TSTP Solution File: LCL548+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL548+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 : n017.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 47.23s 30.60s
% Output : CNFRefutation 47.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 215
% Syntax : Number of formulae : 767 ( 409 unt; 163 typ; 0 def)
% Number of atoms : 846 ( 146 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 504 ( 262 ~; 204 |; 2 &)
% ( 25 <=>; 11 =>; 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 : 647 (; 647 !; 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_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_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_486,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
tff(f_441,axiom,
( op_strict_equiv
=> ! [X,Y] : ( strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
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_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_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_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
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_253,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
tff(f_88,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
tff(f_366,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
tff(f_319,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
tff(f_258,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
tff(f_108,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_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_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
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_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(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_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_489,negated_conjecture,
~ axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
tff(f_395,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m9) ).
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_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_168644,plain,
! [X_10084,Y_10085] : is_a_theorem(implies(implies(X_10084,implies(X_10084,Y_10085)),implies(X_10084,Y_10085))),
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_170299,plain,
! [X_10210,Y_10211] :
( is_a_theorem(implies(X_10210,Y_10211))
| ~ is_a_theorem(implies(X_10210,implies(X_10210,Y_10211))) ),
inference(resolution,[status(thm)],[c_168644,c_411]) ).
tff(c_170364,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_396,c_170299]) ).
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_157061,plain,
! [X_9459,Y_9460] : ( necessarily(implies(X_9459,Y_9460)) = strict_implies(X_9459,Y_9460) ),
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_157073,plain,
! [X_9459,Y_9460] :
( is_a_theorem(strict_implies(X_9459,Y_9460))
| ~ is_a_theorem(implies(X_9459,Y_9460)) ),
inference(superposition,[status(thm),theory(equality)],[c_157061,c_324]) ).
tff(c_292,plain,
op_strict_equiv,
inference(cnfTransformation,[status(thm)],[f_486]) ).
tff(c_268,plain,
! [X_109,Y_110] :
( ( and(strict_implies(X_109,Y_110),strict_implies(Y_110,X_109)) = strict_equiv(X_109,Y_110) )
| ~ op_strict_equiv ),
inference(cnfTransformation,[status(thm)],[f_441]) ).
tff(c_168447,plain,
! [X_10067,Y_10068] : ( and(strict_implies(X_10067,Y_10068),strict_implies(Y_10068,X_10067)) = strict_equiv(X_10067,Y_10068) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
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_143324,plain,
! [X_8327,Y_8328] : is_a_theorem(implies(implies(X_8327,implies(X_8327,Y_8328)),implies(X_8327,Y_8328))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_145132,plain,
! [X_8477,Y_8478] :
( is_a_theorem(implies(X_8477,Y_8478))
| ~ is_a_theorem(implies(X_8477,implies(X_8477,Y_8478))) ),
inference(resolution,[status(thm)],[c_143324,c_411]) ).
tff(c_145191,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_370,c_145132]) ).
tff(c_142826,plain,
! [X_8275,Y_8276] : ( necessarily(implies(X_8275,Y_8276)) = strict_implies(X_8275,Y_8276) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_143233,plain,
! [X_8323,Y_8324] :
( is_a_theorem(strict_implies(X_8323,Y_8324))
| ~ is_a_theorem(implies(X_8323,Y_8324)) ),
inference(superposition,[status(thm),theory(equality)],[c_142826,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_141823,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_143259,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_143233,c_141823]) ).
tff(c_145239,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_145191,c_143259]) ).
tff(c_145240,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_145242,plain,
~ axiom_m4,
inference(splitLeft,[status(thm)],[c_236]) ).
tff(c_145244,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_145240,c_145242]) ).
tff(c_145245,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(splitRight,[status(thm)],[c_236]) ).
tff(c_299,plain,
! [X_107,Y_108] : ( necessarily(implies(X_107,Y_108)) = strict_implies(X_107,Y_108) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
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_146250,plain,
! [Y_8616,X_8617] :
( is_a_theorem(Y_8616)
| ~ is_a_theorem(implies(X_8617,Y_8616))
| ~ is_a_theorem(X_8617) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_146286,plain,
! [X_8618] :
( is_a_theorem(X_8618)
| ~ is_a_theorem(necessarily(X_8618)) ),
inference(resolution,[status(thm)],[c_314,c_146250]) ).
tff(c_146931,plain,
! [X_8688,Y_8689] :
( is_a_theorem(implies(X_8688,Y_8689))
| ~ is_a_theorem(strict_implies(X_8688,Y_8689)) ),
inference(superposition,[status(thm),theory(equality)],[c_299,c_146286]) ).
tff(c_146978,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_145245,c_146931]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_141821,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_146995,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_146978,c_141821]) ).
tff(c_146996,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_157015,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_146996,c_70]) ).
tff(c_168498,plain,
! [Y_10069] : is_a_theorem(implies(strict_implies(Y_10069,Y_10069),strict_equiv(Y_10069,Y_10069))),
inference(superposition,[status(thm),theory(equality)],[c_168447,c_157015]) ).
tff(c_168554,plain,
! [Y_10077] :
( is_a_theorem(strict_equiv(Y_10077,Y_10077))
| ~ is_a_theorem(strict_implies(Y_10077,Y_10077)) ),
inference(resolution,[status(thm)],[c_168498,c_411]) ).
tff(c_168563,plain,
! [Y_9460] :
( is_a_theorem(strict_equiv(Y_9460,Y_9460))
| ~ is_a_theorem(implies(Y_9460,Y_9460)) ),
inference(resolution,[status(thm)],[c_157073,c_168554]) ).
tff(c_170368,plain,
! [Y_9460] : is_a_theorem(strict_equiv(Y_9460,Y_9460)),
inference(demodulation,[status(thm),theory(equality)],[c_170364,c_168563]) ).
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_141806,plain,
! [X_8146] : ( not(necessarily(not(X_8146))) = possibly(X_8146) ),
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_141809,plain,
! [X_8146] : ( possibly(necessarily(not(X_8146))) = not(necessarily(possibly(X_8146))) ),
inference(superposition,[status(thm),theory(equality)],[c_141806,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_157931,plain,
! [X_9560,Y_9561] : ( and(implies(X_9560,Y_9561),implies(Y_9561,X_9560)) = equiv(X_9560,Y_9561) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_178,plain,
( is_a_theorem('#skF_59')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_109303,plain,
adjunction,
inference(splitLeft,[status(thm)],[c_178]) ).
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_157570,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_109303,c_172]) ).
tff(c_163461,plain,
! [X_9876,Y_9877] :
( is_a_theorem(equiv(X_9876,Y_9877))
| ~ is_a_theorem(implies(Y_9877,X_9876))
| ~ is_a_theorem(implies(X_9876,Y_9877)) ),
inference(superposition,[status(thm),theory(equality)],[c_157931,c_157570]) ).
tff(c_163551,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_163461]) ).
tff(c_165738,plain,
! [X_9913] : is_a_theorem(equiv(necessarily(necessarily(X_9913)),necessarily(X_9913))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_163551]) ).
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_165764,plain,
! [X_9913] : ( necessarily(necessarily(X_9913)) = necessarily(X_9913) ),
inference(resolution,[status(thm)],[c_165738,c_406]) ).
tff(c_157515,plain,
! [X_9523,Y_9524] : ( not(and(X_9523,not(Y_9524))) = implies(X_9523,Y_9524) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_157548,plain,
! [X_9523,X_105] : ( implies(X_9523,necessarily(not(X_105))) = not(and(X_9523,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_157515]) ).
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_157025,plain,
! [X_9457,Y_9458] : ( implies(not(X_9457),Y_9458) = or(X_9457,Y_9458) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_157057,plain,
! [X_105,Y_9458] : ( or(necessarily(not(X_105)),Y_9458) = implies(possibly(X_105),Y_9458) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_157025]) ).
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_138,plain,
and_1,
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_34,plain,
! [X_14,Y_15] :
( is_a_theorem(implies(and(X_14,Y_15),X_14))
| ~ and_1 ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_378,plain,
! [X_14,Y_15] : is_a_theorem(implies(and(X_14,Y_15),X_14)),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_34]) ).
tff(c_148362,plain,
! [X_8860,Y_8861] : ( necessarily(implies(X_8860,Y_8861)) = strict_implies(X_8860,Y_8861) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_148876,plain,
! [X_8934,Y_8935] :
( is_a_theorem(strict_implies(X_8934,Y_8935))
| ~ is_a_theorem(implies(X_8934,Y_8935)) ),
inference(superposition,[status(thm),theory(equality)],[c_148362,c_324]) ).
tff(c_228,plain,
! [X_89,Y_90] :
( is_a_theorem(strict_implies(and(X_89,Y_90),X_89))
| ~ axiom_m2 ),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_148382,plain,
~ axiom_m2,
inference(splitLeft,[status(thm)],[c_228]) ).
tff(c_226,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')) ),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_148392,plain,
~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(negUnitSimplification,[status(thm)],[c_148382,c_226]) ).
tff(c_148891,plain,
~ is_a_theorem(implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(resolution,[status(thm)],[c_148876,c_148392]) ).
tff(c_148902,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_378,c_148891]) ).
tff(c_148903,plain,
! [X_89,Y_90] : is_a_theorem(strict_implies(and(X_89,Y_90),X_89)),
inference(splitRight,[status(thm)],[c_228]) ).
tff(c_147785,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_146996,c_70]) ).
tff(c_147034,plain,
! [X_8693,Y_8694] : ( necessarily(implies(X_8693,Y_8694)) = strict_implies(X_8693,Y_8694) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_148290,plain,
! [X_8854,Y_8855] :
( is_a_theorem(strict_implies(X_8854,Y_8855))
| ~ is_a_theorem(implies(X_8854,Y_8855)) ),
inference(superposition,[status(thm),theory(equality)],[c_147034,c_324]) ).
tff(c_146998,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_148302,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_148290,c_146998]) ).
tff(c_148312,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147785,c_148302]) ).
tff(c_148313,plain,
axiom_m4,
inference(splitRight,[status(thm)],[c_234]) ).
tff(c_148317,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_148313,c_236]) ).
tff(c_149674,plain,
! [X_9032,Y_9033] : ( and(strict_implies(X_9032,Y_9033),strict_implies(Y_9033,X_9032)) = strict_equiv(X_9032,Y_9033) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
tff(c_149387,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_109303,c_172]) ).
tff(c_154242,plain,
! [X_9330,Y_9331] :
( is_a_theorem(strict_equiv(X_9330,Y_9331))
| ~ is_a_theorem(strict_implies(Y_9331,X_9330))
| ~ is_a_theorem(strict_implies(X_9330,Y_9331)) ),
inference(superposition,[status(thm),theory(equality)],[c_149674,c_149387]) ).
