TSTP Solution File: LCL537+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL537+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 : n005.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 10:48:19 EDT 2023
% Result : Theorem 14.42s 4.64s
% Output : CNFRefutation 14.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 197
% Syntax : Number of formulae : 305 ( 86 unt; 162 typ; 0 def)
% Number of atoms : 214 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 126 ( 55 ~; 47 |; 2 &)
% ( 15 <=>; 7 =>; 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 : 61 ( 59 usr; 59 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 143 (; 143 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > strict_implies > strict_equiv > or > implies > equiv > and > #nlpp > possibly > not > necessarily > substitution_strict_equiv > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_strict_implies > op_strict_equiv > op_possibly > op_or > op_necessarily > op_implies_or > op_implies_and > op_equiv > op_and > necessitation > modus_tollens > modus_ponens_strict_implies > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > axiom_s4 > axiom_s3 > axiom_s2 > axiom_s1 > axiom_m9 > axiom_m8 > axiom_m7 > axiom_m6 > axiom_m5 > axiom_m4 > axiom_m3 > axiom_m2 > axiom_m10 > axiom_m1 > axiom_M > axiom_K > axiom_B > axiom_5 > axiom_4 > and_3 > and_2 > and_1 > adjunction > #skF_33 > #skF_41 > #skF_60 > #skF_57 > #skF_52 > #skF_76 > #skF_67 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_78 > #skF_94 > #skF_11 > #skF_86 > #skF_31 > #skF_15 > #skF_69 > #skF_25 > #skF_55 > #skF_87 > #skF_38 > #skF_36 > #skF_80 > #skF_56 > #skF_54 > #skF_43 > #skF_79 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_71 > #skF_10 > #skF_16 > #skF_85 > #skF_47 > #skF_92 > #skF_65 > #skF_26 > #skF_81 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_72 > #skF_6 > #skF_13 > #skF_61 > #skF_2 > #skF_68 > #skF_82 > #skF_84 > #skF_3 > #skF_1 > #skF_89 > #skF_21 > #skF_9 > #skF_32 > #skF_64 > #skF_50 > #skF_90 > #skF_8 > #skF_30 > #skF_42 > #skF_77 > #skF_4 > #skF_22 > #skF_93 > #skF_29 > #skF_28 > #skF_35 > #skF_70 > #skF_66 > #skF_24 > #skF_27 > #skF_23 > #skF_63 > #skF_88 > #skF_44 > #skF_83 > #skF_59 > #skF_73 > #skF_91 > #skF_58 > #skF_12 > #skF_62 > #skF_34 > #skF_75 > #skF_74
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $o ).
tff(axiom_s1,type,
axiom_s1: $o ).
tff(equiv,type,
equiv: ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_41',type,
'#skF_41': $i ).
tff(r3,type,
r3: $o ).
tff('#skF_60',type,
'#skF_60': $i ).
tff(op_possibly,type,
op_possibly: $o ).
tff('#skF_57',type,
'#skF_57': $i ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_76',type,
'#skF_76': $i ).
tff(axiom_m8,type,
axiom_m8: $o ).
tff('#skF_67',type,
'#skF_67': $i ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $o ).
tff(axiom_4,type,
axiom_4: $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(op_implies_or,type,
op_implies_or: $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_78',type,
'#skF_78': $i ).
tff(adjunction,type,
adjunction: $o ).
tff('#skF_94',type,
'#skF_94': $i ).
tff(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_86',type,
'#skF_86': $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_69',type,
'#skF_69': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(axiom_m3,type,
axiom_m3: $o ).
tff(cn2,type,
cn2: $o ).
tff(axiom_K,type,
axiom_K: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff('#skF_87',type,
'#skF_87': $i ).
tff(possibly,type,
possibly: $i > $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_80',type,
'#skF_80': $i ).
tff(axiom_B,type,
axiom_B: $o ).
tff('#skF_56',type,
'#skF_56': $i ).
tff(op_strict_equiv,type,
op_strict_equiv: $o ).
tff('#skF_54',type,
'#skF_54': $i ).
tff(axiom_5,type,
axiom_5: $o ).
tff('#skF_43',type,
'#skF_43': $i ).
tff('#skF_79',type,
'#skF_79': $i ).
tff(op_and,type,
op_and: $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_40',type,
'#skF_40': $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_37',type,
'#skF_37': $i ).
tff(and_3,type,
and_3: $o ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(op_implies_and,type,
op_implies_and: $o ).
tff(op_strict_implies,type,
op_strict_implies: $o ).
tff('#skF_71',type,
'#skF_71': $i ).
tff(equivalence_1,type,
equivalence_1: $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(kn2,type,
kn2: $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff('#skF_85',type,
'#skF_85': $i ).
tff(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff('#skF_92',type,
'#skF_92': $i ).
tff('#skF_65',type,
'#skF_65': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_81',type,
'#skF_81': $i ).
tff(necessitation,type,
necessitation: $o ).
tff('#skF_53',type,
'#skF_53': $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff(or_1,type,
or_1: $o ).
tff(implies_3,type,
implies_3: $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_45',type,
'#skF_45': $i ).
tff(axiom_s4,type,
axiom_s4: $o ).
