%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL523+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n003.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 : Mon Sep 7 11:12:06 AM UTC 2026
% Result : Theorem 34.08s 14.93s
% Output : CNFRefutation 34.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 37
% Syntax : Number of formulae : 158 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 129 ( 59 ~; 47 |; 1 &)
% ( 16 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 61 ( 59 usr; 59 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 158 ( 158 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > strict_implies > strict_equiv > or > implies > equiv > and > #nlpp > possibly > not > necessarily > substitution_strict_equiv > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_strict_implies > op_strict_equiv > op_possibly > op_or > op_necessarily > op_implies_or > op_implies_and > op_equiv > op_and > necessitation > modus_tollens > modus_ponens_strict_implies > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > axiom_s4 > axiom_s3 > axiom_s2 > axiom_s1 > axiom_m9 > axiom_m8 > axiom_m7 > axiom_m6 > axiom_m5 > axiom_m4 > axiom_m3 > axiom_m2 > axiom_m10 > axiom_m1 > axiom_M > axiom_K > axiom_B > axiom_5 > axiom_4 > and_3 > and_2 > and_1 > adjunction > #skF_33 > #skF_41 > #skF_60 > #skF_57 > #skF_52 > #skF_76 > #skF_67 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_78 > #skF_94 > #skF_11 > #skF_86 > #skF_31 > #skF_15 > #skF_69 > #skF_25 > #skF_55 > #skF_87 > #skF_38 > #skF_36 > #skF_80 > #skF_56 > #skF_54 > #skF_43 > #skF_79 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_71 > #skF_10 > #skF_16 > #skF_85 > #skF_47 > #skF_92 > #skF_65 > #skF_26 > #skF_81 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_72 > #skF_6 > #skF_13 > #skF_61 > #skF_2 > #skF_68 > #skF_82 > #skF_84 > #skF_3 > #skF_1 > #skF_89 > #skF_21 > #skF_9 > #skF_32 > #skF_64 > #skF_50 > #skF_90 > #skF_8 > #skF_30 > #skF_42 > #skF_77 > #skF_4 > #skF_22 > #skF_93 > #skF_29 > #skF_28 > #skF_35 > #skF_70 > #skF_66 > #skF_24 > #skF_27 > #skF_23 > #skF_63 > #skF_88 > #skF_44 > #skF_83 > #skF_59 > #skF_73 > #skF_91 > #skF_58 > #skF_12 > #skF_62 > #skF_34 > #skF_75 > #skF_74
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $o ).
tff(axiom_s1,type,
axiom_s1: $o ).
tff(equiv,type,
equiv: ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_41',type,
'#skF_41': $i ).
tff(r3,type,
r3: $o ).
tff('#skF_60',type,
'#skF_60': $i ).
tff(op_possibly,type,
op_possibly: $o ).
tff('#skF_57',type,
'#skF_57': $i ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_76',type,
'#skF_76': $i ).
tff(axiom_m8,type,
axiom_m8: $o ).
tff('#skF_67',type,
'#skF_67': $i ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $o ).
tff(axiom_4,type,
axiom_4: $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(op_implies_or,type,
op_implies_or: $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_78',type,
'#skF_78': $i ).
tff(adjunction,type,
adjunction: $o ).
tff('#skF_94',type,
'#skF_94': $i ).
tff(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_86',type,
'#skF_86': $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_69',type,
'#skF_69': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(axiom_m3,type,
axiom_m3: $o ).
tff(cn2,type,
cn2: $o ).
tff(axiom_K,type,
axiom_K: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff('#skF_87',type,
'#skF_87': $i ).
tff(possibly,type,
possibly: $i > $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_80',type,
'#skF_80': $i ).
tff(axiom_B,type,
axiom_B: $o ).
tff('#skF_56',type,
'#skF_56': $i ).
tff(op_strict_equiv,type,
op_strict_equiv: $o ).
tff('#skF_54',type,
'#skF_54': $i ).
tff(axiom_5,type,
axiom_5: $o ).
tff('#skF_43',type,
'#skF_43': $i ).
tff('#skF_79',type,
'#skF_79': $i ).
tff(op_and,type,
op_and: $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_40',type,
'#skF_40': $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_37',type,
'#skF_37': $i ).
tff(and_3,type,
and_3: $o ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(op_implies_and,type,
op_implies_and: $o ).
