TSTP Solution File: LCL550+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL550+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n018.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 10:48:21 EDT 2023
% Result : Theorem 44.14s 29.47s
% Output : CNFRefutation 44.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 191
% Syntax : Number of formulae : 327 ( 112 unt; 163 typ; 0 def)
% Number of atoms : 238 ( 68 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 130 ( 56 ~; 52 |; 3 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 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 : 222 (; 222 !; 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_447,negated_conjecture,
~ modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_432,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
tff(f_316,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
tff(f_434,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
tff(f_324,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
tff(f_425,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
tff(f_391,axiom,
( op_strict_equiv
=> ! [X,Y] : ( strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
tff(f_429,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
tff(f_263,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(Y) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',adjunction) ).
tff(f_428,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
tff(f_269,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
tff(f_423,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
tff(f_387,axiom,
( op_strict_implies
=> ! [X,Y] : ( strict_implies(X,Y) = necessarily(implies(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
tff(f_440,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_439,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_431,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
tff(f_312,axiom,
( axiom_m1
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
tff(f_435,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
tff(f_328,axiom,
( axiom_m5
<=> ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
tff(f_427,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
tff(f_255,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(strict_implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
tff(f_441,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
tff(f_214,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_444,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
tff(f_67,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(c_270,plain,
~ modus_ponens,
inference(cnfTransformation,[status(thm)],[f_447]) ).
tff(c_8,plain,
( is_a_theorem('#skF_1')
| modus_ponens ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_335,plain,
is_a_theorem('#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_270,c_8]) ).
tff(c_254,plain,
axiom_m2,
inference(cnfTransformation,[status(thm)],[f_432]) ).
tff(c_192,plain,
! [X_89,Y_90] :
( is_a_theorem(strict_implies(and(X_89,Y_90),X_89))
| ~ axiom_m2 ),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_292,plain,
! [X_89,Y_90] : is_a_theorem(strict_implies(and(X_89,Y_90),X_89)),
inference(demodulation,[status(thm),theory(equality)],[c_254,c_192]) ).
tff(c_258,plain,
axiom_m4,
inference(cnfTransformation,[status(thm)],[f_434]) ).
tff(c_200,plain,
! [X_94] :
( is_a_theorem(strict_implies(X_94,and(X_94,X_94)))
| ~ axiom_m4 ),
inference(cnfTransformation,[status(thm)],[f_324]) ).
tff(c_284,plain,
! [X_94] : is_a_theorem(strict_implies(X_94,and(X_94,X_94))),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_200]) ).
tff(c_244,plain,
op_strict_equiv,
inference(cnfTransformation,[status(thm)],[f_425]) ).
tff(c_232,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_391]) ).
tff(c_820,plain,
! [X_177,Y_178] : ( and(strict_implies(X_177,Y_178),strict_implies(Y_178,X_177)) = strict_equiv(X_177,Y_178) ),
inference(demodulation,[status(thm),theory(equality)],[c_244,c_232]) ).
tff(c_250,plain,
adjunction,
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_136,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_263]) ).
tff(c_311,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_250,c_136]) ).
tff(c_2007,plain,
! [X_256,Y_257] :
( is_a_theorem(strict_equiv(X_256,Y_257))
| ~ is_a_theorem(strict_implies(Y_257,X_256))
| ~ is_a_theorem(strict_implies(X_256,Y_257)) ),
inference(superposition,[status(thm),theory(equality)],[c_820,c_311]) ).
tff(c_2041,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_284,c_2007]) ).
tff(c_2075,plain,
! [X_258] : is_a_theorem(strict_equiv(and(X_258,X_258),X_258)),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_2041]) ).
tff(c_248,plain,
substitution_strict_equiv,
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_144,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_269]) ).
tff(c_306,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_248,c_144]) ).
tff(c_2098,plain,
! [X_258] : ( and(X_258,X_258) = X_258 ),
inference(resolution,[status(thm)],[c_2075,c_306]) ).
tff(c_2073,plain,
! [X_94] : is_a_theorem(strict_equiv(and(X_94,X_94),X_94)),
inference(demodulation,[status(thm),theory(equality)],[c_292,c_2041]) ).