tff(c_154276,plain,
! [X_94] :
( is_a_theorem(strict_equiv(and(X_94,X_94),X_94))
| ~ is_a_theorem(strict_implies(and(X_94,X_94),X_94)) ),
inference(resolution,[status(thm)],[c_148317,c_154242]) ).
tff(c_154304,plain,
! [X_9332] : is_a_theorem(strict_equiv(and(X_9332,X_9332),X_9332)),
inference(demodulation,[status(thm),theory(equality)],[c_148903,c_154276]) ).
tff(c_182,plain,
( ( '#skF_61' != '#skF_62' )
| substitution_strict_equiv ),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_412,plain,
'#skF_61' != '#skF_62',
inference(splitLeft,[status(thm)],[c_182]) ).
tff(c_74035,plain,
! [X_4282,Y_4283] : is_a_theorem(implies(implies(X_4282,implies(X_4282,Y_4283)),implies(X_4282,Y_4283))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_75888,plain,
! [X_4412,Y_4413] :
( is_a_theorem(implies(X_4412,Y_4413))
| ~ is_a_theorem(implies(X_4412,implies(X_4412,Y_4413))) ),
inference(resolution,[status(thm)],[c_74035,c_411]) ).
tff(c_75953,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_396,c_75888]) ).
tff(c_74100,plain,
! [X_4289,Y_4290] : ( and(implies(X_4289,Y_4290),implies(Y_4290,X_4289)) = equiv(X_4289,Y_4290) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_32099,plain,
! [X_2375,Y_2376] : is_a_theorem(implies(implies(X_2375,implies(X_2375,Y_2376)),implies(X_2375,Y_2376))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_33614,plain,
! [X_2518,Y_2519] :
( is_a_theorem(implies(X_2518,Y_2519))
| ~ is_a_theorem(implies(X_2518,implies(X_2518,Y_2519))) ),
inference(resolution,[status(thm)],[c_32099,c_411]) ).
tff(c_33670,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_370,c_33614]) ).
tff(c_31114,plain,
! [X_2271,Y_2272] : ( necessarily(implies(X_2271,Y_2272)) = strict_implies(X_2271,Y_2272) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_31956,plain,
! [X_2371,Y_2372] :
( is_a_theorem(strict_implies(X_2371,Y_2372))
| ~ is_a_theorem(implies(X_2371,Y_2372)) ),
inference(superposition,[status(thm),theory(equality)],[c_31114,c_324]) ).
tff(c_30432,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_31982,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_31956,c_30432]) ).
tff(c_33874,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_33670,c_31982]) ).
tff(c_33875,plain,
axiom_m4,
inference(splitRight,[status(thm)],[c_234]) ).
tff(c_43385,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_33875,c_236]) ).
tff(c_43389,plain,
! [X_3147,Y_3148] : ( necessarily(implies(X_3147,Y_3148)) = strict_implies(X_3147,Y_3148) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_44991,plain,
! [X_3339,Y_3340] : is_a_theorem(implies(strict_implies(X_3339,Y_3340),implies(X_3339,Y_3340))),
inference(superposition,[status(thm),theory(equality)],[c_43389,c_314]) ).
tff(c_45132,plain,
! [X_3356,Y_3357] :
( is_a_theorem(implies(X_3356,Y_3357))
| ~ is_a_theorem(strict_implies(X_3356,Y_3357)) ),
inference(resolution,[status(thm)],[c_44991,c_411]) ).
tff(c_45179,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_43385,c_45132]) ).
tff(c_43452,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_45196,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_45179,c_43452]) ).
tff(c_45197,plain,
kn1,
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_45873,plain,
~ kn1,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_45875,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_45197,c_45873]) ).
tff(c_45876,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_73196,plain,
! [Y_4198,X_4199] :
( is_a_theorem(Y_4198)
| ~ is_a_theorem(implies(X_4199,Y_4198))
| ~ is_a_theorem(X_4199) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_73232,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_45876,c_73196]) ).
tff(c_74116,plain,
! [Y_4290] :
( is_a_theorem(equiv(Y_4290,Y_4290))
| ~ is_a_theorem(implies(Y_4290,Y_4290)) ),
inference(superposition,[status(thm),theory(equality)],[c_74100,c_73232]) ).
tff(c_75957,plain,
! [Y_4290] : is_a_theorem(equiv(Y_4290,Y_4290)),
inference(demodulation,[status(thm),theory(equality)],[c_75953,c_74116]) ).
tff(c_3230,plain,
! [X_410] : ( not(necessarily(not(X_410))) = possibly(X_410) ),
inference(demodulation,[status(thm),theory(equality)],[c_282,c_262]) ).
tff(c_3233,plain,
! [X_410] : ( possibly(necessarily(not(X_410))) = not(necessarily(possibly(X_410))) ),
inference(superposition,[status(thm),theory(equality)],[c_3230,c_301]) ).
tff(c_13302,plain,
! [X_1383,Y_1384] : ( and(implies(X_1383,Y_1384),implies(Y_1384,X_1383)) = equiv(X_1383,Y_1384) ),
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_13201,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_19203,plain,
! [X_1692,Y_1693] :
( is_a_theorem(equiv(X_1692,Y_1693))
| ~ is_a_theorem(implies(Y_1693,X_1692))
| ~ is_a_theorem(implies(X_1692,Y_1693)) ),
inference(superposition,[status(thm),theory(equality)],[c_13302,c_13201]) ).
tff(c_19293,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_19203]) ).
tff(c_21156,plain,
! [X_1719] : is_a_theorem(equiv(necessarily(necessarily(X_1719)),necessarily(X_1719))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_19293]) ).
tff(c_21182,plain,
! [X_1719] : ( necessarily(necessarily(X_1719)) = necessarily(X_1719) ),
inference(resolution,[status(thm)],[c_21156,c_406]) ).
tff(c_12960,plain,
! [X_1357,Y_1358] : ( not(and(X_1357,not(Y_1358))) = implies(X_1357,Y_1358) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_12993,plain,
! [X_1357,X_105] : ( implies(X_1357,necessarily(not(X_105))) = not(and(X_1357,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_12960]) ).
tff(c_12440,plain,
! [X_1283,Y_1284] : ( implies(not(X_1283),Y_1284) = or(X_1283,Y_1284) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_12472,plain,
! [X_105,Y_1284] : ( or(necessarily(not(X_105)),Y_1284) = implies(possibly(X_105),Y_1284) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_12440]) ).
tff(c_5823,plain,
! [X_706,Y_707] : is_a_theorem(implies(implies(X_706,implies(X_706,Y_707)),implies(X_706,Y_707))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_7837,plain,
! [X_863,Y_864] :
( is_a_theorem(implies(X_863,Y_864))
| ~ is_a_theorem(implies(X_863,implies(X_863,Y_864))) ),
inference(resolution,[status(thm)],[c_5823,c_411]) ).
tff(c_7902,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_396,c_7837]) ).
tff(c_148,plain,
or_3,
inference(cnfTransformation,[status(thm)],[f_258]) ).
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_108]) ).
tff(c_352,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)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_8499,plain,
! [Y_892,Z_893] : is_a_theorem(implies(implies(Y_892,Z_893),implies(or(Y_892,Y_892),Z_893))),
inference(resolution,[status(thm)],[c_352,c_7837]) ).
tff(c_9992,plain,
! [Y_982,Z_983] :
( is_a_theorem(implies(or(Y_982,Y_982),Z_983))
| ~ is_a_theorem(implies(Y_982,Z_983)) ),
inference(resolution,[status(thm)],[c_8499,c_411]) ).
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_3934,plain,
~ cn3,
inference(splitLeft,[status(thm)],[c_333]) ).
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_3977,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_3934,c_334]) ).
tff(c_10005,plain,
~ is_a_theorem(implies('#skF_44','#skF_44')),
inference(resolution,[status(thm)],[c_9992,c_3977]) ).
tff(c_10031,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7902,c_10005]) ).
tff(c_10032,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(splitRight,[status(thm)],[c_333]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_3245,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_10036,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10032,c_3245]) ).
tff(c_10037,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_12427,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_10037,c_94]) ).
tff(c_19295,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_12427,c_19203]) ).
tff(c_19379,plain,
! [P_1694] : is_a_theorem(equiv(P_1694,or(P_1694,P_1694))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_19295]) ).
tff(c_19416,plain,
! [P_1694] : ( or(P_1694,P_1694) = P_1694 ),
inference(resolution,[status(thm)],[c_19379,c_406]) ).
tff(c_11745,plain,
! [X_1190,Y_1191] : ( necessarily(implies(X_1190,Y_1191)) = strict_implies(X_1190,Y_1191) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_12389,plain,
! [X_1273,Y_1274] :
( is_a_theorem(strict_implies(X_1273,Y_1274))
| ~ is_a_theorem(implies(X_1273,Y_1274)) ),
inference(superposition,[status(thm),theory(equality)],[c_11745,c_324]) ).
tff(c_11712,plain,
~ axiom_m2,
inference(splitLeft,[status(thm)],[c_228]) ).
tff(c_11730,plain,
~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(negUnitSimplification,[status(thm)],[c_11712,c_226]) ).
tff(c_12404,plain,
~ is_a_theorem(implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(resolution,[status(thm)],[c_12389,c_11730]) ).
tff(c_12418,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_378,c_12404]) ).
tff(c_12419,plain,
! [X_89,Y_90] : is_a_theorem(strict_implies(and(X_89,Y_90),X_89)),
inference(splitRight,[status(thm)],[c_228]) ).
tff(c_2218,plain,
! [X_333,Y_334] : is_a_theorem(implies(implies(X_333,implies(X_333,Y_334)),implies(X_333,Y_334))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_3132,plain,
! [X_406,Y_407] :
( is_a_theorem(implies(X_406,Y_407))
| ~ is_a_theorem(implies(X_406,implies(X_406,Y_407))) ),
inference(resolution,[status(thm)],[c_2218,c_411]) ).
tff(c_3187,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_370,c_3132]) ).
tff(c_1264,plain,
! [X_230,Y_231] : ( necessarily(implies(X_230,Y_231)) = strict_implies(X_230,Y_231) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_1941,plain,
! [X_317,Y_318] :
( is_a_theorem(strict_implies(X_317,Y_318))
| ~ is_a_theorem(implies(X_317,Y_318)) ),
inference(superposition,[status(thm),theory(equality)],[c_1264,c_324]) ).
tff(c_431,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_1966,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_1941,c_431]) ).
tff(c_3227,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3187,c_1966]) ).
tff(c_3228,plain,
axiom_m4,
inference(splitRight,[status(thm)],[c_234]) ).