tff(op_strict_implies,type,
op_strict_implies: $o ).
tff('#skF_71',type,
'#skF_71': $i ).
tff(equivalence_1,type,
equivalence_1: $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(kn2,type,
kn2: $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_85',type,
'#skF_85': $i ).
tff(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff('#skF_92',type,
'#skF_92': $i ).
tff('#skF_65',type,
'#skF_65': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_81',type,
'#skF_81': $i ).
tff(necessitation,type,
necessitation: $o ).
tff('#skF_53',type,
'#skF_53': $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff(or_1,type,
or_1: $o ).
tff(implies_3,type,
implies_3: $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_45',type,
'#skF_45': $i ).
tff(axiom_s4,type,
axiom_s4: $o ).
tff('#skF_46',type,
'#skF_46': $i ).
tff('#skF_39',type,
'#skF_39': $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(modus_tollens,type,
modus_tollens: $o ).
tff('#skF_72',type,
'#skF_72': $i ).
tff(r2,type,
r2: $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(not,type,
not: $i > $i ).
tff('#skF_61',type,
'#skF_61': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_68',type,
'#skF_68': $i ).
tff(axiom_m2,type,
axiom_m2: $o ).
tff(modus_ponens,type,
modus_ponens: $o ).
tff('#skF_82',type,
'#skF_82': $i ).
tff('#skF_84',type,
'#skF_84': $i ).
tff(op_or,type,
op_or: $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(axiom_s3,type,
axiom_s3: $o ).
tff(substitution_strict_equiv,type,
substitution_strict_equiv: $o ).
tff(axiom_M,type,
axiom_M: $o ).
tff(strict_implies,type,
strict_implies: ( $i * $i ) > $i ).
tff('#skF_89',type,
'#skF_89': $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(necessarily,type,
necessarily: $i > $i ).
tff(axiom_m4,type,
axiom_m4: $o ).
tff('#skF_64',type,
'#skF_64': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_90',type,
'#skF_90': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(modus_ponens_strict_implies,type,
modus_ponens_strict_implies: $o ).
tff(axiom_m7,type,
axiom_m7: $o ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(axiom_s2,type,
axiom_s2: $o ).
tff('#skF_77',type,
'#skF_77': $i ).
tff(or_3,type,
or_3: $o ).
tff(op_necessarily,type,
op_necessarily: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(strict_equiv,type,
strict_equiv: ( $i * $i ) > $i ).
tff('#skF_93',type,
'#skF_93': $i ).
tff(kn1,type,
kn1: $o ).
tff(axiom_m6,type,
axiom_m6: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $i ).
tff('#skF_70',type,
'#skF_70': $i ).
tff('#skF_66',type,
'#skF_66': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff('#skF_63',type,
'#skF_63': $i ).
tff(axiom_m1,type,
axiom_m1: $o ).
tff('#skF_88',type,
'#skF_88': $i ).
tff(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff('#skF_83',type,
'#skF_83': $i ).
tff(axiom_m10,type,
axiom_m10: $o ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff('#skF_59',type,
'#skF_59': $i ).
tff(axiom_m9,type,
axiom_m9: $o ).
tff('#skF_73',type,
'#skF_73': $i ).
tff('#skF_91',type,
'#skF_91': $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_58',type,
'#skF_58': $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(axiom_m5,type,
axiom_m5: $o ).
tff('#skF_62',type,
'#skF_62': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff('#skF_75',type,
'#skF_75': $i ).
tff('#skF_74',type,
'#skF_74': $i ).
tff(f_253,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
tff(f_77,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(f_254,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
tff(f_81,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
tff(f_250,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
tff(f_61,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_248,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
tff(f_215,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_258,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
tff(f_97,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
tff(f_126,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_260,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
tff(f_105,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_2) ).
tff(f_261,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
tff(f_109,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_3) ).
tff(f_152,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_246,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
tff(f_247,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
tff(f_207,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_199,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_147,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_264,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
tff(f_121,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
tff(f_267,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
tff(f_68,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_257,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
tff(f_93,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_473,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).
tff(f_432,axiom,
( op_possibly
=> ! [X] : ( possibly(X) = not(necessarily(not(X))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
tff(f_478,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
tff(f_331,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
tff(f_479,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
tff(f_343,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
tff(f_263,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_2) ).