tff(c_2100,plain,
! [X_94] : is_a_theorem(strict_equiv(X_94,X_94)),
inference(demodulation,[status(thm),theory(equality)],[c_2098,c_2073]) ).
tff(c_274,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_244,c_232]) ).
tff(c_2107,plain,
! [X_259] : ( and(X_259,X_259) = X_259 ),
inference(resolution,[status(thm)],[c_2075,c_306]) ).
tff(c_2195,plain,
! [Y_110] : ( strict_implies(Y_110,Y_110) = strict_equiv(Y_110,Y_110) ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_2107]) ).
tff(c_240,plain,
op_strict_implies,
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_230,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_387]) ).
tff(c_276,plain,
! [X_107,Y_108] : ( necessarily(implies(X_107,Y_108)) = strict_implies(X_107,Y_108) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_230]) ).
tff(c_264,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_440]) ).
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_320,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_264,c_116]) ).
tff(c_2452,plain,
! [Y_265] : ( implies(not(Y_265),Y_265) = not(not(Y_265)) ),
inference(superposition,[status(thm),theory(equality)],[c_2107,c_320]) ).
tff(c_262,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_439]) ).
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_322,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_262,c_320,c_112]) ).
tff(c_2489,plain,
! [Y_265] : ( or(Y_265,Y_265) = not(not(Y_265)) ),
inference(superposition,[status(thm),theory(equality)],[c_2452,c_322]) ).
tff(c_252,plain,
axiom_m1,
inference(cnfTransformation,[status(thm)],[f_431]) ).
tff(c_188,plain,
! [X_87,Y_88] :
( is_a_theorem(strict_implies(and(X_87,Y_88),and(Y_88,X_87)))
| ~ axiom_m1 ),
inference(cnfTransformation,[status(thm)],[f_312]) ).
tff(c_296,plain,
! [X_87,Y_88] : is_a_theorem(strict_implies(and(X_87,Y_88),and(Y_88,X_87))),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_188]) ).
tff(c_2039,plain,
! [Y_88,X_87] :
( is_a_theorem(strict_equiv(and(Y_88,X_87),and(X_87,Y_88)))
| ~ is_a_theorem(strict_implies(and(Y_88,X_87),and(X_87,Y_88))) ),
inference(resolution,[status(thm)],[c_296,c_2007]) ).
tff(c_2936,plain,
! [Y_276,X_277] : is_a_theorem(strict_equiv(and(Y_276,X_277),and(X_277,Y_276))),
inference(demodulation,[status(thm),theory(equality)],[c_296,c_2039]) ).
tff(c_3004,plain,
! [Y_278,X_279] : ( and(Y_278,X_279) = and(X_279,Y_278) ),
inference(resolution,[status(thm)],[c_2936,c_306]) ).
tff(c_3385,plain,
! [Y_290,Y_291] : ( not(and(not(Y_290),Y_291)) = implies(Y_291,Y_290) ),
inference(superposition,[status(thm),theory(equality)],[c_3004,c_320]) ).
tff(c_3471,plain,
! [Y_61,Y_290] : ( implies(not(Y_61),Y_290) = implies(not(Y_290),Y_61) ),
inference(superposition,[status(thm),theory(equality)],[c_3385,c_320]) ).
tff(c_3528,plain,
! [Y_61,Y_290] : ( or(Y_61,Y_290) = or(Y_290,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_322,c_3471]) ).
tff(c_684,plain,
! [X_165,Y_166] : ( not(and(X_165,not(Y_166))) = implies(X_165,Y_166) ),
inference(demodulation,[status(thm),theory(equality)],[c_264,c_116]) ).
tff(c_693,plain,
! [X_165,Y_166,Y_57] : ( or(and(X_165,not(Y_166)),Y_57) = implies(implies(X_165,Y_166),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_684,c_322]) ).
tff(c_2133,plain,
! [Y_166,Y_57] : ( implies(implies(not(Y_166),Y_166),Y_57) = or(not(Y_166),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_2107,c_693]) ).
tff(c_4990,plain,
! [Y_329,Y_330] : ( or(not(Y_329),Y_330) = implies(or(Y_329,Y_329),Y_330) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_2133]) ).
