TSTP Solution File: LCL549+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL549+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 : n002.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 18.59s 6.77s
% Output : CNFRefutation 18.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 204
% Syntax : Number of formulae : 366 ( 123 unt; 163 typ; 0 def)
% Number of atoms : 304 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 187 ( 86 ~; 72 |; 2 &)
% ( 18 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 199 (; 199 !; 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_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_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_476,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_4) ).
tff(f_332,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
tff(f_485,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
tff(f_214,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_313,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(Y) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
tff(f_264,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
tff(f_67,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_482,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_257,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
tff(f_104,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_2) ).
tff(f_254,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
tff(f_92,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_255,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
tff(f_96,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
tff(f_251,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
tff(f_80,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
tff(f_60,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_484,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
tff(f_437,axiom,
( op_strict_implies
=> ! [X,Y] : ( strict_implies(X,Y) = necessarily(implies(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
tff(f_472,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
tff(f_297,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
tff(f_374,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
tff(f_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_250,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
tff(f_76,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(f_249,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
tff(f_72,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
tff(f_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_489,negated_conjecture,
~ axiom_m10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
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(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_12991,plain,
! [X_1053] : ( not(necessarily(not(X_1053))) = possibly(X_1053) ),
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_12994,plain,
! [X_1053] : ( possibly(necessarily(not(X_1053))) = not(necessarily(possibly(X_1053))) ),
inference(superposition,[status(thm),theory(equality)],[c_12991,c_301]) ).
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_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_15696,plain,
! [X_1364,Y_1365] : ( and(implies(X_1364,Y_1365),implies(Y_1365,X_1364)) = equiv(X_1364,Y_1365) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_176,plain,
( is_a_theorem('#skF_60')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_413,plain,
adjunction,
inference(splitLeft,[status(thm)],[c_176]) ).
tff(c_172,plain,
! [X_69,Y_70] :
( is_a_theorem(and(X_69,Y_70))
| ~ is_a_theorem(Y_70)
| ~ is_a_theorem(X_69)
| ~ adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_15325,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_20697,plain,
! [X_1651,Y_1652] :
( is_a_theorem(equiv(X_1651,Y_1652))
| ~ is_a_theorem(implies(Y_1652,X_1651))
| ~ is_a_theorem(implies(X_1651,Y_1652)) ),
inference(superposition,[status(thm),theory(equality)],[c_15696,c_15325]) ).
tff(c_20781,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_20697]) ).
tff(c_22060,plain,
! [X_1673] : is_a_theorem(equiv(necessarily(necessarily(X_1673)),necessarily(X_1673))),
inference(demodulation,[status(thm),theory(equality)],[c_314,c_20781]) ).
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_22086,plain,
! [X_1673] : ( necessarily(necessarily(X_1673)) = necessarily(X_1673) ),
inference(resolution,[status(thm)],[c_22060,c_406]) ).
tff(c_15113,plain,
! [X_1315,Y_1316] : ( not(and(X_1315,not(Y_1316))) = implies(X_1315,Y_1316) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_15146,plain,
! [X_1315,X_105] : ( implies(X_1315,necessarily(not(X_105))) = not(and(X_1315,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_15113]) ).
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_13030,plain,
! [X_1058,Y_1059] : ( implies(not(X_1058),Y_1059) = or(X_1058,Y_1059) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_13061,plain,
! [X_105,Y_1059] : ( or(necessarily(not(X_105)),Y_1059) = implies(possibly(X_105),Y_1059) ),
inference(superposition,[status(thm),theory(equality)],[c_301,c_13030]) ).
tff(c_332,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_146,plain,
or_2,
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_50,plain,
! [Y_23,X_22] :
( is_a_theorem(implies(Y_23,or(X_22,Y_23)))
| ~ or_2 ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_356,plain,
! [Y_23,X_22] : is_a_theorem(implies(Y_23,or(X_22,Y_23))),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_50]) ).
tff(c_140,plain,
and_2,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_38,plain,
! [X_16,Y_17] :
( is_a_theorem(implies(and(X_16,Y_17),Y_17))
| ~ and_2 ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_374,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_38]) ).
