TSTP Solution File: LCL546+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL546+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n010.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 : Tue Aug 22 10:48:20 EDT 2023
% Result : Theorem 20.06s 7.97s
% Output : CNFRefutation 20.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 206
% Syntax : Number of formulae : 394 ( 143 unt; 163 typ; 0 def)
% Number of atoms : 340 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 203 ( 94 ~; 78 |; 2 &)
% ( 20 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 221 (; 221 !; 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_implies > 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(op_implies,type,
op_implies: $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_475,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
tff(f_328,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
tff(f_244,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
tff(f_206,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_481,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
tff(f_429,axiom,
( op_possibly
=> ! [X] : ( possibly(X) = not(necessarily(not(X))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
tff(f_476,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_4) ).
tff(f_332,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(f_485,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
tff(f_214,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_313,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(Y) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
tff(f_264,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
tff(f_67,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_482,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
tff(f_198,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_257,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
tff(f_104,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_254,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
tff(f_92,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_255,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
tff(f_96,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_251,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
tff(f_80,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_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
tff(f_60,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_484,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
tff(f_437,axiom,
( op_strict_implies
=> ! [X,Y] : ( strict_implies(X,Y) = necessarily(implies(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
tff(f_472,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
tff(f_297,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
tff(f_374,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
tff(f_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_250,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
tff(f_76,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_249,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
tff(f_72,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
tff(f_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_146,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_477,axiom,
axiom_B,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_B) ).
tff(f_336,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_B) ).
tff(f_399,axiom,
( axiom_m10
<=> ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
tff(f_340,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_489,negated_conjecture,
~ axiom_m6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
tff(f_383,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m6) ).
tff(c_276,plain,
axiom_M,
inference(cnfTransformation,[status(thm)],[f_475]) ).
tff(c_192,plain,
! [X_75] :
( is_a_theorem(implies(necessarily(X_75),X_75))
| ~ axiom_M ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_314,plain,
! [X_75] : is_a_theorem(implies(necessarily(X_75),X_75)),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_192]) ).
tff(c_124,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_244]) ).
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_206]) ).
tff(c_330,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_282,plain,
op_possibly,
inference(cnfTransformation,[status(thm)],[f_481]) ).
tff(c_262,plain,
! [X_105] :
( ( not(necessarily(not(X_105))) = possibly(X_105) )
| ~ op_possibly ),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_422,plain,
! [X_113] : ( not(necessarily(not(X_113))) = possibly(X_113) ),
inference(demodulation,[status(thm),theory(equality)],[c_282,c_262]) ).
tff(c_301,plain,
! [X_105] : ( not(necessarily(not(X_105))) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_282,c_262]) ).
tff(c_425,plain,
! [X_113] : ( possibly(necessarily(not(X_113))) = not(necessarily(possibly(X_113))) ),
inference(superposition,[status(thm),theory(equality)],[c_422,c_301]) ).
tff(c_278,plain,
axiom_4,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_196,plain,
! [X_76] :
( is_a_theorem(implies(necessarily(X_76),necessarily(necessarily(X_76))))
| ~ axiom_4 ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_310,plain,
! [X_76] : is_a_theorem(implies(necessarily(X_76),necessarily(necessarily(X_76)))),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_196]) ).
tff(c_290,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_485]) ).
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_214]) ).
tff(c_15071,plain,
! [X_1322,Y_1323] : ( and(implies(X_1322,Y_1323),implies(Y_1323,X_1322)) = equiv(X_1322,Y_1323) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_176,plain,
( is_a_theorem('#skF_60')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_413,plain,
adjunction,
inference(splitLeft,[status(thm)],[c_176]) ).
tff(c_172,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69)
| ~ adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_14798,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_413,c_172]) ).
tff(c_20390,plain,
! [X_1633,Y_1634] :
( is_a_theorem(equiv(X_1633,Y_1634))
| ~ is_a_theorem(implies(Y_1634,X_1633))
| ~ is_a_theorem(implies(X_1633,Y_1634)) ),
inference(superposition,[status(thm),theory(equality)],[c_15071,c_14798]) ).