tff(c_12903,plain,
! [Y_518,Y_519] : ( strict_implies(or(Y_518,Y_518),Y_519) = necessarily(or(not(Y_518),Y_519)) ),
inference(superposition,[status(thm),theory(equality)],[c_4990,c_276]) ).
tff(c_13186,plain,
! [Y_518,Y_290] : ( strict_implies(or(Y_518,Y_518),Y_290) = necessarily(or(Y_290,not(Y_518))) ),
inference(superposition,[status(thm),theory(equality)],[c_3528,c_12903]) ).
tff(c_5805,plain,
! [Y_345,Y_346] : ( or(Y_345,not(Y_346)) = implies(or(Y_346,Y_346),Y_345) ),
inference(superposition,[status(thm),theory(equality)],[c_4990,c_3528]) ).
tff(c_617,plain,
! [X_154,Y_155] : ( necessarily(implies(X_154,Y_155)) = strict_implies(X_154,Y_155) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_230]) ).
tff(c_736,plain,
! [X_170,Y_171] : ( strict_implies(not(X_170),Y_171) = necessarily(or(X_170,Y_171)) ),
inference(superposition,[status(thm),theory(equality)],[c_322,c_617]) ).
tff(c_746,plain,
! [X_170] : is_a_theorem(necessarily(or(X_170,and(not(X_170),not(X_170))))),
inference(superposition,[status(thm),theory(equality)],[c_736,c_284]) ).
tff(c_2103,plain,
! [X_170] : is_a_theorem(necessarily(or(X_170,not(X_170)))),
inference(demodulation,[status(thm),theory(equality)],[c_2098,c_746]) ).
tff(c_5898,plain,
! [Y_346] : is_a_theorem(necessarily(implies(or(Y_346,Y_346),Y_346))),
inference(superposition,[status(thm),theory(equality)],[c_5805,c_2103]) ).
tff(c_6030,plain,
! [Y_346] : is_a_theorem(strict_implies(or(Y_346,Y_346),Y_346)),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_5898]) ).
tff(c_260,plain,
axiom_m5,
inference(cnfTransformation,[status(thm)],[f_435]) ).
tff(c_204,plain,
! [X_95,Y_96,Z_97] :
( is_a_theorem(strict_implies(and(strict_implies(X_95,Y_96),strict_implies(Y_96,Z_97)),strict_implies(X_95,Z_97)))
| ~ axiom_m5 ),
inference(cnfTransformation,[status(thm)],[f_328]) ).
tff(c_1122,plain,
! [X_201,Y_202,Z_203] : is_a_theorem(strict_implies(and(strict_implies(X_201,Y_202),strict_implies(Y_202,Z_203)),strict_implies(X_201,Z_203))),
inference(demodulation,[status(thm),theory(equality)],[c_260,c_204]) ).
tff(c_246,plain,
modus_ponens_strict_implies,
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_128,plain,
! [Y_68,X_67] :
( is_a_theorem(Y_68)
| ~ is_a_theorem(strict_implies(X_67,Y_68))
| ~ is_a_theorem(X_67)
| ~ modus_ponens_strict_implies ),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_316,plain,
! [Y_68,X_67] :
( is_a_theorem(Y_68)
| ~ is_a_theorem(strict_implies(X_67,Y_68))
| ~ is_a_theorem(X_67) ),
inference(demodulation,[status(thm),theory(equality)],[c_246,c_128]) ).
tff(c_1982,plain,
! [X_253,Z_254,Y_255] :
( is_a_theorem(strict_implies(X_253,Z_254))
| ~ is_a_theorem(and(strict_implies(X_253,Y_255),strict_implies(Y_255,Z_254))) ),
inference(resolution,[status(thm)],[c_1122,c_316]) ).
tff(c_6425,plain,
! [X_362,Z_363,Y_364] :
( is_a_theorem(strict_implies(X_362,Z_363))
| ~ is_a_theorem(strict_implies(Y_364,Z_363))
| ~ is_a_theorem(strict_implies(X_362,Y_364)) ),
inference(resolution,[status(thm)],[c_311,c_1982]) ).