tff(c_12431,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_3228,c_236]) ).
tff(c_13512,plain,
! [X_1403,Y_1404] : ( and(strict_implies(X_1403,Y_1404),strict_implies(Y_1404,X_1403)) = strict_equiv(X_1403,Y_1404) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
tff(c_17710,plain,
! [X_1676,Y_1677] :
( is_a_theorem(strict_equiv(X_1676,Y_1677))
| ~ is_a_theorem(strict_implies(Y_1677,X_1676))
| ~ is_a_theorem(strict_implies(X_1676,Y_1677)) ),
inference(superposition,[status(thm),theory(equality)],[c_13512,c_13201]) ).
tff(c_17742,plain,
! [X_94] :
( is_a_theorem(strict_equiv(and(X_94,X_94),X_94))
| ~ is_a_theorem(strict_implies(and(X_94,X_94),X_94)) ),
inference(resolution,[status(thm)],[c_12431,c_17710]) ).
tff(c_17771,plain,
! [X_1678] : is_a_theorem(strict_equiv(and(X_1678,X_1678),X_1678)),
inference(demodulation,[status(thm),theory(equality)],[c_12419,c_17742]) ).
tff(c_184,plain,
( is_a_theorem(strict_equiv('#skF_61','#skF_62'))
| substitution_strict_equiv ),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_418,plain,
substitution_strict_equiv,
inference(splitLeft,[status(thm)],[c_184]) ).
tff(c_180,plain,
! [Y_72,X_71] :
( ( Y_72 = X_71 )
| ~ is_a_theorem(strict_equiv(X_71,Y_72))
| ~ substitution_strict_equiv ),
inference(cnfTransformation,[status(thm)],[f_319]) ).
tff(c_12438,plain,
! [Y_72,X_71] :
( ( Y_72 = X_71 )
| ~ is_a_theorem(strict_equiv(X_71,Y_72)) ),
inference(demodulation,[status(thm),theory(equality)],[c_418,c_180]) ).
tff(c_17829,plain,
! [X_1679] : ( and(X_1679,X_1679) = X_1679 ),
inference(resolution,[status(thm)],[c_17771,c_12438]) ).
tff(c_18475,plain,
! [Y_1687] : ( implies(not(Y_1687),Y_1687) = not(not(Y_1687)) ),
inference(superposition,[status(thm),theory(equality)],[c_17829,c_330]) ).
tff(c_18619,plain,
! [Y_1687] : ( or(Y_1687,Y_1687) = not(not(Y_1687)) ),
inference(superposition,[status(thm),theory(equality)],[c_18475,c_332]) ).
tff(c_19597,plain,
! [Y_1696] : ( not(not(Y_1696)) = Y_1696 ),
inference(demodulation,[status(thm),theory(equality)],[c_19416,c_18619]) ).
tff(c_19813,plain,
! [Y_1696] : ( possibly(not(Y_1696)) = not(necessarily(Y_1696)) ),
inference(superposition,[status(thm),theory(equality)],[c_19597,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_12455,plain,
! [X_1283] : is_a_theorem(or(X_1283,necessarily(possibly(not(X_1283))))),
inference(superposition,[status(thm),theory(equality)],[c_12440,c_306]) ).
tff(c_22166,plain,
! [X_1748] : is_a_theorem(or(X_1748,necessarily(not(necessarily(X_1748))))),
inference(demodulation,[status(thm),theory(equality)],[c_19813,c_12455]) ).
tff(c_22196,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(not(necessarily(necessarily(not(X_105))))))),
inference(superposition,[status(thm),theory(equality)],[c_12472,c_22166]) ).
tff(c_22208,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(possibly(X_105)))),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_3233,c_21182,c_12993,c_22196]) ).
tff(c_12478,plain,
! [X_1285,Y_1286] : ( necessarily(implies(X_1285,Y_1286)) = strict_implies(X_1285,Y_1286) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_13054,plain,
! [X_1366,Y_1367] :
( is_a_theorem(strict_implies(X_1366,Y_1367))
| ~ is_a_theorem(implies(X_1366,Y_1367)) ),
inference(superposition,[status(thm),theory(equality)],[c_12478,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_12903,plain,
~ is_a_theorem(strict_implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(splitLeft,[status(thm)],[c_258]) ).
tff(c_13067,plain,
~ is_a_theorem(implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(resolution,[status(thm)],[c_13054,c_12903]) ).
tff(c_22602,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22208,c_13067]) ).
tff(c_22603,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_22690,plain,
! [X_104] : is_a_theorem(strict_implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(demodulation,[status(thm),theory(equality)],[c_22603,c_260]) ).
tff(c_22776,plain,
! [X_1779,Y_1780] : is_a_theorem(implies(strict_implies(X_1779,Y_1780),implies(X_1779,Y_1780))),
inference(superposition,[status(thm),theory(equality)],[c_12478,c_314]) ).
tff(c_22927,plain,
! [X_1793,Y_1794] :
( is_a_theorem(implies(X_1793,Y_1794))
| ~ is_a_theorem(strict_implies(X_1793,Y_1794)) ),
inference(resolution,[status(thm)],[c_22776,c_411]) ).
tff(c_22948,plain,
! [X_104] : is_a_theorem(implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(resolution,[status(thm)],[c_22690,c_22927]) ).
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_22636,plain,
~ axiom_5,
inference(splitLeft,[status(thm)],[c_204]) ).
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_22693,plain,
~ is_a_theorem(implies(possibly('#skF_68'),necessarily(possibly('#skF_68')))),
inference(negUnitSimplification,[status(thm)],[c_22636,c_202]) ).
tff(c_22957,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22948,c_22693]) ).
tff(c_22958,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(splitRight,[status(thm)],[c_204]) ).
tff(c_23376,plain,
! [X_1833,Y_1834] : ( and(implies(X_1833,Y_1834),implies(Y_1834,X_1833)) = equiv(X_1833,Y_1834) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_23248,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_27872,plain,
! [X_2126,Y_2127] :
( is_a_theorem(equiv(X_2126,Y_2127))
| ~ is_a_theorem(implies(Y_2127,X_2126))
| ~ is_a_theorem(implies(X_2126,Y_2127)) ),
inference(superposition,[status(thm),theory(equality)],[c_23376,c_23248]) ).
tff(c_27954,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_22958,c_27872]) ).
tff(c_30289,plain,
! [X_2167] : is_a_theorem(equiv(necessarily(possibly(X_2167)),possibly(X_2167))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_27954]) ).
tff(c_30328,plain,
! [X_2167] : ( necessarily(possibly(X_2167)) = possibly(X_2167) ),
inference(resolution,[status(thm)],[c_30289,c_406]) ).
tff(c_30350,plain,
! [X_77] : is_a_theorem(implies(X_77,possibly(X_77))),
inference(demodulation,[status(thm),theory(equality)],[c_30328,c_306]) ).
tff(c_23142,plain,
! [X_1815,Y_1816] :
( is_a_theorem(strict_implies(X_1815,Y_1816))
| ~ is_a_theorem(implies(X_1815,Y_1816)) ),
inference(superposition,[status(thm),theory(equality)],[c_12478,c_324]) ).
tff(c_242,plain,
( axiom_m6
| ~ is_a_theorem(strict_implies('#skF_88',possibly('#skF_88'))) ),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_423,plain,
~ is_a_theorem(strict_implies('#skF_88',possibly('#skF_88'))),
inference(splitLeft,[status(thm)],[c_242]) ).
tff(c_23160,plain,
~ is_a_theorem(implies('#skF_88',possibly('#skF_88'))),
inference(resolution,[status(thm)],[c_23142,c_423]) ).
tff(c_30419,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_30350,c_23160]) ).
tff(c_30420,plain,
axiom_m6,
inference(splitRight,[status(thm)],[c_242]) ).
tff(c_244,plain,
! [X_98] :
( is_a_theorem(strict_implies(X_98,possibly(X_98)))
| ~ axiom_m6 ),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_30428,plain,
! [X_98] : is_a_theorem(strict_implies(X_98,possibly(X_98))),
inference(demodulation,[status(thm),theory(equality)],[c_30420,c_244]) ).
tff(c_73891,plain,
! [X_4265,Y_4266] : is_a_theorem(implies(strict_implies(X_4265,Y_4266),implies(X_4265,Y_4266))),
inference(superposition,[status(thm),theory(equality)],[c_43389,c_314]) ).
tff(c_73972,plain,
! [X_4279,Y_4280] :
( is_a_theorem(implies(X_4279,Y_4280))
| ~ is_a_theorem(strict_implies(X_4279,Y_4280)) ),
inference(resolution,[status(thm)],[c_73891,c_411]) ).
tff(c_74004,plain,
! [X_98] : is_a_theorem(implies(X_98,possibly(X_98))),
inference(resolution,[status(thm)],[c_30428,c_73972]) ).
tff(c_73237,plain,
! [Y_8,X_7] :
( is_a_theorem(implies(Y_8,X_7))
| ~ is_a_theorem(X_7) ),
inference(resolution,[status(thm)],[c_396,c_73196]) ).
tff(c_73925,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_78972,plain,
! [X_4583,Y_4584] :
( is_a_theorem(equiv(X_4583,Y_4584))
| ~ is_a_theorem(implies(Y_4584,X_4583))
| ~ is_a_theorem(implies(X_4583,Y_4584)) ),
inference(superposition,[status(thm),theory(equality)],[c_74100,c_73925]) ).
tff(c_88951,plain,
! [X_4756,Y_4757] :
( is_a_theorem(equiv(X_4756,Y_4757))
| ~ is_a_theorem(implies(X_4756,Y_4757))
| ~ is_a_theorem(X_4756) ),
inference(resolution,[status(thm)],[c_73237,c_78972]) ).
tff(c_89222,plain,
! [X_4758] :
( is_a_theorem(equiv(X_4758,possibly(X_4758)))
| ~ is_a_theorem(X_4758) ),
inference(resolution,[status(thm)],[c_74004,c_88951]) ).
tff(c_89267,plain,
! [X_4759] :
( ( possibly(X_4759) = X_4759 )
| ~ is_a_theorem(X_4759) ),
inference(resolution,[status(thm)],[c_89222,c_406]) ).
tff(c_89712,plain,
! [Y_4290] : ( possibly(equiv(Y_4290,Y_4290)) = equiv(Y_4290,Y_4290) ),
inference(resolution,[status(thm)],[c_75957,c_89267]) ).