tff(c_142,plain,
and_3,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_42,plain,
! [X_18,Y_19] :
( is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19))))
| ~ and_3 ),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_370,plain,
! [X_18,Y_19] : is_a_theorem(implies(X_18,implies(Y_19,and(X_18,Y_19)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_134,plain,
implies_2,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_26,plain,
! [X_9,Y_10] :
( is_a_theorem(implies(implies(X_9,implies(X_9,Y_10)),implies(X_9,Y_10)))
| ~ implies_2 ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2115,plain,
! [X_325,Y_326] : is_a_theorem(implies(implies(X_325,implies(X_325,Y_326)),implies(X_325,Y_326))),
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_3380,plain,
! [X_440,Y_441] :
( is_a_theorem(implies(X_440,Y_441))
| ~ is_a_theorem(implies(X_440,implies(X_440,Y_441))) ),
inference(resolution,[status(thm)],[c_2115,c_411]) ).
tff(c_3435,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_370,c_3380]) ).
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_1232,plain,
! [X_226,Y_227] : ( necessarily(implies(X_226,Y_227)) = strict_implies(X_226,Y_227) ),
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_1726,plain,
! [X_293,Y_294] :
( is_a_theorem(strict_implies(X_293,Y_294))
| ~ is_a_theorem(implies(X_293,Y_294)) ),
inference(superposition,[status(thm),theory(equality)],[c_1232,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_431,plain,
~ is_a_theorem(strict_implies('#skF_84',and('#skF_84','#skF_84'))),
inference(splitLeft,[status(thm)],[c_234]) ).
tff(c_1744,plain,
~ is_a_theorem(implies('#skF_84',and('#skF_84','#skF_84'))),
inference(resolution,[status(thm)],[c_1726,c_431]) ).
tff(c_3479,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3435,c_1744]) ).
tff(c_3480,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_3524,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_3480,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_4220,plain,
! [Y_539,X_540] :
( is_a_theorem(Y_539)
| ~ is_a_theorem(implies(X_540,Y_539))
| ~ is_a_theorem(X_540) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_4256,plain,
! [X_541] :
( is_a_theorem(X_541)
| ~ is_a_theorem(necessarily(X_541)) ),
inference(resolution,[status(thm)],[c_314,c_4220]) ).
tff(c_4892,plain,
! [X_617,Y_618] :
( is_a_theorem(implies(X_617,Y_618))
| ~ is_a_theorem(strict_implies(X_617,Y_618)) ),
inference(superposition,[status(thm),theory(equality)],[c_299,c_4256]) ).
tff(c_4914,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_3524,c_4892]) ).
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_4173,plain,
~ kn1,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_4174,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(negUnitSimplification,[status(thm)],[c_4173,c_68]) ).
tff(c_4917,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4914,c_4174]) ).
tff(c_4918,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_6233,plain,
! [X_754,Y_755] : ( and(implies(X_754,Y_755),implies(Y_755,X_754)) = equiv(X_754,Y_755) ),
inference(demodulation,[status(thm),theory(equality)],[c_290,c_120]) ).
tff(c_5509,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_10734,plain,
! [X_1020,Y_1021] :
( is_a_theorem(equiv(X_1020,Y_1021))
| ~ is_a_theorem(implies(Y_1021,X_1020))
| ~ is_a_theorem(implies(X_1020,Y_1021)) ),
inference(superposition,[status(thm),theory(equality)],[c_6233,c_5509]) ).
tff(c_10824,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_4918,c_10734]) ).
tff(c_10914,plain,
! [P_1022] : is_a_theorem(equiv(and(P_1022,P_1022),P_1022)),
inference(demodulation,[status(thm),theory(equality)],[c_374,c_10824]) ).
tff(c_10963,plain,
! [P_1023] : ( and(P_1023,P_1023) = P_1023 ),
inference(resolution,[status(thm)],[c_10914,c_406]) ).
tff(c_11694,plain,
! [Y_1031] : ( implies(not(Y_1031),Y_1031) = not(not(Y_1031)) ),
inference(superposition,[status(thm),theory(equality)],[c_10963,c_330]) ).
tff(c_11843,plain,
! [Y_1031] : ( or(Y_1031,Y_1031) = not(not(Y_1031)) ),
inference(superposition,[status(thm),theory(equality)],[c_11694,c_332]) ).
