @ ( strict_equiv @ A @ B ) )
=> ( A = B ) ) )
& ( ! [A: $i,B: $i] :
( ( is_a_theorem @ ( strict_equiv @ A @ B ) )
=> ( A = B ) )
=> substitution_strict_equiv ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(67,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
thf(244,plain,
( ( implies_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
=> implies_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(56,axiom,
( adjunction
<=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ B ) )
=> ( is_a_theorem @ ( and @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction) ).
thf(205,plain,
( ( adjunction
=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ B ) )
=> ( is_a_theorem @ ( and @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ B ) )
=> ( is_a_theorem @ ( and @ A @ B ) ) )
=> adjunction ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(36,axiom,
( and_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
thf(144,plain,
( ( and_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) )
=> and_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(48,axiom,
( kn3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
thf(181,plain,
( ( kn3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) )
=> kn3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(12,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)],[12]) ).
thf(41,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(159,plain,
( ( kn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> kn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
( r4
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(187,plain,
( ( r4
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
=> r4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(60,axiom,
( r3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
thf(219,plain,
( ( r3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
=> r3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,axiom,
axiom_m3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m3) ).
thf(81,plain,
axiom_m3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(2,negated_conjecture,
~ or_1,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(76,plain,
~ or_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(75,axiom,
( or_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
thf(271,plain,
( ( or_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) )
=> or_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(21,axiom,
( axiom_s2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ A @ B ) ) @ ( and @ ( possibly @ A ) @ ( possibly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s2) ).
thf(103,plain,
( ( axiom_s2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ A @ B ) ) @ ( and @ ( possibly @ A ) @ ( possibly @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ A @ B ) ) @ ( and @ ( possibly @ A ) @ ( possibly @ B ) ) ) )
=> axiom_s2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(58,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
thf(213,plain,
( ( and_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> and_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(33,axiom,
( axiom_m7
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ A @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m7) ).
thf(135,plain,
( ( axiom_m7
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ A @ B ) ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ A @ B ) ) @ A ) )
=> axiom_m7 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
( equivalence_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
thf(241,plain,
( ( equivalence_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) )
=> equivalence_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(6,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
thf(80,plain,
axiom_m1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
( axiom_m9
<=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ A ) ) @ ( possibly @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m9) ).
thf(162,plain,
( ( axiom_m9
=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ A ) ) @ ( possibly @ A ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ A ) ) @ ( possibly @ A ) ) )
=> axiom_m9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
thf(112,plain,
( op_equiv
=> ! [A: $i,B: $i] :
( ( equiv @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(54,axiom,
( implies_3
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
thf(199,plain,
( ( implies_3
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
=> implies_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(47,axiom,
( necessitation
<=> ! [A: $i] :
( ( is_a_theorem @ A )
=> ( is_a_theorem @ ( necessarily @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
thf(177,plain,
( ( necessitation
=> ! [A: $i] :
( ( is_a_theorem @ A )
=> ( is_a_theorem @ ( necessarily @ A ) ) ) )
& ( ! [A: $i] :
( ( is_a_theorem @ A )
=> ( is_a_theorem @ ( necessarily @ A ) ) )
=> necessitation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(69,axiom,
( axiom_s1
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ A @ B ) ) @ ( necessarily @ ( implies @ B @ C ) ) ) @ ( necessarily @ ( implies @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s1) ).
thf(250,plain,
( ( axiom_s1
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ A @ B ) ) @ ( necessarily @ ( implies @ B @ C ) ) ) @ ( necessarily @ ( implies @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ A @ B ) ) @ ( necessarily @ ( implies @ B @ C ) ) ) @ ( necessarily @ ( implies @ A @ C ) ) ) )
=> axiom_s1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(13,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)],[13]) ).
thf(27,axiom,
( op_possibly
=> ! [A: $i] :
( ( possibly @ A )
= ( not @ ( necessarily @ ( not @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_possibly) ).
thf(119,plain,
( op_possibly
=> ! [A: $i] :
( ( possibly @ A )
= ( not @ ( necessarily @ ( not @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(64,axiom,
( equivalence_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
thf(235,plain,
( ( equivalence_3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) )
=> equivalence_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(8,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
thf(82,plain,
op_strict_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,axiom,
( axiom_m8
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ A @ B ) @ ( strict_implies @ ( possibly @ A ) @ ( possibly @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m8) ).