tff(f_117,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
tff(f_483,negated_conjecture,
~ axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_4) ).
tff(f_335,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
tff(c_132,plain,
implies_1,
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_22,plain,
! [X_7,Y_8] :
( is_a_theorem(implies(X_7,implies(Y_8,X_7)))
| ~ implies_1 ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_369,plain,
! [X_7,Y_8] : is_a_theorem(implies(X_7,implies(Y_8,X_7))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_22]) ).
tff(c_134,plain,
implies_2,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_26,plain,
! [X_9,Y_10] :
( is_a_theorem(implies(implies(X_9,implies(X_9,Y_10)),implies(X_9,Y_10)))
| ~ implies_2 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_26442,plain,
! [X_1707,Y_1708] : is_a_theorem(implies(implies(X_1707,implies(X_1707,Y_1708)),implies(X_1707,Y_1708))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(implies(X_1,Y_2))
| ~ is_a_theorem(X_1)
| ~ modus_ponens ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_384,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(implies(X_1,Y_2))
| ~ is_a_theorem(X_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_27657,plain,
! [X_1799,Y_1800] :
( is_a_theorem(implies(X_1799,Y_1800))
| ~ is_a_theorem(implies(X_1799,implies(X_1799,Y_1800))) ),
inference(resolution,[status(thm)],[c_26442,c_384]) ).
tff(c_27717,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_369,c_27657]) ).
tff(c_126,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_248]) ).
tff(c_120,plain,
! [X_64,Y_65] :
( ( and(implies(X_64,Y_65),implies(Y_65,X_64)) = equiv(X_64,Y_65) )
| ~ op_equiv ),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_26518,plain,
! [X_1718,Y_1719] : ( and(implies(X_1718,Y_1719),implies(Y_1719,X_1718)) = equiv(X_1718,Y_1719) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_120]) ).
tff(c_142,plain,
and_3,
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_42,plain,
! [X_18,Y_19] :
( is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19))))
| ~ and_3 ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_343,plain,
! [X_18,Y_19] : is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_22076,plain,
! [X_1335,Y_1336] : is_a_theorem(implies(implies(X_1335,implies(X_1335,Y_1336)),implies(X_1335,Y_1336))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_23084,plain,
! [X_1424,Y_1425] :
( is_a_theorem(implies(X_1424,Y_1425))
| ~ is_a_theorem(implies(X_1424,implies(X_1424,Y_1425))) ),
inference(resolution,[status(thm)],[c_22076,c_384]) ).
tff(c_23139,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_343,c_23084]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_21650,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_23184,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23139,c_21650]) ).
tff(c_23185,plain,
kn1,
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_70,plain,
! [P_33] :
( is_a_theorem(implies(P_33,and(P_33,P_33)))
| ~ kn1 ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_23191,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_23185,c_70]) ).
tff(c_26090,plain,
! [Y_1658,X_1659] :
( is_a_theorem(Y_1658)
| ~ is_a_theorem(implies(X_1659,Y_1658))
| ~ is_a_theorem(X_1659) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_26126,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_23191,c_26090]) ).
tff(c_26534,plain,
! [Y_1719] :
( is_a_theorem(equiv(Y_1719,Y_1719))
| ~ is_a_theorem(implies(Y_1719,Y_1719)) ),
inference(superposition,[status(thm),theory(equality)],[c_26518,c_26126]) ).
tff(c_27722,plain,
! [Y_1719] : is_a_theorem(equiv(Y_1719,Y_1719)),
inference(demodulation,[status(thm),theory(equality)],[c_27717,c_26534]) ).
tff(c_146,plain,
or_2,
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_50,plain,
! [Y_23,X_22] :
( is_a_theorem(implies(Y_23,or(X_22,Y_23)))
| ~ or_2 ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_329,plain,
! [Y_23,X_22] : is_a_theorem(implies(Y_23,or(X_22,Y_23))),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_50]) ).
tff(c_23777,plain,
! [X_1493,Y_1494] : is_a_theorem(implies(implies(X_1493,implies(X_1493,Y_1494)),implies(X_1493,Y_1494))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_24820,plain,
! [X_1582,Y_1583] :
( is_a_theorem(implies(X_1582,Y_1583))
| ~ is_a_theorem(implies(X_1582,implies(X_1582,Y_1583))) ),
inference(resolution,[status(thm)],[c_23777,c_384]) ).