tff(c_50746,plain,
! [X_966,Y_967] :
( is_a_theorem(strict_implies(X_966,Y_967))
| ~ is_a_theorem(strict_implies(X_966,or(Y_967,Y_967))) ),
inference(resolution,[status(thm)],[c_6030,c_6425]) ).
tff(c_50894,plain,
! [Y_967] : is_a_theorem(strict_implies(or(or(Y_967,Y_967),or(Y_967,Y_967)),Y_967)),
inference(resolution,[status(thm)],[c_6030,c_50746]) ).
tff(c_51793,plain,
! [Y_977] : is_a_theorem(necessarily(or(Y_977,not(or(Y_977,Y_977))))),
inference(demodulation,[status(thm),theory(equality)],[c_13186,c_50894]) ).
tff(c_51880,plain,
! [Y_265] : is_a_theorem(necessarily(or(Y_265,not(not(not(Y_265)))))),
inference(superposition,[status(thm),theory(equality)],[c_2489,c_51793]) ).
tff(c_699,plain,
! [X_165,X_60,Y_61] : ( implies(X_165,and(X_60,not(Y_61))) = not(and(X_165,implies(X_60,Y_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_320,c_684]) ).
tff(c_2118,plain,
! [X_165,Y_61] : ( not(and(X_165,implies(not(Y_61),Y_61))) = implies(X_165,not(Y_61)) ),
inference(superposition,[status(thm),theory(equality)],[c_2107,c_699]) ).
tff(c_10893,plain,
! [X_496,Y_497] : ( not(and(X_496,or(Y_497,Y_497))) = implies(X_496,not(Y_497)) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_2118]) ).
tff(c_11147,plain,
! [Y_497] : ( implies(or(Y_497,Y_497),not(Y_497)) = not(or(Y_497,Y_497)) ),
inference(superposition,[status(thm),theory(equality)],[c_2098,c_10893]) ).
tff(c_2198,plain,
! [Y_166,Y_57] : ( or(not(Y_166),Y_57) = implies(or(Y_166,Y_166),Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_2133]) ).
tff(c_3150,plain,
! [Y_61,Y_278] : ( not(and(not(Y_61),Y_278)) = implies(Y_278,Y_61) ),
inference(superposition,[status(thm),theory(equality)],[c_3004,c_320]) ).
tff(c_13237,plain,
! [Y_520,Y_521] : ( implies(or(Y_520,Y_520),Y_521) = implies(not(Y_521),not(Y_520)) ),
inference(superposition,[status(thm),theory(equality)],[c_10893,c_3150]) ).
tff(c_13481,plain,
! [Y_521,Y_166] : ( implies(not(Y_521),not(not(Y_166))) = implies(implies(or(Y_166,Y_166),not(Y_166)),Y_521) ),
inference(superposition,[status(thm),theory(equality)],[c_2198,c_13237]) ).
tff(c_27691,plain,
! [Y_719,Y_720] : ( or(or(Y_719,Y_719),Y_720) = or(Y_720,not(not(Y_719))) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_11147,c_322,c_13481]) ).
tff(c_28239,plain,
! [Y_720,Y_719] : ( or(Y_720,or(Y_719,Y_719)) = or(Y_720,not(not(Y_719))) ),
inference(superposition,[status(thm),theory(equality)],[c_27691,c_3528]) ).
tff(c_11532,plain,
! [Y_504] : ( implies(or(Y_504,Y_504),not(Y_504)) = not(or(Y_504,Y_504)) ),
inference(superposition,[status(thm),theory(equality)],[c_2098,c_10893]) ).
tff(c_11574,plain,
! [Y_504] : ( or(not(Y_504),not(Y_504)) = not(or(Y_504,Y_504)) ),
inference(superposition,[status(thm),theory(equality)],[c_11532,c_2198]) ).
tff(c_626,plain,
! [X_56,Y_57] : ( strict_implies(not(X_56),Y_57) = necessarily(or(X_56,Y_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_322,c_617]) ).
tff(c_7847,plain,
! [X_408,Y_409] : ( and(necessarily(or(X_408,Y_409)),strict_implies(Y_409,not(X_408))) = strict_equiv(not(X_408),Y_409) ),
inference(superposition,[status(thm),theory(equality)],[c_626,c_820]) ).