tff(c_20476,plain,
! [X_76] :
( is_a_theorem(equiv(necessarily(necessarily(X_76)),necessarily(X_76)))
| ~ is_a_theorem(implies(necessarily(necessarily(X_76)),necessarily(X_76))) ),
inference(resolution,[status(thm)],[c_310,c_20390]) ).
tff(c_21777,plain,
! [X_1658] : is_a_theorem(equiv(necessarily(necessarily(X_1658)),necessarily(X_1658))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_20476]) ).
tff(c_156,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_264]) ).
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_67]) ).
tff(c_406,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_21803,plain,
! [X_1658] : ( necessarily(necessarily(X_1658)) = necessarily(X_1658) ),
inference(resolution,[status(thm)],[c_21777,c_406]) ).
tff(c_14734,plain,
! [X_1294,Y_1295] : ( not(and(X_1294,not(Y_1295))) = implies(X_1294,Y_1295) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_14767,plain,
! [X_1294,X_105] : ( implies(X_1294,necessarily(not(X_105))) = not(and(X_1294,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_14734]) ).
tff(c_284,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_482]) ).
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_198]) ).
tff(c_14389,plain,
! [X_1245,Y_1246] : ( implies(not(X_1245),Y_1246) = or(X_1245,Y_1246) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_14424,plain,
! [X_105,Y_1246] : ( or(necessarily(not(X_105)),Y_1246) = implies(possibly(X_105),Y_1246) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_14389]) ).
tff(c_332,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_146,plain,
or_2,
inference(cnfTransformation,[status(thm)],[f_257]) ).
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_104]) ).
tff(c_356,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_140,plain,
and_2,
inference(cnfTransformation,[status(thm)],[f_254]) ).
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_92]) ).
tff(c_374,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_142,plain,
and_3,
inference(cnfTransformation,[status(thm)],[f_255]) ).
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_96]) ).
tff(c_370,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_134,plain,
implies_2,
inference(cnfTransformation,[status(thm)],[f_251]) ).
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_80]) ).
tff(c_2079,plain,
! [X_309,Y_310] : is_a_theorem(implies(implies(X_309,implies(X_309,Y_310)),implies(X_309,Y_310))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_247]) ).
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_60]) ).
tff(c_411,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_3417,plain,
! [X_407,Y_408] :
( is_a_theorem(implies(X_407,Y_408))
| ~ is_a_theorem(implies(X_407,implies(X_407,Y_408))) ),
inference(resolution,[status(thm)],[c_2079,c_411]) ).
tff(c_3476,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_370,c_3417]) ).
tff(c_288,plain,
op_strict_implies,
inference(cnfTransformation,[status(thm)],[f_484]) ).
tff(c_266,plain,
! [X_107,Y_108] :
( ( necessarily(implies(X_107,Y_108)) = strict_implies(X_107,Y_108) )
| ~ op_strict_implies ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_1120,plain,
! [X_207,Y_208] : ( necessarily(implies(X_207,Y_208)) = strict_implies(X_207,Y_208) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_272,plain,
necessitation,
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_158,plain,
! [X_66] :
( is_a_theorem(necessarily(X_66))
| ~ is_a_theorem(X_66)
| ~ necessitation ),
inference(cnfTransformation,[status(thm)],[f_297]) ).
tff(c_324,plain,
! [X_66] :
( is_a_theorem(necessarily(X_66))
| ~ is_a_theorem(X_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_272,c_158]) ).
tff(c_1826,plain,
! [X_291,Y_292] :
( is_a_theorem(strict_implies(X_291,Y_292))
| ~ is_a_theorem(implies(X_291,Y_292)) ),
inference(superposition,[status(thm),theory(equality)],[c_1120,c_324]) ).
tff(c_234,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))) ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_437,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_1852,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_1826,c_437]) ).