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_79068,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_45876,c_78972]) ).
tff(c_79186,plain,
! [P_4585] : is_a_theorem(equiv(and(P_4585,P_4585),P_4585)),
inference(demodulation,[status(thm),theory(equality)],[c_374,c_79068]) ).
tff(c_79233,plain,
! [P_4586] : ( and(P_4586,P_4586) = P_4586 ),
inference(resolution,[status(thm)],[c_79186,c_406]) ).
tff(c_297,plain,
! [X_109,Y_110] : ( and(strict_implies(X_109,Y_110),strict_implies(Y_110,X_109)) = strict_equiv(X_109,Y_110) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
tff(c_79338,plain,
! [X_109] : ( strict_implies(X_109,X_109) = strict_equiv(X_109,X_109) ),
inference(superposition,[status(thm),theory(equality)],[c_79233,c_297]) ).
tff(c_328,plain,
! [X_64,Y_65] : ( and(implies(X_64,Y_65),implies(Y_65,X_64)) = equiv(X_64,Y_65) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_79811,plain,
! [X_4598] : ( implies(X_4598,X_4598) = equiv(X_4598,X_4598) ),
inference(superposition,[status(thm),theory(equality)],[c_79233,c_328]) ).
tff(c_79990,plain,
! [X_4598] : ( necessarily(equiv(X_4598,X_4598)) = strict_implies(X_4598,X_4598) ),
inference(superposition,[status(thm),theory(equality)],[c_79811,c_299]) ).
tff(c_82993,plain,
! [X_4598] : ( necessarily(equiv(X_4598,X_4598)) = strict_equiv(X_4598,X_4598) ),
inference(demodulation,[status(thm),theory(equality)],[c_79338,c_79990]) ).
tff(c_90276,plain,
! [Y_4768] : ( possibly(equiv(Y_4768,Y_4768)) = equiv(Y_4768,Y_4768) ),
inference(resolution,[status(thm)],[c_75957,c_89267]) ).
tff(c_43369,plain,
! [X_3145] : ( not(necessarily(not(X_3145))) = possibly(X_3145) ),
inference(demodulation,[status(thm),theory(equality)],[c_282,c_262]) ).
tff(c_43378,plain,
! [X_105] : ( possibly(necessarily(not(X_105))) = not(necessarily(possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_43369]) ).
tff(c_46807,plain,
! [X_3562,Y_3563] : ( and(implies(X_3562,Y_3563),implies(Y_3563,X_3562)) = equiv(X_3562,Y_3563) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_46654,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_51972,plain,
! [X_3868,Y_3869] :
( is_a_theorem(equiv(X_3868,Y_3869))
| ~ is_a_theorem(implies(Y_3869,X_3868))
| ~ is_a_theorem(implies(X_3868,Y_3869)) ),
inference(superposition,[status(thm),theory(equality)],[c_46807,c_46654]) ).
tff(c_52064,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_51972]) ).
tff(c_55194,plain,
! [X_3918] : is_a_theorem(equiv(necessarily(necessarily(X_3918)),necessarily(X_3918))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_52064]) ).
tff(c_55220,plain,
! [X_3918] : ( necessarily(necessarily(X_3918)) = necessarily(X_3918) ),
inference(resolution,[status(thm)],[c_55194,c_406]) ).
tff(c_46405,plain,
! [X_3527,Y_3528] : ( not(and(X_3527,not(Y_3528))) = implies(X_3527,Y_3528) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_46438,plain,
! [X_3527,X_105] : ( implies(X_3527,necessarily(not(X_105))) = not(and(X_3527,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_46405]) ).
tff(c_43404,plain,
! [X_3149,Y_3150] : ( implies(not(X_3149),Y_3150) = or(X_3149,Y_3150) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_43435,plain,
! [X_105,Y_3150] : ( or(necessarily(not(X_105)),Y_3150) = implies(possibly(X_105),Y_3150) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_43404]) ).
tff(c_33899,plain,
! [X_2527,Y_2528] : ( necessarily(implies(X_2527,Y_2528)) = strict_implies(X_2527,Y_2528) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_34668,plain,
! [X_2616,Y_2617] :
( is_a_theorem(strict_implies(X_2616,Y_2617))
| ~ is_a_theorem(implies(X_2616,Y_2617)) ),
inference(superposition,[status(thm),theory(equality)],[c_33899,c_324]) ).
tff(c_33922,plain,
~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(splitLeft,[status(thm)],[c_226]) ).
tff(c_34680,plain,
~ is_a_theorem(implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(resolution,[status(thm)],[c_34668,c_33922]) ).
tff(c_34693,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_378,c_34680]) ).
tff(c_34694,plain,
axiom_m2,
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_34696,plain,
~ axiom_m2,
inference(splitLeft,[status(thm)],[c_228]) ).
tff(c_34698,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_34694,c_34696]) ).
tff(c_34699,plain,
! [X_89,Y_90] : is_a_theorem(strict_implies(and(X_89,Y_90),X_89)),
inference(splitRight,[status(thm)],[c_228]) ).
tff(c_33895,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_33875,c_236]) ).
tff(c_36837,plain,
! [X_2834,Y_2835] : ( and(strict_implies(X_2834,Y_2835),strict_implies(Y_2835,X_2834)) = strict_equiv(X_2834,Y_2835) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
tff(c_36358,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_41180,plain,
! [X_3113,Y_3114] :
( is_a_theorem(strict_equiv(X_3113,Y_3114))
| ~ is_a_theorem(strict_implies(Y_3114,X_3113))
| ~ is_a_theorem(strict_implies(X_3113,Y_3114)) ),
inference(superposition,[status(thm),theory(equality)],[c_36837,c_36358]) ).
tff(c_41218,plain,
! [X_94] :
( is_a_theorem(strict_equiv(and(X_94,X_94),X_94))
| ~ is_a_theorem(strict_implies(and(X_94,X_94),X_94)) ),
inference(resolution,[status(thm)],[c_33895,c_41180]) ).
tff(c_41252,plain,
! [X_3115] : is_a_theorem(strict_equiv(and(X_3115,X_3115),X_3115)),
inference(demodulation,[status(thm),theory(equality)],[c_34699,c_41218]) ).
tff(c_35528,plain,
! [Y_72,X_71] :
( ( Y_72 = X_71 )
| ~ is_a_theorem(strict_equiv(X_71,Y_72)) ),
inference(demodulation,[status(thm),theory(equality)],[c_418,c_180]) ).
tff(c_41310,plain,
! [X_3116] : ( and(X_3116,X_3116) = X_3116 ),
inference(resolution,[status(thm)],[c_41252,c_35528]) ).
tff(c_41964,plain,
! [Y_3124] : ( implies(not(Y_3124),Y_3124) = not(not(Y_3124)) ),
inference(superposition,[status(thm),theory(equality)],[c_41310,c_330]) ).
tff(c_42203,plain,
! [Y_3127] : ( or(Y_3127,Y_3127) = not(not(Y_3127)) ),
inference(superposition,[status(thm),theory(equality)],[c_332,c_41964]) ).
tff(c_42111,plain,
! [Y_3124] : is_a_theorem(implies(Y_3124,not(not(Y_3124)))),
inference(superposition,[status(thm),theory(equality)],[c_41964,c_396]) ).
tff(c_42212,plain,
! [Y_3127] : is_a_theorem(implies(not(Y_3127),not(or(Y_3127,Y_3127)))),
inference(superposition,[status(thm),theory(equality)],[c_42203,c_42111]) ).
tff(c_43320,plain,
! [Y_3144] : is_a_theorem(or(Y_3144,not(or(Y_3144,Y_3144)))),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_42212]) ).
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_36418,plain,
! [Y_2804,X_2805] : is_a_theorem(implies(or(Y_2804,not(X_2805)),implies(X_2805,Y_2804))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_36431,plain,
! [X_2805,Y_2804] :
( is_a_theorem(implies(X_2805,Y_2804))
| ~ is_a_theorem(or(Y_2804,not(X_2805))) ),
inference(resolution,[status(thm)],[c_36418,c_411]) ).
tff(c_43351,plain,
! [Y_3144] : is_a_theorem(implies(or(Y_3144,Y_3144),Y_3144)),
inference(resolution,[status(thm)],[c_43320,c_36431]) ).
tff(c_34704,plain,
~ cn3,
inference(splitLeft,[status(thm)],[c_333]) ).
tff(c_34705,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_34704,c_334]) ).
tff(c_43361,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_43351,c_34705]) ).
tff(c_43362,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(splitRight,[status(thm)],[c_333]) ).
tff(c_33877,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_43366,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_43362,c_33877]) ).
tff(c_43367,plain,
r1,
inference(splitRight,[status(thm)],[c_92]) ).
tff(c_45886,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_43367,c_94]) ).
tff(c_52066,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_45886,c_51972]) ).
tff(c_52756,plain,
! [P_3879] : is_a_theorem(equiv(P_3879,or(P_3879,P_3879))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_52066]) ).
tff(c_52790,plain,
! [P_3879] : ( or(P_3879,P_3879) = P_3879 ),
inference(resolution,[status(thm)],[c_52756,c_406]) ).
tff(c_49798,plain,
! [X_3762,X_3763,Y_3764] : ( implies(X_3762,and(X_3763,not(Y_3764))) = not(and(X_3762,implies(X_3763,Y_3764))) ),
inference(superposition,[status(thm),theory(equality)],[c_330,c_46405]) ).
tff(c_49941,plain,
! [Y_3764] : is_a_theorem(not(and(not(Y_3764),implies(not(Y_3764),Y_3764)))),
inference(superposition,[status(thm),theory(equality)],[c_49798,c_45876]) ).
tff(c_49998,plain,
! [Y_3764] : is_a_theorem(not(and(not(Y_3764),or(Y_3764,Y_3764)))),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_49941]) ).
tff(c_53033,plain,
! [Y_3885] : is_a_theorem(not(and(not(Y_3885),Y_3885))),
inference(demodulation,[status(thm),theory(equality)],[c_52790,c_49998]) ).
tff(c_53049,plain,
! [Y_61] : is_a_theorem(implies(not(not(Y_61)),Y_61)),
inference(superposition,[status(thm),theory(equality)],[c_330,c_53033]) ).
tff(c_53056,plain,
! [Y_61] : is_a_theorem(or(not(Y_61),Y_61)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_53049]) ).
tff(c_53057,plain,
! [Y_3886] : is_a_theorem(or(not(Y_3886),Y_3886)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_53049]) ).
tff(c_46699,plain,
! [Y_3549,X_3550] : is_a_theorem(implies(or(Y_3549,not(X_3550)),implies(X_3550,Y_3549))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_46712,plain,
! [X_3550,Y_3549] :
( is_a_theorem(implies(X_3550,Y_3549))
| ~ is_a_theorem(or(Y_3549,not(X_3550))) ),
inference(resolution,[status(thm)],[c_46699,c_411]) ).