tff(c_83310,plain,
! [X_1300,Y_1301] :
( is_a_theorem(strict_equiv(not(X_1300),Y_1301))
| ~ is_a_theorem(strict_implies(Y_1301,not(X_1300)))
| ~ is_a_theorem(necessarily(or(X_1300,Y_1301))) ),
inference(superposition,[status(thm),theory(equality)],[c_7847,c_311]) ).
tff(c_83559,plain,
! [X_1300] :
( is_a_theorem(strict_equiv(not(X_1300),or(not(X_1300),not(X_1300))))
| ~ is_a_theorem(necessarily(or(X_1300,or(not(X_1300),not(X_1300))))) ),
inference(resolution,[status(thm)],[c_6030,c_83310]) ).
tff(c_83703,plain,
! [X_1302] : is_a_theorem(strict_equiv(not(X_1302),not(or(X_1302,X_1302)))),
inference(demodulation,[status(thm),theory(equality)],[c_51880,c_28239,c_11574,c_83559]) ).
tff(c_83900,plain,
! [X_1302] : ( not(or(X_1302,X_1302)) = not(X_1302) ),
inference(resolution,[status(thm)],[c_83703,c_306]) ).
tff(c_13453,plain,
! [Y_497] : ( implies(not(not(Y_497)),not(Y_497)) = not(or(Y_497,Y_497)) ),
inference(superposition,[status(thm),theory(equality)],[c_11147,c_13237]) ).
tff(c_88121,plain,
! [Y_1314] : ( implies(not(not(Y_1314)),not(Y_1314)) = not(Y_1314) ),
inference(demodulation,[status(thm),theory(equality)],[c_83900,c_13453]) ).
tff(c_1859,plain,
! [X_248,X_249,Y_250] : ( implies(X_248,and(X_249,not(Y_250))) = not(and(X_248,implies(X_249,Y_250))) ),
inference(superposition,[status(thm),theory(equality)],[c_320,c_684]) ).
tff(c_1885,plain,
! [X_248,X_249,Y_250] : ( necessarily(not(and(X_248,implies(X_249,Y_250)))) = strict_implies(X_248,and(X_249,not(Y_250))) ),
inference(superposition,[status(thm),theory(equality)],[c_1859,c_276]) ).
tff(c_88283,plain,
! [X_248,Y_1314] : ( strict_implies(X_248,and(not(not(Y_1314)),not(not(Y_1314)))) = necessarily(not(and(X_248,not(Y_1314)))) ),
inference(superposition,[status(thm),theory(equality)],[c_88121,c_1885]) ).
tff(c_88535,plain,
! [X_248,Y_1314] : ( strict_implies(X_248,not(not(Y_1314))) = strict_implies(X_248,Y_1314) ),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_320,c_2098,c_88283]) ).
tff(c_25308,plain,
! [Y_698] : ( implies(not(not(Y_698)),not(Y_698)) = not(or(Y_698,Y_698)) ),
inference(superposition,[status(thm),theory(equality)],[c_11147,c_13237]) ).
tff(c_25378,plain,
! [X_248,Y_698] : ( strict_implies(X_248,and(not(not(Y_698)),not(not(Y_698)))) = necessarily(not(and(X_248,not(or(Y_698,Y_698))))) ),
inference(superposition,[status(thm),theory(equality)],[c_25308,c_1885]) ).
tff(c_25568,plain,
! [X_248,Y_698] : ( strict_implies(X_248,or(Y_698,Y_698)) = strict_implies(X_248,not(not(Y_698))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2098,c_276,c_320,c_25378]) ).
tff(c_93130,plain,
! [X_1328,Y_1329] : ( strict_implies(X_1328,or(Y_1329,Y_1329)) = strict_implies(X_1328,Y_1329) ),
inference(demodulation,[status(thm),theory(equality)],[c_88535,c_25568]) ).
tff(c_112170,plain,
! [Y_1410,X_1411] :
( is_a_theorem(or(Y_1410,Y_1410))
| ~ is_a_theorem(strict_implies(X_1411,Y_1410))
| ~ is_a_theorem(X_1411) ),
inference(superposition,[status(thm),theory(equality)],[c_93130,c_316]) ).