tff(c_3524,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3476,c_1852]) ).
tff(c_3525,plain,
axiom_m4,
inference(splitRight,[status(thm)],[c_234]) ).
tff(c_236,plain,
! [X_94] :
( is_a_theorem(strict_implies(X_94,and(X_94,X_94)))
| ~ axiom_m4 ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_3538,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_3525,c_236]) ).
tff(c_3542,plain,
! [X_427,Y_428] : ( necessarily(implies(X_427,Y_428)) = strict_implies(X_427,Y_428) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_4963,plain,
! [X_601,Y_602] : is_a_theorem(implies(strict_implies(X_601,Y_602),implies(X_601,Y_602))),
inference(superposition,[status(thm),theory(equality)],[c_3542,c_314]) ).
tff(c_5427,plain,
! [X_635,Y_636] :
( is_a_theorem(implies(X_635,Y_636))
| ~ is_a_theorem(strict_implies(X_635,Y_636)) ),
inference(resolution,[status(thm)],[c_4963,c_411]) ).
tff(c_5471,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_3538,c_5427]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_4367,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_5485,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5471,c_4367]) ).
tff(c_5486,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_125]) ).
tff(c_5490,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_5486,c_70]) ).
tff(c_6179,plain,
! [X_718,Y_719] : ( and(implies(X_718,Y_719),implies(Y_719,X_718)) = equiv(X_718,Y_719) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_6042,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_413,c_172]) ).
tff(c_10526,plain,
! [X_1013,Y_1014] :
( is_a_theorem(equiv(X_1013,Y_1014))
| ~ is_a_theorem(implies(Y_1014,X_1013))
| ~ is_a_theorem(implies(X_1013,Y_1014)) ),
inference(superposition,[status(thm),theory(equality)],[c_6179,c_6042]) ).
tff(c_10616,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_5490,c_10526]) ).
tff(c_10703,plain,
! [P_1015] : is_a_theorem(equiv(and(P_1015,P_1015),P_1015)),
inference(demodulation,[status(thm),theory(equality)],[c_374,c_10616]) ).
tff(c_10750,plain,
! [P_1016] : ( and(P_1016,P_1016) = P_1016 ),
inference(resolution,[status(thm)],[c_10703,c_406]) ).
tff(c_11547,plain,
! [Y_1029] : ( implies(not(Y_1029),Y_1029) = not(not(Y_1029)) ),
inference(superposition,[status(thm),theory(equality)],[c_10750,c_330]) ).
tff(c_11690,plain,
! [Y_1029] : ( or(Y_1029,Y_1029) = not(not(Y_1029)) ),
inference(superposition,[status(thm),theory(equality)],[c_11547,c_332]) ).
tff(c_5497,plain,
! [X_642,Y_643] : ( implies(not(X_642),Y_643) = or(X_642,Y_643) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_132,plain,
implies_1,
inference(cnfTransformation,[status(thm)],[f_250]) ).
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_76]) ).
tff(c_396,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_5514,plain,
! [X_642,Y_8] : is_a_theorem(or(X_642,implies(Y_8,not(X_642)))),
inference(superposition,[status(thm),theory(equality)],[c_5497,c_396]) ).
tff(c_12338,plain,
! [X_1038] : is_a_theorem(or(X_1038,not(not(not(X_1038))))),
inference(superposition,[status(thm),theory(equality)],[c_11547,c_5514]) ).
tff(c_12573,plain,
! [Y_1045] : is_a_theorem(or(Y_1045,not(or(Y_1045,Y_1045)))),
inference(superposition,[status(thm),theory(equality)],[c_11690,c_12338]) ).
tff(c_130,plain,
modus_tollens,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_18,plain,
! [Y_6,X_5] :
( is_a_theorem(implies(implies(not(Y_6),not(X_5)),implies(X_5,Y_6)))
| ~ modus_tollens ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_6140,plain,
! [Y_716,X_717] : is_a_theorem(implies(or(Y_716,not(X_717)),implies(X_717,Y_716))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_6153,plain,
! [X_717,Y_716] :
( is_a_theorem(implies(X_717,Y_716))
| ~ is_a_theorem(or(Y_716,not(X_717))) ),
inference(resolution,[status(thm)],[c_6140,c_411]) ).