thf(190,plain,
( ( axiom_m8
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ A @ B ) @ ( strict_implies @ ( possibly @ A ) @ ( possibly @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ A @ B ) @ ( strict_implies @ ( possibly @ A ) @ ( possibly @ B ) ) ) )
=> axiom_m8 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
( and_3
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
thf(168,plain,
( ( and_3
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) )
=> and_3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(72,axiom,
( r1
<=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(262,plain,
( ( r1
=> ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) )
=> r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(57,axiom,
( equivalence_2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
thf(210,plain,
( ( equivalence_2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) )
=> equivalence_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,axiom,
( op_strict_equiv
=> ! [A: $i,B: $i] :
( ( strict_equiv @ A @ B )
= ( and @ ( strict_implies @ A @ B ) @ ( strict_implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
thf(126,plain,
( op_strict_equiv
=> ! [A: $i,B: $i] :
( ( strict_equiv @ A @ B )
= ( and @ ( strict_implies @ A @ B ) @ ( strict_implies @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,axiom,
( r5
<=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(268,plain,
( ( r5
=> ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) )
& ( ! [A: $i,B: $i,C: $i] : ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) )
=> r5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(5,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
thf(79,plain,
op_strict_implies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
( op_strict_implies
=> ! [A: $i,B: $i] :
( ( strict_implies @ A @ B )
= ( necessarily @ ( implies @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
thf(90,plain,
( op_strict_implies
=> ! [A: $i,B: $i] :
( ( strict_implies @ A @ B )
= ( necessarily @ ( implies @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(62,axiom,
( modus_ponens
<=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
thf(227,plain,
( ( modus_ponens
=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) )
& ( ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) )
=> modus_ponens ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(28,axiom,
( op_necessarily
=> ! [A: $i] :
( ( necessarily @ A )
= ( not @ ( possibly @ ( not @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_necessarily) ).
thf(122,plain,
( op_necessarily
=> ! [A: $i] :
( ( necessarily @ A )
= ( not @ ( possibly @ ( not @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(9,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
thf(83,plain,
op_equiv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(61,axiom,
( modus_ponens_strict_implies
<=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( strict_implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
thf(222,plain,
( ( modus_ponens_strict_implies
=> ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( strict_implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) ) )
& ( ! [A: $i,B: $i] :
( ( ( is_a_theorem @ A )
& ( is_a_theorem @ ( strict_implies @ A @ B ) ) )
=> ( is_a_theorem @ B ) )
=> modus_ponens_strict_implies ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(63,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(232,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(20,axiom,
( axiom_m10
<=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ A ) @ ( necessarily @ ( possibly @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m10) ).
thf(100,plain,
( ( axiom_m10
=> ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ A ) @ ( necessarily @ ( possibly @ A ) ) ) ) )
& ( ! [A: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ A ) @ ( necessarily @ ( possibly @ A ) ) ) )
=> axiom_m10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(304,plain,
$false,
inference(e,[status(thm)],[153,174,85,165,97,129,150,171,138,88,115,247,202,184,125,196,93,78,216,253,106,238,84,147,132,89,116,265,156,141,77,193,96,109,256,244,205,144,181,86,159,187,219,81,76,271,103,213,135,241,80,162,112,199,177,250,87,119,235,82,190,168,262,210,126,268,79,90,227,122,83,222,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 15:57:33 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/0.94 % [INFO] Parsing done (148ms).
% 1.33/0.95 % [INFO] Running in sequential loop mode.
% 1.80/1.15 % [INFO] eprover registered as external prover.
% 1.80/1.15 % [INFO] cvc4 registered as external prover.
% 1.80/1.15 % [INFO] Scanning for conjecture ...
% 1.88/1.22 % [INFO] Found a conjecture and 76 axioms. Running axiom selection ...
% 2.15/1.29 % [INFO] Axiom selection finished. Selected 73 axioms (removed 3 axioms).
% 2.47/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.47/1.38 % [INFO] Type checking passed.
% 2.47/1.38 % [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 ...
% 5.92/2.30 % External prover 'e' found a proof!
% 5.92/2.30 % [INFO] Killing All external provers ...
% 5.92/2.30 % Time passed: 1780ms (effective reasoning time: 1348ms)
% 5.92/2.30 % 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)>
% 5.92/2.30 % Axioms used in derivation (73): op_equiv, kn2, s1_0_axiom_m5, s1_0_axiom_m2, kn1, op_necessarily, op_possibly, modus_ponens_strict_implies, s1_0_axiom_m4, 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, 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, op_or, op_implies_or, hilbert_op_equiv, necessitation, axiom_4, op_strict_implies, substitution_strict_equiv, implies_2
% 5.92/2.30 % No. of inferences in proof: 150
% 5.92/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1780 ms resp. 1348 ms w/o parsing
% 5.92/2.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.92/2.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------