tff(c_53275,plain,
! [X_3890] : is_a_theorem(implies(X_3890,not(not(X_3890)))),
inference(resolution,[status(thm)],[c_53057,c_46712]) ).
tff(c_46813,plain,
! [X_3562,Y_3563] :
( is_a_theorem(equiv(X_3562,Y_3563))
| ~ is_a_theorem(implies(Y_3563,X_3562))
| ~ is_a_theorem(implies(X_3562,Y_3563)) ),
inference(superposition,[status(thm),theory(equality)],[c_46807,c_46654]) ).
tff(c_53277,plain,
! [X_3890] :
( is_a_theorem(equiv(not(not(X_3890)),X_3890))
| ~ is_a_theorem(implies(not(not(X_3890)),X_3890)) ),
inference(resolution,[status(thm)],[c_53275,c_46813]) ).
tff(c_53303,plain,
! [X_3891] : is_a_theorem(equiv(not(not(X_3891)),X_3891)),
inference(demodulation,[status(thm),theory(equality)],[c_53056,c_332,c_53277]) ).
tff(c_53402,plain,
! [X_3895] : ( not(not(X_3895)) = X_3895 ),
inference(resolution,[status(thm)],[c_53303,c_406]) ).
tff(c_53648,plain,
! [X_3895] : ( possibly(not(X_3895)) = not(necessarily(X_3895)) ),
inference(superposition,[status(thm),theory(equality)],[c_53402,c_301]) ).
tff(c_43422,plain,
! [X_3149] : is_a_theorem(or(X_3149,necessarily(possibly(not(X_3149))))),
inference(superposition,[status(thm),theory(equality)],[c_43404,c_306]) ).
tff(c_56145,plain,
! [X_3943] : is_a_theorem(or(X_3943,necessarily(not(necessarily(X_3943))))),
inference(demodulation,[status(thm),theory(equality)],[c_53648,c_43422]) ).
tff(c_56171,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(not(necessarily(necessarily(not(X_105))))))),
inference(superposition,[status(thm),theory(equality)],[c_43435,c_56145]) ).
tff(c_56182,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(possibly(X_105)))),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_43378,c_55220,c_46438,c_56171]) ).
tff(c_46540,plain,
! [X_3541,Y_3542] :
( is_a_theorem(strict_implies(X_3541,Y_3542))
| ~ is_a_theorem(implies(X_3541,Y_3542)) ),
inference(superposition,[status(thm),theory(equality)],[c_43389,c_324]) ).
tff(c_45912,plain,
~ axiom_m10,
inference(splitLeft,[status(thm)],[c_260]) ).
tff(c_46270,plain,
~ is_a_theorem(strict_implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(negUnitSimplification,[status(thm)],[c_45912,c_258]) ).
tff(c_46555,plain,
~ is_a_theorem(implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(resolution,[status(thm)],[c_46540,c_46270]) ).
tff(c_72854,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_56182,c_46555]) ).
tff(c_72855,plain,
! [X_104] : is_a_theorem(strict_implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(splitRight,[status(thm)],[c_260]) ).
tff(c_73613,plain,
! [X_4241,Y_4242] : is_a_theorem(implies(strict_implies(X_4241,Y_4242),implies(X_4241,Y_4242))),
inference(superposition,[status(thm),theory(equality)],[c_43389,c_314]) ).
tff(c_73630,plain,
! [X_4247,Y_4248] :
( is_a_theorem(implies(X_4247,Y_4248))
| ~ is_a_theorem(strict_implies(X_4247,Y_4248)) ),
inference(resolution,[status(thm)],[c_73613,c_411]) ).
tff(c_73656,plain,
! [X_104] : is_a_theorem(implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(resolution,[status(thm)],[c_72855,c_73630]) ).
tff(c_73347,plain,
~ is_a_theorem(implies(possibly('#skF_68'),necessarily(possibly('#skF_68')))),
inference(splitLeft,[status(thm)],[c_202]) ).
tff(c_73678,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_73656,c_73347]) ).
tff(c_73679,plain,
axiom_5,
inference(splitRight,[status(thm)],[c_202]) ).
tff(c_73696,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(demodulation,[status(thm),theory(equality)],[c_73679,c_204]) ).
tff(c_79054,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_73696,c_78972]) ).
tff(c_82321,plain,
! [X_4635] : is_a_theorem(equiv(necessarily(possibly(X_4635)),possibly(X_4635))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_79054]) ).
tff(c_82360,plain,
! [X_4635] : ( necessarily(possibly(X_4635)) = possibly(X_4635) ),
inference(resolution,[status(thm)],[c_82321,c_406]) ).
tff(c_90333,plain,
! [Y_4768] : ( possibly(equiv(Y_4768,Y_4768)) = necessarily(equiv(Y_4768,Y_4768)) ),
inference(superposition,[status(thm),theory(equality)],[c_90276,c_82360]) ).
tff(c_90423,plain,
! [Y_4768] : ( strict_equiv(Y_4768,Y_4768) = equiv(Y_4768,Y_4768) ),
inference(demodulation,[status(thm),theory(equality)],[c_89712,c_82993,c_90333]) ).
tff(c_79066,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_45886,c_78972]) ).
tff(c_79511,plain,
! [P_4592] : is_a_theorem(equiv(P_4592,or(P_4592,P_4592))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_79066]) ).
tff(c_79545,plain,
! [P_4592] : ( or(P_4592,P_4592) = P_4592 ),
inference(resolution,[status(thm)],[c_79511,c_406]) ).
tff(c_73277,plain,
! [X_4214,Y_4215] : ( not(and(X_4214,not(Y_4215))) = implies(X_4214,Y_4215) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_77478,plain,
! [X_4515,X_4516,Y_4517] : ( implies(X_4515,and(X_4516,not(Y_4517))) = not(and(X_4515,implies(X_4516,Y_4517))) ),
inference(superposition,[status(thm),theory(equality)],[c_73277,c_330]) ).
tff(c_77624,plain,
! [Y_4517] : is_a_theorem(not(and(not(Y_4517),implies(not(Y_4517),Y_4517)))),
inference(superposition,[status(thm),theory(equality)],[c_77478,c_45876]) ).
tff(c_77682,plain,
! [Y_4517] : is_a_theorem(not(and(not(Y_4517),or(Y_4517,Y_4517)))),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_77624]) ).
tff(c_79756,plain,
! [Y_4596] : is_a_theorem(not(and(not(Y_4596),Y_4596))),
inference(demodulation,[status(thm),theory(equality)],[c_79545,c_77682]) ).
tff(c_79772,plain,
! [Y_61] : is_a_theorem(implies(not(not(Y_61)),Y_61)),
inference(superposition,[status(thm),theory(equality)],[c_330,c_79756]) ).
tff(c_79779,plain,
! [Y_61] : is_a_theorem(or(not(Y_61),Y_61)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_79772]) ).
tff(c_79780,plain,
! [Y_4597] : is_a_theorem(or(not(Y_4597),Y_4597)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_79772]) ).
tff(c_73958,plain,
! [Y_4277,X_4278] : is_a_theorem(implies(or(Y_4277,not(X_4278)),implies(X_4278,Y_4277))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_73971,plain,
! [X_4278,Y_4277] :
( is_a_theorem(implies(X_4278,Y_4277))
| ~ is_a_theorem(or(Y_4277,not(X_4278))) ),
inference(resolution,[status(thm)],[c_73958,c_411]) ).
tff(c_80326,plain,
! [X_4605] : is_a_theorem(implies(X_4605,not(not(X_4605)))),
inference(resolution,[status(thm)],[c_79780,c_73971]) ).
tff(c_74106,plain,
! [X_4289,Y_4290] :
( is_a_theorem(equiv(X_4289,Y_4290))
| ~ is_a_theorem(implies(Y_4290,X_4289))
| ~ is_a_theorem(implies(X_4289,Y_4290)) ),
inference(superposition,[status(thm),theory(equality)],[c_74100,c_73925]) ).
tff(c_80328,plain,
! [X_4605] :
( is_a_theorem(equiv(not(not(X_4605)),X_4605))
| ~ is_a_theorem(implies(not(not(X_4605)),X_4605)) ),
inference(resolution,[status(thm)],[c_80326,c_74106]) ).
tff(c_80358,plain,
! [X_4606] : is_a_theorem(equiv(not(not(X_4606)),X_4606)),
inference(demodulation,[status(thm),theory(equality)],[c_79779,c_332,c_80328]) ).
tff(c_80394,plain,
! [X_4606] : ( not(not(X_4606)) = X_4606 ),
inference(resolution,[status(thm)],[c_80358,c_406]) ).
tff(c_43395,plain,
! [X_3147,Y_3148] :
( is_a_theorem(strict_implies(X_3147,Y_3148))
| ~ is_a_theorem(implies(X_3147,Y_3148)) ),
inference(superposition,[status(thm),theory(equality)],[c_43389,c_324]) ).
tff(c_74241,plain,
! [X_4299,Y_4300] : ( and(strict_implies(X_4299,Y_4300),strict_implies(Y_4300,X_4299)) = strict_equiv(X_4299,Y_4300) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
tff(c_74304,plain,
! [Y_4303] : is_a_theorem(implies(strict_implies(Y_4303,Y_4303),strict_equiv(Y_4303,Y_4303))),
inference(superposition,[status(thm),theory(equality)],[c_74241,c_45876]) ).
tff(c_74344,plain,
! [Y_4309] :
( is_a_theorem(strict_equiv(Y_4309,Y_4309))
| ~ is_a_theorem(strict_implies(Y_4309,Y_4309)) ),
inference(resolution,[status(thm)],[c_74304,c_411]) ).
tff(c_74353,plain,
! [Y_3148] :
( is_a_theorem(strict_equiv(Y_3148,Y_3148))
| ~ is_a_theorem(implies(Y_3148,Y_3148)) ),
inference(resolution,[status(thm)],[c_43395,c_74344]) ).
tff(c_75955,plain,
! [Y_3148] : is_a_theorem(strict_equiv(Y_3148,Y_3148)),
inference(demodulation,[status(thm),theory(equality)],[c_75953,c_74353]) ).
tff(c_73333,plain,
! [X_4219,Y_4220] : is_a_theorem(implies(X_4219,implies(Y_4220,and(X_4219,Y_4220)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_73345,plain,
! [Y_4220,X_4219] :
( is_a_theorem(implies(Y_4220,and(X_4219,Y_4220)))
| ~ is_a_theorem(X_4219) ),
inference(resolution,[status(thm)],[c_73333,c_411]) ).