tff(c_112422,plain,
! [Y_110] :
( is_a_theorem(or(Y_110,Y_110))
| ~ is_a_theorem(strict_equiv(Y_110,Y_110))
| ~ is_a_theorem(Y_110) ),
inference(superposition,[status(thm),theory(equality)],[c_2195,c_112170]) ).
tff(c_112663,plain,
! [Y_1412] :
( is_a_theorem(or(Y_1412,Y_1412))
| ~ is_a_theorem(Y_1412) ),
inference(demodulation,[status(thm),theory(equality)],[c_2100,c_112422]) ).
tff(c_6653,plain,
! [X_367,X_368,Y_369] :
( is_a_theorem(strict_implies(X_367,X_368))
| ~ is_a_theorem(strict_implies(X_367,and(X_368,Y_369))) ),
inference(resolution,[status(thm)],[c_292,c_6425]) ).
tff(c_6657,plain,
! [X_368,Y_369] : is_a_theorem(strict_implies(or(and(X_368,Y_369),and(X_368,Y_369)),X_368)),
inference(resolution,[status(thm)],[c_6030,c_6653]) ).
tff(c_7613,plain,
! [X_402,Y_403] : is_a_theorem(necessarily(or(X_402,not(and(X_402,Y_403))))),
inference(demodulation,[status(thm),theory(equality)],[c_3528,c_626,c_2489,c_6657]) ).
tff(c_7620,plain,
! [Y_166,Y_403] : is_a_theorem(necessarily(implies(or(Y_166,Y_166),not(and(not(Y_166),Y_403))))),
inference(superposition,[status(thm),theory(equality)],[c_2198,c_7613]) ).
tff(c_8486,plain,
! [Y_421,Y_422] : is_a_theorem(strict_implies(or(Y_421,Y_421),implies(Y_422,Y_421))),
inference(demodulation,[status(thm),theory(equality)],[c_3150,c_276,c_7620]) ).
tff(c_8550,plain,
! [Y_422,Y_421] :
( is_a_theorem(implies(Y_422,Y_421))
| ~ is_a_theorem(or(Y_421,Y_421)) ),
inference(resolution,[status(thm)],[c_8486,c_316]) ).
tff(c_113388,plain,
! [Y_1421,Y_1422] :
( is_a_theorem(implies(Y_1421,Y_1422))
| ~ is_a_theorem(Y_1422) ),
inference(resolution,[status(thm)],[c_112663,c_8550]) ).
tff(c_266,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_441]) ).
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_318,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_266,c_120]) ).
tff(c_888,plain,
! [X_186,Y_187] : ( and(implies(X_186,Y_187),implies(Y_187,X_186)) = equiv(X_186,Y_187) ),
inference(demodulation,[status(thm),theory(equality)],[c_266,c_120]) ).
tff(c_896,plain,
! [X_186,Y_187] : is_a_theorem(strict_implies(equiv(X_186,Y_187),and(implies(Y_187,X_186),implies(X_186,Y_187)))),
inference(superposition,[status(thm),theory(equality)],[c_888,c_296]) ).
tff(c_928,plain,
! [X_186,Y_187] : is_a_theorem(strict_implies(equiv(X_186,Y_187),equiv(Y_187,X_186))),
inference(demodulation,[status(thm),theory(equality)],[c_318,c_896]) ).
tff(c_2029,plain,
! [Y_187,X_186] :
( is_a_theorem(strict_equiv(equiv(Y_187,X_186),equiv(X_186,Y_187)))
| ~ is_a_theorem(strict_implies(equiv(Y_187,X_186),equiv(X_186,Y_187))) ),
inference(resolution,[status(thm)],[c_928,c_2007]) ).
tff(c_2806,plain,
! [Y_272,X_273] : is_a_theorem(strict_equiv(equiv(Y_272,X_273),equiv(X_273,Y_272))),
inference(demodulation,[status(thm),theory(equality)],[c_928,c_2029]) ).
tff(c_2824,plain,
! [Y_272,X_273] : ( equiv(Y_272,X_273) = equiv(X_273,Y_272) ),
inference(resolution,[status(thm)],[c_2806,c_306]) ).