tff(c_12604,plain,
! [Y_1045] : is_a_theorem(implies(or(Y_1045,Y_1045),Y_1045)),
inference(resolution,[status(thm)],[c_12573,c_6153]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_4364,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_12615,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12604,c_4364]) ).
tff(c_12616,plain,
r1,
inference(splitRight,[status(thm)],[c_92]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_12667,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_12616,c_94]) ).
tff(c_88,plain,
( cn3
| ~ is_a_theorem(implies(implies(not('#skF_44'),'#skF_44'),'#skF_44')) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_334,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_88]) ).
tff(c_3541,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(splitLeft,[status(thm)],[c_334]) ).
tff(c_12671,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12667,c_3541]) ).
tff(c_12672,plain,
cn3,
inference(splitRight,[status(thm)],[c_334]) ).
tff(c_90,plain,
! [P_44] :
( is_a_theorem(implies(implies(not(P_44),P_44),P_44))
| ~ cn3 ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_333,plain,
! [P_44] :
( is_a_theorem(implies(or(P_44,P_44),P_44))
| ~ cn3 ),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_90]) ).
tff(c_13410,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_12672,c_333]) ).
tff(c_13370,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_13371,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(negUnitSimplification,[status(thm)],[c_13370,c_92]) ).
tff(c_13414,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13410,c_13371]) ).
tff(c_13415,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_20478,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_13415,c_20390]) ).
tff(c_20559,plain,
! [P_1635] : is_a_theorem(equiv(P_1635,or(P_1635,P_1635))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_20478]) ).
tff(c_20593,plain,
! [P_1635] : ( or(P_1635,P_1635) = P_1635 ),
inference(resolution,[status(thm)],[c_20559,c_406]) ).
tff(c_18997,plain,
! [X_1592,X_1593,Y_1594] : ( implies(X_1592,and(X_1593,not(Y_1594))) = not(and(X_1592,implies(X_1593,Y_1594))) ),
inference(superposition,[status(thm),theory(equality)],[c_14734,c_330]) ).
tff(c_12674,plain,
! [X_1049,Y_1050] : ( necessarily(implies(X_1049,Y_1050)) = strict_implies(X_1049,Y_1050) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_14047,plain,
! [X_1219,Y_1220] : is_a_theorem(implies(strict_implies(X_1219,Y_1220),implies(X_1219,Y_1220))),
inference(superposition,[status(thm),theory(equality)],[c_12674,c_314]) ).
tff(c_14345,plain,
! [X_1241,Y_1242] :
( is_a_theorem(implies(X_1241,Y_1242))
| ~ is_a_theorem(strict_implies(X_1241,Y_1242)) ),
inference(resolution,[status(thm)],[c_14047,c_411]) ).
tff(c_14367,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_3538,c_14345]) ).
tff(c_13421,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_14371,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14367,c_13421]) ).
tff(c_14372,plain,
kn1,
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_14375,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_14372,c_70]) ).
tff(c_19168,plain,
! [Y_1594] : is_a_theorem(not(and(not(Y_1594),implies(not(Y_1594),Y_1594)))),
inference(superposition,[status(thm),theory(equality)],[c_18997,c_14375]) ).
tff(c_19233,plain,
! [Y_1594] : is_a_theorem(not(and(not(Y_1594),or(Y_1594,Y_1594)))),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_19168]) ).
tff(c_20780,plain,
! [Y_1638] : is_a_theorem(not(and(not(Y_1638),Y_1638))),
inference(demodulation,[status(thm),theory(equality)],[c_20593,c_19233]) ).