tff(c_79052,plain,
! [X_4219,Y_4220] :
( is_a_theorem(equiv(and(X_4219,Y_4220),Y_4220))
| ~ is_a_theorem(implies(and(X_4219,Y_4220),Y_4220))
| ~ is_a_theorem(X_4219) ),
inference(resolution,[status(thm)],[c_73345,c_78972]) ).
tff(c_83925,plain,
! [X_4671,Y_4672] :
( is_a_theorem(equiv(and(X_4671,Y_4672),Y_4672))
| ~ is_a_theorem(X_4671) ),
inference(demodulation,[status(thm),theory(equality)],[c_374,c_79052]) ).
tff(c_83967,plain,
! [X_4673,Y_4674] :
( ( and(X_4673,Y_4674) = Y_4674 )
| ~ is_a_theorem(X_4673) ),
inference(resolution,[status(thm)],[c_83925,c_406]) ).
tff(c_84259,plain,
! [Y_4675,Y_4676] : ( and(strict_equiv(Y_4675,Y_4675),Y_4676) = Y_4676 ),
inference(resolution,[status(thm)],[c_75955,c_83967]) ).
tff(c_84376,plain,
! [Y_4675,Y_61] : ( implies(strict_equiv(Y_4675,Y_4675),Y_61) = not(not(Y_61)) ),
inference(superposition,[status(thm),theory(equality)],[c_84259,c_330]) ).
tff(c_84820,plain,
! [Y_4691,Y_4692] : ( implies(strict_equiv(Y_4691,Y_4691),Y_4692) = Y_4692 ),
inference(demodulation,[status(thm),theory(equality)],[c_80394,c_84376]) ).
tff(c_85071,plain,
! [Y_4691,Y_4692] : ( strict_implies(strict_equiv(Y_4691,Y_4691),Y_4692) = necessarily(Y_4692) ),
inference(superposition,[status(thm),theory(equality)],[c_84820,c_299]) ).
tff(c_93101,plain,
! [Y_4691,Y_4692] : ( strict_implies(equiv(Y_4691,Y_4691),Y_4692) = necessarily(Y_4692) ),
inference(demodulation,[status(thm),theory(equality)],[c_90423,c_85071]) ).
tff(c_80455,plain,
! [X_4610] : ( not(not(X_4610)) = X_4610 ),
inference(resolution,[status(thm)],[c_80358,c_406]) ).
tff(c_80710,plain,
! [X_105] : ( not(possibly(X_105)) = necessarily(not(X_105)) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_80455]) ).
tff(c_73811,plain,
! [X_4262] : ( possibly(necessarily(not(X_4262))) = not(necessarily(possibly(X_4262))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_43369]) ).
tff(c_73844,plain,
! [X_60,Y_61] : ( not(necessarily(possibly(and(X_60,not(Y_61))))) = possibly(necessarily(implies(X_60,Y_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_330,c_73811]) ).
tff(c_73854,plain,
! [X_60,Y_61] : ( not(necessarily(possibly(and(X_60,not(Y_61))))) = possibly(strict_implies(X_60,Y_61)) ),
inference(demodulation,[status(thm),theory(equality)],[c_299,c_73844]) ).
tff(c_96136,plain,
! [X_4826,Y_4827] : ( possibly(strict_implies(X_4826,Y_4827)) = strict_implies(X_4826,Y_4827) ),
inference(demodulation,[status(thm),theory(equality)],[c_299,c_330,c_80710,c_82360,c_73854]) ).
tff(c_96293,plain,
! [Y_4691,Y_4692] : ( strict_implies(equiv(Y_4691,Y_4691),Y_4692) = possibly(necessarily(Y_4692)) ),
inference(superposition,[status(thm),theory(equality)],[c_93101,c_96136]) ).
tff(c_96342,plain,
! [Y_4828] : ( possibly(necessarily(Y_4828)) = necessarily(Y_4828) ),
inference(demodulation,[status(thm),theory(equality)],[c_93101,c_96293]) ).
tff(c_96505,plain,
! [X_4635] : ( possibly(possibly(X_4635)) = necessarily(possibly(X_4635)) ),
inference(superposition,[status(thm),theory(equality)],[c_82360,c_96342]) ).
tff(c_96541,plain,
! [X_4635] : ( possibly(possibly(X_4635)) = possibly(X_4635) ),
inference(demodulation,[status(thm),theory(equality)],[c_82360,c_96505]) ).
tff(c_74328,plain,
! [X_4305,Y_4306] : is_a_theorem(implies(strict_equiv(X_4305,Y_4306),strict_implies(Y_4306,X_4305))),
inference(superposition,[status(thm),theory(equality)],[c_74241,c_374]) ).
tff(c_74401,plain,
! [Y_4314,X_4315] :
( is_a_theorem(strict_implies(Y_4314,X_4315))
| ~ is_a_theorem(strict_equiv(X_4315,Y_4314)) ),
inference(resolution,[status(thm)],[c_74328,c_411]) ).
tff(c_294,plain,
~ axiom_m9,
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_254,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly('#skF_93')),possibly('#skF_93'))) ),
inference(cnfTransformation,[status(thm)],[f_395]) ).
tff(c_302,plain,
~ is_a_theorem(strict_implies(possibly(possibly('#skF_93')),possibly('#skF_93'))),
inference(negUnitSimplification,[status(thm)],[c_294,c_254]) ).
tff(c_74433,plain,
~ is_a_theorem(strict_equiv(possibly('#skF_93'),possibly(possibly('#skF_93')))),
inference(resolution,[status(thm)],[c_74401,c_302]) ).
tff(c_96548,plain,
~ is_a_theorem(strict_equiv(possibly('#skF_93'),possibly('#skF_93'))),
inference(demodulation,[status(thm),theory(equality)],[c_96541,c_74433]) ).
tff(c_96556,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_75957,c_90423,c_96548]) ).
tff(c_96557,plain,
is_a_theorem(strict_equiv('#skF_61','#skF_62')),
inference(splitRight,[status(thm)],[c_184]) ).
tff(c_102860,plain,
! [X_5503,Y_5504] : ( and(strict_implies(X_5503,Y_5504),strict_implies(Y_5504,X_5503)) = strict_equiv(X_5503,Y_5504) ),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_268]) ).
tff(c_103042,plain,
! [X_5515,Y_5516] : is_a_theorem(implies(strict_equiv(X_5515,Y_5516),strict_implies(X_5515,Y_5516))),
inference(superposition,[status(thm),theory(equality)],[c_102860,c_378]) ).
tff(c_103146,plain,
! [X_5528,Y_5529] :
( is_a_theorem(strict_implies(X_5528,Y_5529))
| ~ is_a_theorem(strict_equiv(X_5528,Y_5529)) ),
inference(resolution,[status(thm)],[c_103042,c_411]) ).
tff(c_102249,plain,
! [Y_5443,X_5444] :
( is_a_theorem(Y_5443)
| ~ is_a_theorem(implies(X_5444,Y_5443))
| ~ is_a_theorem(X_5444) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_102289,plain,
! [X_5445] :
( is_a_theorem(X_5445)
| ~ is_a_theorem(necessarily(X_5445)) ),
inference(resolution,[status(thm)],[c_314,c_102249]) ).
tff(c_102292,plain,
! [X_107,Y_108] :
( is_a_theorem(implies(X_107,Y_108))
| ~ is_a_theorem(strict_implies(X_107,Y_108)) ),
inference(superposition,[status(thm),theory(equality)],[c_299,c_102289]) ).
tff(c_103355,plain,
! [X_5541,Y_5542] :
( is_a_theorem(implies(X_5541,Y_5542))
| ~ is_a_theorem(strict_equiv(X_5541,Y_5542)) ),
inference(resolution,[status(thm)],[c_103146,c_102292]) ).
tff(c_103363,plain,
is_a_theorem(implies('#skF_61','#skF_62')),
inference(resolution,[status(thm)],[c_96557,c_103355]) ).
tff(c_103059,plain,
! [X_5518,Y_5519] : is_a_theorem(implies(strict_equiv(X_5518,Y_5519),strict_implies(Y_5519,X_5518))),
inference(superposition,[status(thm),theory(equality)],[c_102860,c_374]) ).
tff(c_103110,plain,
! [Y_5526,X_5527] :
( is_a_theorem(strict_implies(Y_5526,X_5527))
| ~ is_a_theorem(strict_equiv(X_5527,Y_5526)) ),
inference(resolution,[status(thm)],[c_103059,c_411]) ).
tff(c_103281,plain,
! [Y_5536,X_5537] :
( is_a_theorem(implies(Y_5536,X_5537))
| ~ is_a_theorem(strict_equiv(X_5537,Y_5536)) ),
inference(resolution,[status(thm)],[c_103110,c_102292]) ).
tff(c_103285,plain,
is_a_theorem(implies('#skF_62','#skF_61')),
inference(resolution,[status(thm)],[c_96557,c_103281]) ).
tff(c_102953,plain,
! [X_5509,Y_5510] : ( and(implies(X_5509,Y_5510),implies(Y_5510,X_5509)) = equiv(X_5509,Y_5510) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_102636,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_107634,plain,
! [X_5796,Y_5797] :
( is_a_theorem(equiv(X_5796,Y_5797))
| ~ is_a_theorem(implies(Y_5797,X_5796))
| ~ is_a_theorem(implies(X_5796,Y_5797)) ),
inference(superposition,[status(thm),theory(equality)],[c_102953,c_102636]) ).
tff(c_107686,plain,
( is_a_theorem(equiv('#skF_61','#skF_62'))
| ~ is_a_theorem(implies('#skF_61','#skF_62')) ),
inference(resolution,[status(thm)],[c_103285,c_107634]) ).
tff(c_107781,plain,
is_a_theorem(equiv('#skF_61','#skF_62')),
inference(demodulation,[status(thm),theory(equality)],[c_103363,c_107686]) ).
tff(c_107875,plain,
'#skF_61' = '#skF_62',
inference(resolution,[status(thm)],[c_107781,c_406]) ).
tff(c_107885,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_412,c_107875]) ).
tff(c_107887,plain,
~ adjunction,
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_107889,plain,
is_a_theorem('#skF_59'),
inference(negUnitSimplification,[status(thm)],[c_107887,c_178]) ).
tff(c_107886,plain,
is_a_theorem('#skF_60'),
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_108942,plain,
! [X_5944,Y_5945] : is_a_theorem(implies(X_5944,implies(Y_5945,and(X_5944,Y_5945)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_109114,plain,
! [Y_5956,X_5957] :
( is_a_theorem(implies(Y_5956,and(X_5957,Y_5956)))
| ~ is_a_theorem(X_5957) ),
inference(resolution,[status(thm)],[c_108942,c_411]) ).