tff(c_24880,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_369,c_24820]) ).
tff(c_148,plain,
or_3,
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_54,plain,
! [X_24,Z_26,Y_25] :
( is_a_theorem(implies(implies(X_24,Z_26),implies(implies(Y_25,Z_26),implies(or(X_24,Y_25),Z_26))))
| ~ or_3 ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_24997,plain,
! [X_1588,Z_1589,Y_1590] : is_a_theorem(implies(implies(X_1588,Z_1589),implies(implies(Y_1590,Z_1589),implies(or(X_1588,Y_1590),Z_1589)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_23791,plain,
! [X_1493,Y_1494] :
( is_a_theorem(implies(X_1493,Y_1494))
| ~ is_a_theorem(implies(X_1493,implies(X_1493,Y_1494))) ),
inference(resolution,[status(thm)],[c_23777,c_384]) ).
tff(c_25836,plain,
! [Y_1634,Z_1635] : is_a_theorem(implies(implies(Y_1634,Z_1635),implies(or(Y_1634,Y_1634),Z_1635))),
inference(resolution,[status(thm)],[c_24997,c_23791]) ).
tff(c_25925,plain,
! [Y_1641,Z_1642] :
( is_a_theorem(implies(or(Y_1641,Y_1641),Z_1642))
| ~ is_a_theorem(implies(Y_1641,Z_1642)) ),
inference(resolution,[status(thm)],[c_25836,c_384]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_23231,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_23236,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(negUnitSimplification,[status(thm)],[c_23231,c_92]) ).
tff(c_25938,plain,
~ is_a_theorem(implies('#skF_45','#skF_45')),
inference(resolution,[status(thm)],[c_25925,c_23236]) ).
tff(c_25960,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24880,c_25938]) ).
tff(c_25961,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_122,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_124,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_116,plain,
! [X_60,Y_61] :
( ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) )
| ~ op_implies_and ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_303,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_112,plain,
! [X_56,Y_57] :
( ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) )
| ~ op_or ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_305,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_303,c_112]) ).
tff(c_88,plain,
( cn3
| ~ is_a_theorem(implies(implies(not('#skF_44'),'#skF_44'),'#skF_44')) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_307,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_88]) ).
tff(c_23194,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(splitLeft,[status(thm)],[c_307]) ).
tff(c_25966,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25961,c_23194]) ).
tff(c_25967,plain,
cn3,
inference(splitRight,[status(thm)],[c_307]) ).
tff(c_90,plain,
! [P_44] :
( is_a_theorem(implies(implies(not(P_44),P_44),P_44))
| ~ cn3 ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_306,plain,
! [P_44] :
( is_a_theorem(implies(or(P_44,P_44),P_44))
| ~ cn3 ),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_90]) ).
tff(c_26014,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_25967,c_306]) ).
tff(c_25975,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_25976,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(negUnitSimplification,[status(thm)],[c_25975,c_92]) ).
tff(c_26018,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_26014,c_25976]) ).
tff(c_26019,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_154,plain,
equivalence_3,
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_66,plain,
! [X_31,Y_32] :
( is_a_theorem(implies(implies(X_31,Y_32),implies(implies(Y_32,X_31),equiv(X_31,Y_32))))
| ~ equivalence_3 ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_27077,plain,
! [X_1753,Y_1754] : is_a_theorem(implies(implies(X_1753,Y_1754),implies(implies(Y_1754,X_1753),equiv(X_1753,Y_1754)))),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_66]) ).
tff(c_29610,plain,
! [Y_1910,X_1911] :
( is_a_theorem(implies(implies(Y_1910,X_1911),equiv(X_1911,Y_1910)))
| ~ is_a_theorem(implies(X_1911,Y_1910)) ),
inference(resolution,[status(thm)],[c_27077,c_384]) ).
tff(c_36390,plain,
! [X_2303,Y_2304] :
( is_a_theorem(equiv(X_2303,Y_2304))
| ~ is_a_theorem(implies(Y_2304,X_2303))
| ~ is_a_theorem(implies(X_2303,Y_2304)) ),
inference(resolution,[status(thm)],[c_29610,c_384]) ).