tff(c_4929,plain,
! [X_622,Y_623] : ( implies(not(X_622),Y_623) = or(X_622,Y_623) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_330,c_112]) ).
tff(c_132,plain,
implies_1,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_22,plain,
! [X_7,Y_8] :
( is_a_theorem(implies(X_7,implies(Y_8,X_7)))
| ~ implies_1 ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_396,plain,
! [X_7,Y_8] : is_a_theorem(implies(X_7,implies(Y_8,X_7))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_22]) ).
tff(c_4958,plain,
! [X_622,Y_8] : is_a_theorem(or(X_622,implies(Y_8,not(X_622)))),
inference(superposition,[status(thm),theory(equality)],[c_4929,c_396]) ).
tff(c_12445,plain,
! [X_1037] : is_a_theorem(or(X_1037,not(not(not(X_1037))))),
inference(superposition,[status(thm),theory(equality)],[c_11694,c_4958]) ).
tff(c_12941,plain,
! [Y_1052] : is_a_theorem(or(Y_1052,not(or(Y_1052,Y_1052)))),
inference(superposition,[status(thm),theory(equality)],[c_11843,c_12445]) ).
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_5584,plain,
! [Y_701,X_702] : is_a_theorem(implies(or(Y_701,not(X_702)),implies(X_702,Y_701))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_5597,plain,
! [X_702,Y_701] :
( is_a_theorem(implies(X_702,Y_701))
| ~ is_a_theorem(or(Y_701,not(X_702))) ),
inference(resolution,[status(thm)],[c_5584,c_411]) ).
tff(c_12971,plain,
! [Y_1052] : is_a_theorem(implies(or(Y_1052,Y_1052),Y_1052)),
inference(resolution,[status(thm)],[c_12941,c_5597]) ).
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_3528,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_4926,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_3528,c_334]) ).
tff(c_12982,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12971,c_4926]) ).
tff(c_12983,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_3482,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_12988,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12983,c_3482]) ).
tff(c_12989,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_13027,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_12989,c_94]) ).
tff(c_20785,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_13027,c_20697]) ).
tff(c_20866,plain,
! [P_1653] : is_a_theorem(equiv(P_1653,or(P_1653,P_1653))),
inference(demodulation,[status(thm),theory(equality)],[c_356,c_20785]) ).
tff(c_20900,plain,
! [P_1653] : ( or(P_1653,P_1653) = P_1653 ),
inference(resolution,[status(thm)],[c_20866,c_406]) ).
tff(c_18530,plain,
! [X_1562,X_1563,Y_1564] : ( implies(X_1562,and(X_1563,not(Y_1564))) = not(and(X_1562,implies(X_1563,Y_1564))) ),
inference(superposition,[status(thm),theory(equality)],[c_330,c_15113]) ).
tff(c_13022,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_3480,c_236]) ).
tff(c_13006,plain,
! [X_1054,Y_1055] : ( necessarily(implies(X_1054,Y_1055)) = strict_implies(X_1054,Y_1055) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_14449,plain,
! [X_1233,Y_1234] : is_a_theorem(implies(strict_implies(X_1233,Y_1234),implies(X_1233,Y_1234))),
inference(superposition,[status(thm),theory(equality)],[c_13006,c_314]) ).
tff(c_14610,plain,
! [X_1245,Y_1246] :
( is_a_theorem(implies(X_1245,Y_1246))
| ~ is_a_theorem(strict_implies(X_1245,Y_1246)) ),
inference(resolution,[status(thm)],[c_14449,c_411]) ).
tff(c_14632,plain,
! [X_94] : is_a_theorem(implies(X_94,and(X_94,X_94))),
inference(resolution,[status(thm)],[c_13022,c_14610]) ).
tff(c_13867,plain,
~ kn1,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_13871,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(negUnitSimplification,[status(thm)],[c_13867,c_68]) ).
tff(c_14635,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14632,c_13871]) ).
tff(c_14636,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_18675,plain,
! [Y_1564] : is_a_theorem(not(and(not(Y_1564),implies(not(Y_1564),Y_1564)))),
inference(superposition,[status(thm),theory(equality)],[c_18530,c_14636]) ).