tff(c_20796,plain,
! [Y_61] : is_a_theorem(implies(not(not(Y_61)),Y_61)),
inference(superposition,[status(thm),theory(equality)],[c_330,c_20780]) ).
tff(c_20803,plain,
! [Y_61] : is_a_theorem(or(not(Y_61),Y_61)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_20796]) ).
tff(c_20804,plain,
! [Y_1639] : is_a_theorem(or(not(Y_1639),Y_1639)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_20796]) ).
tff(c_15030,plain,
! [Y_1314,X_1315] : is_a_theorem(implies(or(Y_1314,not(X_1315)),implies(X_1315,Y_1314))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_15043,plain,
! [X_1315,Y_1314] :
( is_a_theorem(implies(X_1315,Y_1314))
| ~ is_a_theorem(or(Y_1314,not(X_1315))) ),
inference(resolution,[status(thm)],[c_15030,c_411]) ).
tff(c_20830,plain,
! [X_1640] : is_a_theorem(implies(X_1640,not(not(X_1640)))),
inference(resolution,[status(thm)],[c_20804,c_15043]) ).
tff(c_15080,plain,
! [X_1322,Y_1323] :
( is_a_theorem(equiv(X_1322,Y_1323))
| ~ is_a_theorem(implies(Y_1323,X_1322))
| ~ is_a_theorem(implies(X_1322,Y_1323)) ),
inference(superposition,[status(thm),theory(equality)],[c_15071,c_14798]) ).
tff(c_20832,plain,
! [X_1640] :
( is_a_theorem(equiv(not(not(X_1640)),X_1640))
| ~ is_a_theorem(implies(not(not(X_1640)),X_1640)) ),
inference(resolution,[status(thm)],[c_20830,c_15080]) ).
tff(c_20919,plain,
! [X_1645] : is_a_theorem(equiv(not(not(X_1645)),X_1645)),
inference(demodulation,[status(thm),theory(equality)],[c_20803,c_332,c_20832]) ).
tff(c_20965,plain,
! [X_1646] : ( not(not(X_1646)) = X_1646 ),
inference(resolution,[status(thm)],[c_20919,c_406]) ).
tff(c_21190,plain,
! [X_1646] : ( possibly(not(X_1646)) = not(necessarily(X_1646)) ),
inference(superposition,[status(thm),theory(equality)],[c_20965,c_301]) ).
tff(c_280,plain,
axiom_B,
inference(cnfTransformation,[status(thm)],[f_477]) ).
tff(c_200,plain,
! [X_77] :
( is_a_theorem(implies(X_77,necessarily(possibly(X_77))))
| ~ axiom_B ),
inference(cnfTransformation,[status(thm)],[f_336]) ).
tff(c_306,plain,
! [X_77] : is_a_theorem(implies(X_77,necessarily(possibly(X_77)))),
inference(demodulation,[status(thm),theory(equality)],[c_280,c_200]) ).
tff(c_14410,plain,
! [X_1245] : is_a_theorem(or(X_1245,necessarily(possibly(not(X_1245))))),
inference(superposition,[status(thm),theory(equality)],[c_14389,c_306]) ).
tff(c_23458,plain,
! [X_1689] : is_a_theorem(or(X_1689,necessarily(not(necessarily(X_1689))))),
inference(demodulation,[status(thm),theory(equality)],[c_21190,c_14410]) ).
tff(c_23488,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(not(necessarily(necessarily(not(X_105))))))),
inference(superposition,[status(thm),theory(equality)],[c_14424,c_23458]) ).
tff(c_23500,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(possibly(X_105)))),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_425,c_21803,c_14767,c_23488]) ).
tff(c_14910,plain,
! [X_1312,Y_1313] :
( is_a_theorem(strict_implies(X_1312,Y_1313))
| ~ is_a_theorem(implies(X_1312,Y_1313)) ),
inference(superposition,[status(thm),theory(equality)],[c_12674,c_324]) ).
tff(c_258,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))) ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_14536,plain,
~ is_a_theorem(strict_implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(splitLeft,[status(thm)],[c_258]) ).