tff(c_36504,plain,
! [P_45] :
( is_a_theorem(equiv(P_45,or(P_45,P_45)))
| ~ is_a_theorem(implies(P_45,or(P_45,P_45))) ),
inference(resolution,[status(thm)],[c_26019,c_36390]) ).
tff(c_36614,plain,
! [P_2305] : is_a_theorem(equiv(P_2305,or(P_2305,P_2305))),
inference(demodulation,[status(thm),theory(equality)],[c_329,c_36504]) ).
tff(c_156,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_10,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4))
| ~ substitution_of_equivalents ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_379,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_10]) ).
tff(c_36682,plain,
! [P_2305] : ( or(P_2305,P_2305) = P_2305 ),
inference(resolution,[status(thm)],[c_36614,c_379]) ).
tff(c_140,plain,
and_2,
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_38,plain,
! [X_16,Y_17] :
( is_a_theorem(implies(and(X_16,Y_17),Y_17))
| ~ and_2 ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_347,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_38]) ).
tff(c_36506,plain,
! [P_33] :
( is_a_theorem(equiv(and(P_33,P_33),P_33))
| ~ is_a_theorem(implies(and(P_33,P_33),P_33)) ),
inference(resolution,[status(thm)],[c_23191,c_36390]) ).
tff(c_37109,plain,
! [P_2310] : is_a_theorem(equiv(and(P_2310,P_2310),P_2310)),
inference(demodulation,[status(thm),theory(equality)],[c_347,c_36506]) ).
tff(c_37191,plain,
! [P_2311] : ( and(P_2311,P_2311) = P_2311 ),
inference(resolution,[status(thm)],[c_37109,c_379]) ).
tff(c_38709,plain,
! [Y_2326] : ( implies(not(Y_2326),Y_2326) = not(not(Y_2326)) ),
inference(superposition,[status(thm),theory(equality)],[c_37191,c_303]) ).
tff(c_39001,plain,
! [Y_2326] : ( or(Y_2326,Y_2326) = not(not(Y_2326)) ),
inference(superposition,[status(thm),theory(equality)],[c_38709,c_305]) ).
tff(c_39071,plain,
! [Y_2326] : ( not(not(Y_2326)) = Y_2326 ),
inference(demodulation,[status(thm),theory(equality)],[c_36682,c_39001]) ).
tff(c_26200,plain,
! [X_1677,Y_1678] : ( not(and(X_1677,not(Y_1678))) = implies(X_1677,Y_1678) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_270,plain,
op_possibly,
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_262,plain,
! [X_105] :
( ( not(necessarily(not(X_105))) = possibly(X_105) )
| ~ op_possibly ),
inference(cnfTransformation,[status(thm)],[f_432]) ).
tff(c_282,plain,
! [X_105] : ( not(necessarily(not(X_105))) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_270,c_262]) ).
tff(c_26224,plain,
! [X_1677,Y_1678] : ( possibly(and(X_1677,not(Y_1678))) = not(necessarily(implies(X_1677,Y_1678))) ),
inference(superposition,[status(thm),theory(equality)],[c_26200,c_282]) ).
tff(c_37447,plain,
! [Y_1678] : ( not(necessarily(implies(not(Y_1678),Y_1678))) = possibly(not(Y_1678)) ),
inference(superposition,[status(thm),theory(equality)],[c_37191,c_26224]) ).
tff(c_37535,plain,
! [Y_1678] : ( possibly(not(Y_1678)) = not(necessarily(Y_1678)) ),
inference(demodulation,[status(thm),theory(equality)],[c_36682,c_305,c_37447]) ).
tff(c_276,plain,
axiom_M,
inference(cnfTransformation,[status(thm)],[f_478]) ).
tff(c_192,plain,
! [X_75] :
( is_a_theorem(implies(necessarily(X_75),X_75))
| ~ axiom_M ),
inference(cnfTransformation,[status(thm)],[f_331]) ).
tff(c_289,plain,
! [X_75] : is_a_theorem(implies(necessarily(X_75),X_75)),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_192]) ).
tff(c_278,plain,
axiom_5,
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_204,plain,
! [X_78] :
( is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78))))
| ~ axiom_5 ),
inference(cnfTransformation,[status(thm)],[f_343]) ).
tff(c_284,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_204]) ).