tff(c_109271,plain,
! [X_5967,Y_5968] :
( is_a_theorem(and(X_5967,Y_5968))
| ~ is_a_theorem(Y_5968)
| ~ is_a_theorem(X_5967) ),
inference(resolution,[status(thm)],[c_109114,c_411]) ).
tff(c_174,plain,
( ~ is_a_theorem(and('#skF_59','#skF_60'))
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_107894,plain,
~ is_a_theorem(and('#skF_59','#skF_60')),
inference(negUnitSimplification,[status(thm)],[c_107887,c_174]) ).
tff(c_109286,plain,
( ~ is_a_theorem('#skF_60')
| ~ is_a_theorem('#skF_59') ),
inference(resolution,[status(thm)],[c_109271,c_107894]) ).
tff(c_109294,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_107889,c_107886,c_109286]) ).
tff(c_109295,plain,
substitution_strict_equiv,
inference(splitRight,[status(thm)],[c_182]) ).
tff(c_148916,plain,
! [Y_72,X_71] :
( ( Y_72 = X_71 )
| ~ is_a_theorem(strict_equiv(X_71,Y_72)) ),
inference(demodulation,[status(thm),theory(equality)],[c_109295,c_180]) ).
tff(c_154355,plain,
! [X_9333] : ( and(X_9333,X_9333) = X_9333 ),
inference(resolution,[status(thm)],[c_154304,c_148916]) ).
tff(c_155287,plain,
! [Y_9346] : ( implies(not(Y_9346),Y_9346) = not(not(Y_9346)) ),
inference(superposition,[status(thm),theory(equality)],[c_154355,c_330]) ).
tff(c_155454,plain,
! [Y_57] : ( or(Y_57,Y_57) = not(not(Y_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_332,c_155287]) ).
tff(c_148326,plain,
! [X_8858,Y_8859] : ( implies(not(X_8858),Y_8859) = or(X_8858,Y_8859) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_148340,plain,
! [X_8858,Y_8] : is_a_theorem(or(X_8858,implies(Y_8,not(X_8858)))),
inference(superposition,[status(thm),theory(equality)],[c_148326,c_396]) ).
tff(c_156103,plain,
! [X_9353] : is_a_theorem(or(X_9353,not(not(not(X_9353))))),
inference(superposition,[status(thm),theory(equality)],[c_155287,c_148340]) ).
tff(c_156285,plain,
! [Y_9359] : is_a_theorem(or(Y_9359,not(or(Y_9359,Y_9359)))),
inference(superposition,[status(thm),theory(equality)],[c_155454,c_156103]) ).
tff(c_149551,plain,
! [Y_9024,X_9025] : is_a_theorem(implies(or(Y_9024,not(X_9025)),implies(X_9025,Y_9024))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_149564,plain,
! [X_9025,Y_9024] :
( is_a_theorem(implies(X_9025,Y_9024))
| ~ is_a_theorem(or(Y_9024,not(X_9025))) ),
inference(resolution,[status(thm)],[c_149551,c_411]) ).
tff(c_156315,plain,
! [Y_9359] : is_a_theorem(implies(or(Y_9359,Y_9359),Y_9359)),
inference(resolution,[status(thm)],[c_156285,c_149564]) ).
tff(c_148315,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_148381,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(negUnitSimplification,[status(thm)],[c_148315,c_92]) ).
tff(c_156326,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_156315,c_148381]) ).
tff(c_156327,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_163553,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_156327,c_163461]) ).
tff(c_163637,plain,
! [P_9878] : is_a_theorem(equiv(P_9878,or(P_9878,P_9878))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_163553]) ).
tff(c_163671,plain,
! [P_9878] : ( or(P_9878,P_9878) = P_9878 ),
inference(resolution,[status(thm)],[c_163637,c_406]) ).
tff(c_160757,plain,
! [X_9752,X_9753,Y_9754] : ( implies(X_9752,and(X_9753,not(Y_9754))) = not(and(X_9752,implies(X_9753,Y_9754))) ),
inference(superposition,[status(thm),theory(equality)],[c_330,c_157515]) ).
tff(c_160902,plain,
! [Y_9754] : is_a_theorem(not(and(not(Y_9754),implies(not(Y_9754),Y_9754)))),
inference(superposition,[status(thm),theory(equality)],[c_160757,c_157015]) ).
tff(c_160955,plain,
! [Y_9754] : is_a_theorem(not(and(not(Y_9754),or(Y_9754,Y_9754)))),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_160902]) ).
tff(c_163858,plain,
! [Y_9881] : is_a_theorem(not(and(not(Y_9881),Y_9881))),
inference(demodulation,[status(thm),theory(equality)],[c_163671,c_160955]) ).
tff(c_163874,plain,
! [Y_61] : is_a_theorem(implies(not(not(Y_61)),Y_61)),
inference(superposition,[status(thm),theory(equality)],[c_330,c_163858]) ).
tff(c_163881,plain,
! [Y_61] : is_a_theorem(or(not(Y_61),Y_61)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_163874]) ).
tff(c_163882,plain,
! [Y_9882] : is_a_theorem(or(not(Y_9882),Y_9882)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_163874]) ).
tff(c_157787,plain,
! [Y_9547,X_9548] : is_a_theorem(implies(or(Y_9547,not(X_9548)),implies(X_9548,Y_9547))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_157800,plain,
! [X_9548,Y_9547] :
( is_a_theorem(implies(X_9548,Y_9547))
| ~ is_a_theorem(or(Y_9547,not(X_9548))) ),
inference(resolution,[status(thm)],[c_157787,c_411]) ).
tff(c_163925,plain,
! [X_9884] : is_a_theorem(implies(X_9884,not(not(X_9884)))),
inference(resolution,[status(thm)],[c_163882,c_157800]) ).
tff(c_157940,plain,
! [X_9560,Y_9561] :
( is_a_theorem(equiv(X_9560,Y_9561))
| ~ is_a_theorem(implies(Y_9561,X_9560))
| ~ is_a_theorem(implies(X_9560,Y_9561)) ),
inference(superposition,[status(thm),theory(equality)],[c_157931,c_157570]) ).
tff(c_163927,plain,
! [X_9884] :
( is_a_theorem(equiv(not(not(X_9884)),X_9884))
| ~ is_a_theorem(implies(not(not(X_9884)),X_9884)) ),
inference(resolution,[status(thm)],[c_163925,c_157940]) ).
tff(c_163995,plain,
! [X_9888] : is_a_theorem(equiv(not(not(X_9888)),X_9888)),
inference(demodulation,[status(thm),theory(equality)],[c_163881,c_332,c_163927]) ).
tff(c_164041,plain,
! [X_9889] : ( not(not(X_9889)) = X_9889 ),
inference(resolution,[status(thm)],[c_163995,c_406]) ).
tff(c_164287,plain,
! [X_9889] : ( possibly(not(X_9889)) = not(necessarily(X_9889)) ),
inference(superposition,[status(thm),theory(equality)],[c_164041,c_301]) ).
tff(c_157043,plain,
! [X_9457] : is_a_theorem(or(X_9457,necessarily(possibly(not(X_9457))))),
inference(superposition,[status(thm),theory(equality)],[c_157025,c_306]) ).
tff(c_166922,plain,
! [X_9943] : is_a_theorem(or(X_9943,necessarily(not(necessarily(X_9943))))),
inference(demodulation,[status(thm),theory(equality)],[c_164287,c_157043]) ).
tff(c_166952,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(not(necessarily(necessarily(not(X_105))))))),
inference(superposition,[status(thm),theory(equality)],[c_157057,c_166922]) ).
tff(c_166964,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(possibly(X_105)))),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_141809,c_165764,c_157548,c_166952]) ).
tff(c_157750,plain,
! [X_9545,Y_9546] :
( is_a_theorem(strict_implies(X_9545,Y_9546))
| ~ is_a_theorem(implies(X_9545,Y_9546)) ),
inference(superposition,[status(thm),theory(equality)],[c_157061,c_324]) ).
tff(c_157391,plain,
~ axiom_m10,
inference(splitLeft,[status(thm)],[c_260]) ).
tff(c_157473,plain,
~ is_a_theorem(strict_implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(negUnitSimplification,[status(thm)],[c_157391,c_258]) ).
tff(c_157767,plain,
~ is_a_theorem(implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(resolution,[status(thm)],[c_157750,c_157473]) ).
tff(c_167329,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_166964,c_157767]) ).
tff(c_167330,plain,
! [X_104] : is_a_theorem(strict_implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(splitRight,[status(thm)],[c_260]) ).
tff(c_167345,plain,
! [Y_9955,X_9956] :
( is_a_theorem(Y_9955)
| ~ is_a_theorem(implies(X_9956,Y_9955))
| ~ is_a_theorem(X_9956) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_167430,plain,
! [X_9959] :
( is_a_theorem(X_9959)
| ~ is_a_theorem(necessarily(X_9959)) ),
inference(resolution,[status(thm)],[c_314,c_167345]) ).
tff(c_167772,plain,
! [X_10000,Y_10001] :
( is_a_theorem(implies(X_10000,Y_10001))
| ~ is_a_theorem(strict_implies(X_10000,Y_10001)) ),
inference(superposition,[status(thm),theory(equality)],[c_299,c_167430]) ).
tff(c_167796,plain,
! [X_104] : is_a_theorem(implies(possibly(X_104),necessarily(possibly(X_104)))),
inference(resolution,[status(thm)],[c_167330,c_167772]) ).
tff(c_167332,plain,
~ is_a_theorem(implies(possibly('#skF_68'),necessarily(possibly('#skF_68')))),
inference(splitLeft,[status(thm)],[c_202]) ).
tff(c_167819,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_167796,c_167332]) ).
tff(c_167820,plain,
axiom_5,
inference(splitRight,[status(thm)],[c_202]) ).
tff(c_167828,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(demodulation,[status(thm),theory(equality)],[c_167820,c_204]) ).
tff(c_168323,plain,
! [X_10059,Y_10060] : ( and(implies(X_10059,Y_10060),implies(Y_10060,X_10059)) = equiv(X_10059,Y_10060) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_168121,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_109303,c_172]) ).
tff(c_174451,plain,
! [X_10403,Y_10404] :
( is_a_theorem(equiv(X_10403,Y_10404))
| ~ is_a_theorem(implies(Y_10404,X_10403))
| ~ is_a_theorem(implies(X_10403,Y_10404)) ),
inference(superposition,[status(thm),theory(equality)],[c_168323,c_168121]) ).
tff(c_174539,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_167828,c_174451]) ).
tff(c_177258,plain,
! [X_10443] : is_a_theorem(equiv(necessarily(possibly(X_10443)),possibly(X_10443))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_174539]) ).