tff(c_14931,plain,
~ is_a_theorem(implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(resolution,[status(thm)],[c_14910,c_14536]) ).
tff(c_23637,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23500,c_14931]) ).
tff(c_23638,plain,
axiom_m10,
inference(splitRight,[status(thm)],[c_258]) ).
tff(c_260,plain,
! [X_104] :
( is_a_theorem(strict_implies(possibly(X_104),necessarily(possibly(X_104))))
| ~ axiom_m10 ),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_23655,plain,
! [X_104] : is_a_theorem(strict_implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(demodulation,[status(thm),theory(equality)],[c_23638,c_260]) ).
tff(c_24094,plain,
! [X_1745,Y_1746] : is_a_theorem(implies(strict_implies(X_1745,Y_1746),implies(X_1745,Y_1746))),
inference(superposition,[status(thm),theory(equality)],[c_12674,c_314]) ).
tff(c_24130,plain,
! [X_1747,Y_1748] :
( is_a_theorem(implies(X_1747,Y_1748))
| ~ is_a_theorem(strict_implies(X_1747,Y_1748)) ),
inference(resolution,[status(thm)],[c_24094,c_411]) ).
tff(c_24153,plain,
! [X_104] : is_a_theorem(implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(resolution,[status(thm)],[c_23655,c_24130]) ).
tff(c_202,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly('#skF_68'),necessarily(possibly('#skF_68')))) ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_23675,plain,
~ is_a_theorem(implies(possibly('#skF_68'),necessarily(possibly('#skF_68')))),
inference(splitLeft,[status(thm)],[c_202]) ).
tff(c_24160,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24153,c_23675]) ).
tff(c_24161,plain,
axiom_5,
inference(splitRight,[status(thm)],[c_202]) ).
tff(c_204,plain,
! [X_78] :
( is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78))))
| ~ axiom_5 ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_24379,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(demodulation,[status(thm),theory(equality)],[c_24161,c_204]) ).
tff(c_24773,plain,
! [X_1805,Y_1806] : ( and(implies(X_1805,Y_1806),implies(Y_1806,X_1805)) = equiv(X_1805,Y_1806) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_24492,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69) ),
inference(demodulation,[status(thm),theory(equality)],[c_413,c_172]) ).
tff(c_29977,plain,
! [X_2109,Y_2110] :
( is_a_theorem(equiv(X_2109,Y_2110))
| ~ is_a_theorem(implies(Y_2110,X_2109))
| ~ is_a_theorem(implies(X_2109,Y_2110)) ),
inference(superposition,[status(thm),theory(equality)],[c_24773,c_24492]) ).
tff(c_30055,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_24379,c_29977]) ).
tff(c_31505,plain,
! [X_2136] : is_a_theorem(equiv(necessarily(possibly(X_2136)),possibly(X_2136))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_30055]) ).
tff(c_31544,plain,
! [X_2136] : ( necessarily(possibly(X_2136)) = possibly(X_2136) ),
inference(resolution,[status(thm)],[c_31505,c_406]) ).
tff(c_31565,plain,
! [X_77] : is_a_theorem(implies(X_77,possibly(X_77))),
inference(demodulation,[status(thm),theory(equality)],[c_31544,c_306]) ).
tff(c_24452,plain,
! [X_1776,Y_1777] :
( is_a_theorem(strict_implies(X_1776,Y_1777))
| ~ is_a_theorem(implies(X_1776,Y_1777)) ),
inference(superposition,[status(thm),theory(equality)],[c_12674,c_324]) ).
tff(c_294,plain,
~ axiom_m6,
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_242,plain,
( axiom_m6
| ~ is_a_theorem(strict_implies('#skF_88',possibly('#skF_88'))) ),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_302,plain,
~ is_a_theorem(strict_implies('#skF_88',possibly('#skF_88'))),
inference(negUnitSimplification,[status(thm)],[c_294,c_242]) ).