tff(c_36502,plain,
! [X_78] :
( is_a_theorem(equiv(necessarily(possibly(X_78)),possibly(X_78)))
| ~ is_a_theorem(implies(necessarily(possibly(X_78)),possibly(X_78))) ),
inference(resolution,[status(thm)],[c_284,c_36390]) ).
tff(c_41475,plain,
! [X_2353] : is_a_theorem(equiv(necessarily(possibly(X_2353)),possibly(X_2353))),
inference(demodulation,[status(thm),theory(equality)],[c_289,c_36502]) ).
tff(c_41619,plain,
! [X_2356] : ( necessarily(possibly(X_2356)) = possibly(X_2356) ),
inference(resolution,[status(thm)],[c_41475,c_379]) ).
tff(c_41673,plain,
! [Y_1678] : ( necessarily(not(necessarily(Y_1678))) = possibly(not(Y_1678)) ),
inference(superposition,[status(thm),theory(equality)],[c_37535,c_41619]) ).
tff(c_42607,plain,
! [Y_2370] : ( necessarily(not(necessarily(Y_2370))) = not(necessarily(Y_2370)) ),
inference(demodulation,[status(thm),theory(equality)],[c_37535,c_41673]) ).
tff(c_42790,plain,
! [Y_2370] : ( not(not(necessarily(Y_2370))) = possibly(necessarily(Y_2370)) ),
inference(superposition,[status(thm),theory(equality)],[c_42607,c_282]) ).
tff(c_42838,plain,
! [Y_2370] : ( possibly(necessarily(Y_2370)) = necessarily(Y_2370) ),
inference(demodulation,[status(thm),theory(equality)],[c_39071,c_42790]) ).
tff(c_42909,plain,
! [Y_2373] : ( possibly(necessarily(Y_2373)) = necessarily(Y_2373) ),
inference(demodulation,[status(thm),theory(equality)],[c_39071,c_42790]) ).
tff(c_41539,plain,
! [X_2353] : ( necessarily(possibly(X_2353)) = possibly(X_2353) ),
inference(resolution,[status(thm)],[c_41475,c_379]) ).
tff(c_42921,plain,
! [Y_2373] : ( possibly(necessarily(Y_2373)) = necessarily(necessarily(Y_2373)) ),
inference(superposition,[status(thm),theory(equality)],[c_42909,c_41539]) ).
tff(c_43038,plain,
! [Y_2373] : ( necessarily(necessarily(Y_2373)) = necessarily(Y_2373) ),
inference(demodulation,[status(thm),theory(equality)],[c_42838,c_42921]) ).
tff(c_152,plain,
equivalence_2,
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_62,plain,
! [X_29,Y_30] :
( is_a_theorem(implies(equiv(X_29,Y_30),implies(Y_30,X_29)))
| ~ equivalence_2 ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_26236,plain,
! [X_1679,Y_1680] : is_a_theorem(implies(equiv(X_1679,Y_1680),implies(Y_1680,X_1679))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_62]) ).
tff(c_26344,plain,
! [Y_1691,X_1692] :
( is_a_theorem(implies(Y_1691,X_1692))
| ~ is_a_theorem(equiv(X_1692,Y_1691)) ),
inference(resolution,[status(thm)],[c_26236,c_384]) ).
tff(c_280,plain,
~ axiom_4,
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_194,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily('#skF_66'),necessarily(necessarily('#skF_66')))) ),
inference(cnfTransformation,[status(thm)],[f_335]) ).
tff(c_287,plain,
~ is_a_theorem(implies(necessarily('#skF_66'),necessarily(necessarily('#skF_66')))),
inference(negUnitSimplification,[status(thm)],[c_280,c_194]) ).
tff(c_26355,plain,
~ is_a_theorem(equiv(necessarily(necessarily('#skF_66')),necessarily('#skF_66'))),
inference(resolution,[status(thm)],[c_26344,c_287]) ).
tff(c_43085,plain,
~ is_a_theorem(equiv(necessarily('#skF_66'),necessarily('#skF_66'))),
inference(demodulation,[status(thm),theory(equality)],[c_43038,c_26355]) ).
tff(c_43093,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_27722,c_43085]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL523+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.08/0.37 % Computer : n003.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 5 19:29:36 UTC 2026
% 0.08/0.37 % CPUTime :
% 34.08/14.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.08/14.96
% 34.08/14.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------