tff(c_177297,plain,
! [X_10443] : ( necessarily(possibly(X_10443)) = possibly(X_10443) ),
inference(resolution,[status(thm)],[c_177258,c_406]) ).
tff(c_156385,plain,
! [X_9367,Y_9368] : ( necessarily(implies(X_9367,Y_9368)) = strict_implies(X_9367,Y_9368) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_156984,plain,
! [X_9449,Y_9450] :
( is_a_theorem(strict_implies(X_9449,Y_9450))
| ~ is_a_theorem(implies(X_9449,Y_9450)) ),
inference(superposition,[status(thm),theory(equality)],[c_156385,c_324]) ).
tff(c_156335,plain,
~ axiom_m2,
inference(splitLeft,[status(thm)],[c_228]) ).
tff(c_156336,plain,
~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(negUnitSimplification,[status(thm)],[c_156335,c_226]) ).
tff(c_156996,plain,
~ is_a_theorem(implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(resolution,[status(thm)],[c_156984,c_156336]) ).
tff(c_157006,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_378,c_156996]) ).
tff(c_157007,plain,
! [X_89,Y_90] : is_a_theorem(strict_implies(and(X_89,Y_90),X_89)),
inference(splitRight,[status(thm)],[c_228]) ).
tff(c_156331,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_148313,c_236]) ).
tff(c_173600,plain,
! [X_10394,Y_10395] :
( is_a_theorem(strict_equiv(X_10394,Y_10395))
| ~ is_a_theorem(strict_implies(Y_10395,X_10394))
| ~ is_a_theorem(strict_implies(X_10394,Y_10395)) ),
inference(superposition,[status(thm),theory(equality)],[c_168447,c_168121]) ).
tff(c_173638,plain,
! [X_94] :
( is_a_theorem(strict_equiv(and(X_94,X_94),X_94))
| ~ is_a_theorem(strict_implies(and(X_94,X_94),X_94)) ),
inference(resolution,[status(thm)],[c_156331,c_173600]) ).
tff(c_173670,plain,
! [X_10396] : is_a_theorem(strict_equiv(and(X_10396,X_10396),X_10396)),
inference(demodulation,[status(thm),theory(equality)],[c_157007,c_173638]) ).
tff(c_157012,plain,
! [Y_72,X_71] :
( ( Y_72 = X_71 )
| ~ is_a_theorem(strict_equiv(X_71,Y_72)) ),
inference(demodulation,[status(thm),theory(equality)],[c_109295,c_180]) ).
tff(c_173718,plain,
! [X_10396] : ( and(X_10396,X_10396) = X_10396 ),
inference(resolution,[status(thm)],[c_173670,c_157012]) ).
tff(c_167906,plain,
! [X_10013,Y_10014] : ( not(and(X_10013,not(Y_10014))) = implies(X_10013,Y_10014) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_167939,plain,
! [X_10013,X_105] : ( implies(X_10013,necessarily(not(X_105))) = not(and(X_10013,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_167906]) ).
tff(c_174547,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_156327,c_174451]) ).
tff(c_175010,plain,
! [P_10409] : is_a_theorem(equiv(P_10409,or(P_10409,P_10409))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_174547]) ).
tff(c_175044,plain,
! [P_10409] : ( or(P_10409,P_10409) = P_10409 ),
inference(resolution,[status(thm)],[c_175010,c_406]) ).
tff(c_173733,plain,
! [X_10397] : ( and(X_10397,X_10397) = X_10397 ),
inference(resolution,[status(thm)],[c_173670,c_157012]) ).
tff(c_174788,plain,
! [Y_10408] : ( implies(not(Y_10408),Y_10408) = not(not(Y_10408)) ),
inference(superposition,[status(thm),theory(equality)],[c_173733,c_330]) ).
tff(c_174969,plain,
! [Y_57] : ( or(Y_57,Y_57) = not(not(Y_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_332,c_174788]) ).
tff(c_175339,plain,
! [Y_57] : ( not(not(Y_57)) = Y_57 ),
inference(demodulation,[status(thm),theory(equality)],[c_175044,c_174969]) ).
tff(c_173878,plain,
! [Y_61] : ( implies(not(Y_61),Y_61) = not(not(Y_61)) ),
inference(superposition,[status(thm),theory(equality)],[c_173733,c_330]) ).
tff(c_175628,plain,
! [Y_10418] : ( implies(not(Y_10418),Y_10418) = Y_10418 ),
inference(demodulation,[status(thm),theory(equality)],[c_175339,c_173878]) ).
tff(c_175805,plain,
! [X_105] : ( not(and(not(necessarily(not(X_105))),possibly(X_105))) = necessarily(not(X_105)) ),
inference(superposition,[status(thm),theory(equality)],[c_167939,c_175628]) ).
tff(c_175846,plain,
! [X_105] : ( not(possibly(X_105)) = necessarily(not(X_105)) ),
inference(demodulation,[status(thm),theory(equality)],[c_173718,c_301,c_175805]) ).
tff(c_141815,plain,
! [X_105] : ( possibly(necessarily(not(X_105))) = not(necessarily(possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_141806]) ).
tff(c_177398,plain,
! [X_105] : ( possibly(necessarily(not(X_105))) = not(possibly(X_105)) ),
inference(demodulation,[status(thm),theory(equality)],[c_177297,c_141815]) ).
tff(c_178360,plain,
! [X_10470] : ( possibly(necessarily(not(X_10470))) = necessarily(not(X_10470)) ),
inference(demodulation,[status(thm),theory(equality)],[c_175846,c_177398]) ).
tff(c_178451,plain,
! [X_105] : ( necessarily(not(necessarily(not(X_105)))) = possibly(necessarily(possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_178360]) ).
tff(c_178478,plain,
! [X_105] : ( possibly(possibly(X_105)) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_177297,c_177297,c_301,c_178451]) ).
tff(c_167841,plain,
! [Y_10009,X_10010] :
( is_a_theorem(Y_10009)
| ~ is_a_theorem(implies(X_10010,Y_10009))
| ~ is_a_theorem(X_10010) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_167890,plain,
! [X_14,Y_15] :
( is_a_theorem(X_14)
| ~ is_a_theorem(and(X_14,Y_15)) ),
inference(resolution,[status(thm)],[c_378,c_167841]) ).
tff(c_168611,plain,
! [X_10082,Y_10083] :
( is_a_theorem(strict_implies(X_10082,Y_10083))
| ~ is_a_theorem(strict_equiv(X_10082,Y_10083)) ),
inference(superposition,[status(thm),theory(equality)],[c_168447,c_167890]) ).
tff(c_168643,plain,
~ is_a_theorem(strict_equiv(possibly(possibly('#skF_93')),possibly('#skF_93'))),
inference(resolution,[status(thm)],[c_168611,c_302]) ).
tff(c_178593,plain,
~ is_a_theorem(strict_equiv(possibly('#skF_93'),possibly('#skF_93'))),
inference(demodulation,[status(thm),theory(equality)],[c_178478,c_168643]) ).
tff(c_178601,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_170368,c_178593]) ).
tff(c_178602,plain,
is_a_theorem('#skF_59'),
inference(splitRight,[status(thm)],[c_178]) ).
tff(c_178603,plain,
~ adjunction,
inference(splitRight,[status(thm)],[c_178]) ).
tff(c_178604,plain,
is_a_theorem('#skF_60'),
inference(negUnitSimplification,[status(thm)],[c_178603,c_176]) ).
tff(c_179537,plain,
! [X_10606,Y_10607] : is_a_theorem(implies(X_10606,implies(Y_10607,and(X_10606,Y_10607)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_179726,plain,
! [Y_10630,X_10631] :
( is_a_theorem(implies(Y_10630,and(X_10631,Y_10630)))
| ~ is_a_theorem(X_10631) ),
inference(resolution,[status(thm)],[c_179537,c_411]) ).
tff(c_179994,plain,
! [X_10646,Y_10647] :
( is_a_theorem(and(X_10646,Y_10647))
| ~ is_a_theorem(Y_10647)
| ~ is_a_theorem(X_10646) ),
inference(resolution,[status(thm)],[c_179726,c_411]) ).
tff(c_178608,plain,
~ is_a_theorem(and('#skF_59','#skF_60')),
inference(negUnitSimplification,[status(thm)],[c_178603,c_174]) ).
tff(c_180009,plain,
( ~ is_a_theorem('#skF_60')
| ~ is_a_theorem('#skF_59') ),
inference(resolution,[status(thm)],[c_179994,c_178608]) ).
tff(c_180020,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_178602,c_178604,c_180009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL548+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14 % 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 : n017.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 13:36:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 47.23/30.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.37/30.67
% 47.37/30.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.84/30.77
% 47.84/30.77 Inference rules
% 47.84/30.77 ----------------------
% 47.84/30.77 #Ref : 0
% 47.84/30.77 #Sup : 43529
% 47.84/30.77 #Fact : 0
% 47.84/30.77 #Define : 0
% 47.84/30.77 #Split : 1397
% 47.84/30.77 #Chain : 0
% 47.84/30.77 #Close : 0
% 47.84/30.77
% 47.84/30.77 Ordering : KBO
% 47.84/30.77
% 47.84/30.77 Simplification rules
% 47.84/30.77 ----------------------
% 47.84/30.77 #Subsume : 7539
% 47.84/30.77 #Demod : 27489
% 47.84/30.77 #Tautology : 11030
% 47.84/30.77 #SimpNegUnit : 660
% 47.84/30.77 #BackRed : 941
% 47.84/30.77
% 47.84/30.77 #Partial instantiations: 0
% 47.84/30.77 #Strategies tried : 1
% 47.84/30.77
% 47.84/30.77 Timing (in seconds)
% 47.84/30.77 ----------------------
% 47.84/30.77 Preprocessing : 0.74
% 47.84/30.77 Parsing : 0.36
% 47.84/30.77 CNF conversion : 0.07
% 47.84/30.77 Main loop : 28.73
% 47.84/30.77 Inferencing : 6.55
% 47.84/30.77 Reduction : 13.93
% 47.84/30.77 Demodulation : 10.17
% 47.84/30.77 BG Simplification : 0.23
% 47.84/30.77 Subsumption : 6.42
% 47.84/30.77 Abstraction : 0.34
% 47.84/30.77 MUC search : 0.00
% 47.84/30.77 Cooper : 0.00
% 47.84/30.77 Total : 29.65
% 47.84/30.77 Index Insertion : 0.00
% 47.84/30.77 Index Deletion : 0.00
% 47.84/30.77 Index Matching : 0.00
% 47.84/30.77 BG Taut test : 0.00
%------------------------------------------------------------------------------