tff(c_6,plain,
( is_a_theorem(implies('#skF_1','#skF_2'))
| modus_ponens ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_336,plain,
is_a_theorem(implies('#skF_1','#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_270,c_6]) ).
tff(c_3307,plain,
! [X_284,Y_285] :
( is_a_theorem(equiv(X_284,Y_285))
| ~ is_a_theorem(implies(Y_285,X_284))
| ~ is_a_theorem(implies(X_284,Y_285)) ),
inference(superposition,[status(thm),theory(equality)],[c_888,c_311]) ).
tff(c_3321,plain,
( is_a_theorem(equiv('#skF_2','#skF_1'))
| ~ is_a_theorem(implies('#skF_2','#skF_1')) ),
inference(resolution,[status(thm)],[c_336,c_3307]) ).
tff(c_3325,plain,
( is_a_theorem(equiv('#skF_1','#skF_2'))
| ~ is_a_theorem(implies('#skF_2','#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_2824,c_3321]) ).
tff(c_3326,plain,
~ is_a_theorem(implies('#skF_2','#skF_1')),
inference(splitLeft,[status(thm)],[c_3325]) ).
tff(c_113425,plain,
~ is_a_theorem('#skF_1'),
inference(resolution,[status(thm)],[c_113388,c_3326]) ).
tff(c_113576,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_335,c_113425]) ).
tff(c_113577,plain,
is_a_theorem(equiv('#skF_1','#skF_2')),
inference(splitRight,[status(thm)],[c_3325]) ).
tff(c_268,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_444]) ).
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_334,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_268,c_10]) ).
tff(c_113586,plain,
'#skF_2' = '#skF_1',
inference(resolution,[status(thm)],[c_113577,c_334]) ).
tff(c_4,plain,
( ~ is_a_theorem('#skF_2')
| modus_ponens ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_337,plain,
~ is_a_theorem('#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_270,c_4]) ).
tff(c_113589,plain,
~ is_a_theorem('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_113586,c_337]) ).
tff(c_113593,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_335,c_113589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL550+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 13:38:51 EDT 2023
% 0.15/0.37 % CPUTime :
% 44.14/29.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.14/29.49
% 44.14/29.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.37/29.54
% 44.37/29.54 Inference rules
% 44.37/29.54 ----------------------
% 44.37/29.54 #Ref : 0
% 44.37/29.54 #Sup : 29821
% 44.37/29.54 #Fact : 0
% 44.37/29.54 #Define : 0
% 44.37/29.54 #Split : 95
% 44.37/29.54 #Chain : 0
% 44.37/29.54 #Close : 0
% 44.37/29.54
% 44.37/29.54 Ordering : KBO
% 44.37/29.54
% 44.37/29.54 Simplification rules
% 44.37/29.54 ----------------------
% 44.37/29.54 #Subsume : 4086
% 44.37/29.54 #Demod : 29189
% 44.37/29.54 #Tautology : 7176
% 44.37/29.54 #SimpNegUnit : 290
% 44.37/29.54 #BackRed : 220
% 44.37/29.54
% 44.37/29.54 #Partial instantiations: 0
% 44.37/29.54 #Strategies tried : 1
% 44.37/29.54
% 44.37/29.54 Timing (in seconds)
% 44.37/29.54 ----------------------
% 44.37/29.54 Preprocessing : 0.77
% 44.37/29.54 Parsing : 0.39
% 44.37/29.55 CNF conversion : 0.07
% 44.37/29.55 Main loop : 27.58
% 44.37/29.55 Inferencing : 2.42
% 44.37/29.55 Reduction : 17.20
% 44.37/29.55 Demodulation : 14.74
% 44.37/29.55 BG Simplification : 0.27
% 44.37/29.55 Subsumption : 6.24
% 44.37/29.55 Abstraction : 0.32
% 44.37/29.55 MUC search : 0.00
% 44.37/29.55 Cooper : 0.00
% 44.37/29.55 Total : 28.44
% 44.37/29.55 Index Insertion : 0.00
% 44.37/29.55 Index Deletion : 0.00
% 44.37/29.55 Index Matching : 0.00
% 44.37/29.55 BG Taut test : 0.00
%------------------------------------------------------------------------------