tff(c_24464,plain,
~ is_a_theorem(implies('#skF_88',possibly('#skF_88'))),
inference(resolution,[status(thm)],[c_24452,c_302]) ).
tff(c_31629,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_31565,c_24464]) ).
tff(c_31631,plain,
~ adjunction,
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_178,plain,
( is_a_theorem('#skF_59')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_31634,plain,
is_a_theorem('#skF_59'),
inference(negUnitSimplification,[status(thm)],[c_31631,c_178]) ).
tff(c_31630,plain,
is_a_theorem('#skF_60'),
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_32902,plain,
! [X_2309,Y_2310] : is_a_theorem(implies(X_2309,implies(Y_2310,and(X_2309,Y_2310)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_33033,plain,
! [Y_2319,X_2320] :
( is_a_theorem(implies(Y_2319,and(X_2320,Y_2319)))
| ~ is_a_theorem(X_2320) ),
inference(resolution,[status(thm)],[c_32902,c_411]) ).
tff(c_33511,plain,
! [X_2356,Y_2357] :
( is_a_theorem(and(X_2356,Y_2357))
| ~ is_a_theorem(Y_2357)
| ~ is_a_theorem(X_2356) ),
inference(resolution,[status(thm)],[c_33033,c_411]) ).
tff(c_174,plain,
( ~ is_a_theorem(and('#skF_59','#skF_60'))
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_31636,plain,
~ is_a_theorem(and('#skF_59','#skF_60')),
inference(negUnitSimplification,[status(thm)],[c_31631,c_174]) ).
tff(c_33526,plain,
( ~ is_a_theorem('#skF_60')
| ~ is_a_theorem('#skF_59') ),
inference(resolution,[status(thm)],[c_33511,c_31636]) ).
tff(c_33540,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_31634,c_31630,c_33526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL546+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n010.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 Aug 3 13:39:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.06/7.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.06/7.99
% 20.06/7.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.06/8.05
% 20.06/8.05 Inference rules
% 20.06/8.05 ----------------------
% 20.06/8.05 #Ref : 0
% 20.06/8.05 #Sup : 8011
% 20.06/8.05 #Fact : 0
% 20.06/8.05 #Define : 0
% 20.06/8.05 #Split : 335
% 20.06/8.05 #Chain : 0
% 20.06/8.05 #Close : 0
% 20.06/8.05
% 20.06/8.05 Ordering : KBO
% 20.06/8.05
% 20.06/8.05 Simplification rules
% 20.06/8.05 ----------------------
% 20.06/8.05 #Subsume : 1250
% 20.06/8.05 #Demod : 4841
% 20.06/8.05 #Tautology : 1948
% 20.06/8.05 #SimpNegUnit : 109
% 20.06/8.05 #BackRed : 177
% 20.06/8.05
% 20.06/8.05 #Partial instantiations: 0
% 20.06/8.05 #Strategies tried : 1
% 20.06/8.05
% 20.06/8.05 Timing (in seconds)
% 20.06/8.05 ----------------------
% 20.06/8.05 Preprocessing : 0.73
% 20.06/8.05 Parsing : 0.35
% 20.06/8.05 CNF conversion : 0.07
% 20.06/8.05 Main loop : 6.23
% 20.06/8.05 Inferencing : 1.70
% 20.06/8.05 Reduction : 2.77
% 20.06/8.05 Demodulation : 1.99
% 20.06/8.05 BG Simplification : 0.10
% 20.06/8.05 Subsumption : 1.26
% 20.06/8.05 Abstraction : 0.12
% 20.06/8.05 MUC search : 0.00
% 20.06/8.05 Cooper : 0.00
% 20.06/8.05 Total : 7.06
% 20.06/8.05 Index Insertion : 0.00
% 20.06/8.05 Index Deletion : 0.00
% 20.06/8.05 Index Matching : 0.00
% 20.06/8.05 BG Taut test : 0.00
%------------------------------------------------------------------------------