tff(c_18737,plain,
! [Y_1564] : is_a_theorem(not(and(not(Y_1564),or(Y_1564,Y_1564)))),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_18675]) ).
tff(c_21085,plain,
! [Y_1656] : is_a_theorem(not(and(not(Y_1656),Y_1656))),
inference(demodulation,[status(thm),theory(equality)],[c_20900,c_18737]) ).
tff(c_21101,plain,
! [Y_61] : is_a_theorem(implies(not(not(Y_61)),Y_61)),
inference(superposition,[status(thm),theory(equality)],[c_330,c_21085]) ).
tff(c_21108,plain,
! [Y_61] : is_a_theorem(or(not(Y_61),Y_61)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_21101]) ).
tff(c_21109,plain,
! [Y_1657] : is_a_theorem(or(not(Y_1657),Y_1657)),
inference(demodulation,[status(thm),theory(equality)],[c_332,c_21101]) ).
tff(c_15371,plain,
! [Y_1333,X_1334] : is_a_theorem(implies(or(Y_1333,not(X_1334)),implies(X_1334,Y_1333))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_332,c_18]) ).
tff(c_15384,plain,
! [X_1334,Y_1333] :
( is_a_theorem(implies(X_1334,Y_1333))
| ~ is_a_theorem(or(Y_1333,not(X_1334))) ),
inference(resolution,[status(thm)],[c_15371,c_411]) ).
tff(c_21135,plain,
! [X_1658] : is_a_theorem(implies(X_1658,not(not(X_1658)))),
inference(resolution,[status(thm)],[c_21109,c_15384]) ).
tff(c_15702,plain,
! [X_1364,Y_1365] :
( is_a_theorem(equiv(X_1364,Y_1365))
| ~ is_a_theorem(implies(Y_1365,X_1364))
| ~ is_a_theorem(implies(X_1364,Y_1365)) ),
inference(superposition,[status(thm),theory(equality)],[c_15696,c_15325]) ).
tff(c_21137,plain,
! [X_1658] :
( is_a_theorem(equiv(not(not(X_1658)),X_1658))
| ~ is_a_theorem(implies(not(not(X_1658)),X_1658)) ),
inference(resolution,[status(thm)],[c_21135,c_15702]) ).
tff(c_21192,plain,
! [X_1660] : is_a_theorem(equiv(not(not(X_1660)),X_1660)),
inference(demodulation,[status(thm),theory(equality)],[c_21108,c_332,c_21137]) ).
tff(c_21238,plain,
! [X_1661] : ( not(not(X_1661)) = X_1661 ),
inference(resolution,[status(thm)],[c_21192,c_406]) ).
tff(c_21460,plain,
! [X_1661] : ( possibly(not(X_1661)) = not(necessarily(X_1661)) ),
inference(superposition,[status(thm),theory(equality)],[c_21238,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_13044,plain,
! [X_1058] : is_a_theorem(or(X_1058,necessarily(possibly(not(X_1058))))),
inference(superposition,[status(thm),theory(equality)],[c_13030,c_306]) ).
tff(c_23652,plain,
! [X_1704] : is_a_theorem(or(X_1704,necessarily(not(necessarily(X_1704))))),
inference(demodulation,[status(thm),theory(equality)],[c_21460,c_13044]) ).
tff(c_23682,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(not(necessarily(necessarily(not(X_105))))))),
inference(superposition,[status(thm),theory(equality)],[c_13061,c_23652]) ).
tff(c_23694,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(possibly(X_105)))),
inference(demodulation,[status(thm),theory(equality)],[c_330,c_12994,c_22086,c_15146,c_23682]) ).
tff(c_15283,plain,
! [X_1329,Y_1330] :
( is_a_theorem(strict_implies(X_1329,Y_1330))
| ~ is_a_theorem(implies(X_1329,Y_1330)) ),
inference(superposition,[status(thm),theory(equality)],[c_13006,c_324]) ).
tff(c_294,plain,
~ axiom_m10,
inference(cnfTransformation,[status(thm)],[f_489]) ).
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_302,plain,
~ is_a_theorem(strict_implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(negUnitSimplification,[status(thm)],[c_294,c_258]) ).
tff(c_15306,plain,
~ is_a_theorem(implies(possibly('#skF_94'),necessarily(possibly('#skF_94')))),
inference(resolution,[status(thm)],[c_15283,c_302]) ).
tff(c_23967,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23694,c_15306]) ).
tff(c_23969,plain,
~ adjunction,
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_178,plain,
( is_a_theorem('#skF_59')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_23971,plain,
is_a_theorem('#skF_59'),
inference(negUnitSimplification,[status(thm)],[c_23969,c_178]) ).
tff(c_23968,plain,
is_a_theorem('#skF_60'),
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_24896,plain,
! [Y_1840,X_1841] :
( is_a_theorem(Y_1840)
| ~ is_a_theorem(implies(X_1841,Y_1840))
| ~ is_a_theorem(X_1841) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_25056,plain,
! [Y_1860,X_1861] :
( is_a_theorem(implies(Y_1860,and(X_1861,Y_1860)))
| ~ is_a_theorem(X_1861) ),
inference(resolution,[status(thm)],[c_370,c_24896]) ).
tff(c_25427,plain,
! [X_1889,Y_1890] :
( is_a_theorem(and(X_1889,Y_1890))
| ~ is_a_theorem(Y_1890)
| ~ is_a_theorem(X_1889) ),
inference(resolution,[status(thm)],[c_25056,c_411]) ).
tff(c_174,plain,
( ~ is_a_theorem(and('#skF_59','#skF_60'))
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_23976,plain,
~ is_a_theorem(and('#skF_59','#skF_60')),
inference(negUnitSimplification,[status(thm)],[c_23969,c_174]) ).
tff(c_25442,plain,
( ~ is_a_theorem('#skF_60')
| ~ is_a_theorem('#skF_59') ),
inference(resolution,[status(thm)],[c_25427,c_23976]) ).
tff(c_25453,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23971,c_23968,c_25442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL549+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.35 % Computer : n002.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 3 14:08:46 EDT 2023
% 0.16/0.35 % CPUTime :
% 18.59/6.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.76/6.79
% 18.76/6.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.95/6.84
% 18.95/6.84 Inference rules
% 18.95/6.84 ----------------------
% 18.95/6.84 #Ref : 0
% 18.95/6.84 #Sup : 6032
% 18.95/6.84 #Fact : 0
% 18.95/6.84 #Define : 0
% 18.95/6.84 #Split : 273
% 18.95/6.84 #Chain : 0
% 18.95/6.84 #Close : 0
% 18.95/6.84
% 18.95/6.84 Ordering : KBO
% 18.95/6.84
% 18.95/6.84 Simplification rules
% 18.95/6.84 ----------------------
% 18.95/6.84 #Subsume : 953
% 18.95/6.84 #Demod : 3490
% 18.95/6.84 #Tautology : 1445
% 18.95/6.84 #SimpNegUnit : 77
% 18.95/6.84 #BackRed : 111
% 18.95/6.84
% 18.95/6.84 #Partial instantiations: 0
% 18.95/6.84 #Strategies tried : 1
% 18.95/6.84
% 18.95/6.84 Timing (in seconds)
% 18.95/6.84 ----------------------
% 18.95/6.84 Preprocessing : 0.69
% 18.95/6.84 Parsing : 0.34
% 18.95/6.84 CNF conversion : 0.06
% 18.95/6.84 Main loop : 5.06
% 18.95/6.84 Inferencing : 1.38
% 18.95/6.84 Reduction : 2.23
% 18.95/6.84 Demodulation : 1.56
% 18.95/6.84 BG Simplification : 0.09
% 18.95/6.84 Subsumption : 1.02
% 18.95/6.84 Abstraction : 0.09
% 18.95/6.84 MUC search : 0.00
% 18.95/6.84 Cooper : 0.00
% 18.95/6.84 Total : 5.83
% 18.95/6.84 Index Insertion : 0.00
% 18.95/6.84 Index Deletion : 0.00
% 18.95/6.84 Index Matching : 0.00
% 18.95/6.84 BG Taut test : 0.00
%------------------------------------------------------------------------------