tff('#skF_46',type,
'#skF_46': $i ).
tff('#skF_39',type,
'#skF_39': $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(modus_tollens,type,
modus_tollens: $o ).
tff('#skF_72',type,
'#skF_72': $i ).
tff(r2,type,
r2: $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(not,type,
not: $i > $i ).
tff('#skF_61',type,
'#skF_61': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_68',type,
'#skF_68': $i ).
tff(axiom_m2,type,
axiom_m2: $o ).
tff(modus_ponens,type,
modus_ponens: $o ).
tff('#skF_82',type,
'#skF_82': $i ).
tff('#skF_84',type,
'#skF_84': $i ).
tff(op_or,type,
op_or: $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(axiom_s3,type,
axiom_s3: $o ).
tff(substitution_strict_equiv,type,
substitution_strict_equiv: $o ).
tff(axiom_M,type,
axiom_M: $o ).
tff(strict_implies,type,
strict_implies: ( $i * $i ) > $i ).
tff('#skF_89',type,
'#skF_89': $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(necessarily,type,
necessarily: $i > $i ).
tff(axiom_m4,type,
axiom_m4: $o ).
tff('#skF_64',type,
'#skF_64': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_90',type,
'#skF_90': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(modus_ponens_strict_implies,type,
modus_ponens_strict_implies: $o ).
tff(axiom_m7,type,
axiom_m7: $o ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(axiom_s2,type,
axiom_s2: $o ).
tff('#skF_77',type,
'#skF_77': $i ).
tff(or_3,type,
or_3: $o ).
tff(op_necessarily,type,
op_necessarily: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(strict_equiv,type,
strict_equiv: ( $i * $i ) > $i ).
tff('#skF_93',type,
'#skF_93': $i ).
tff(kn1,type,
kn1: $o ).
tff(axiom_m6,type,
axiom_m6: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $i ).
tff('#skF_70',type,
'#skF_70': $i ).
tff('#skF_66',type,
'#skF_66': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff('#skF_63',type,
'#skF_63': $i ).
tff(axiom_m1,type,
axiom_m1: $o ).
tff('#skF_88',type,
'#skF_88': $i ).
tff(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff('#skF_83',type,
'#skF_83': $i ).
tff(axiom_m10,type,
axiom_m10: $o ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff('#skF_59',type,
'#skF_59': $i ).
tff(axiom_m9,type,
axiom_m9: $o ).
tff('#skF_73',type,
'#skF_73': $i ).
tff('#skF_91',type,
'#skF_91': $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_58',type,
'#skF_58': $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(axiom_m5,type,
axiom_m5: $o ).
tff('#skF_62',type,
'#skF_62': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff('#skF_75',type,
'#skF_75': $i ).
tff('#skF_74',type,
'#skF_74': $i ).
tff(f_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_470,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_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_245,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_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_243,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_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_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_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_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
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_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
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_481,negated_conjecture,
~ axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_5) ).
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(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_309,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_270,plain,
op_possibly,
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_262,plain,
! [X_105] :
( ( not(necessarily(not(X_105))) = possibly(X_105) )
| ~ op_possibly ),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_284,plain,
! [X_105] : ( not(necessarily(not(X_105))) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_270,c_262]) ).
tff(c_409,plain,
! [X_124] : ( not(necessarily(not(X_124))) = possibly(X_124) ),
inference(demodulation,[status(thm),theory(equality)],[c_270,c_262]) ).
tff(c_418,plain,
! [X_105] : ( possibly(necessarily(not(X_105))) = not(necessarily(possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_409]) ).
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_295,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_291,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_126,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_245]) ).
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_4602,plain,
! [X_526,Y_527] : ( and(implies(X_526,Y_527),implies(Y_527,X_526)) = equiv(X_526,Y_527) ),
inference(demodulation,[status(thm),theory(equality)],[c_126,c_120]) ).
tff(c_178,plain,
( is_a_theorem('#skF_59')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_392,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_4481,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_392,c_172]) ).
tff(c_9088,plain,
! [X_821,Y_822] :
( is_a_theorem(equiv(X_821,Y_822))
| ~ is_a_theorem(implies(Y_822,X_821))
| ~ is_a_theorem(implies(X_821,Y_822)) ),
inference(superposition,[status(thm),theory(equality)],[c_4602,c_4481]) ).
tff(c_9170,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_291,c_9088]) ).
tff(c_12003,plain,
! [X_858] : is_a_theorem(equiv(necessarily(necessarily(X_858)),necessarily(X_858))),
inference(demodulation,[status(thm),theory(equality)],[c_295,c_9170]) ).
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_385,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_12023,plain,
! [X_858] : ( necessarily(necessarily(X_858)) = necessarily(X_858) ),
inference(resolution,[status(thm)],[c_12003,c_385]) ).
tff(c_4307,plain,
! [X_483,Y_484] : ( not(and(X_483,not(Y_484))) = implies(X_483,Y_484) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_4340,plain,
! [X_483,X_105] : ( implies(X_483,necessarily(not(X_105))) = not(and(X_483,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_4307]) ).
tff(c_122,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_243]) ).
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_1595,plain,
! [X_263,Y_264] : ( implies(not(X_263),Y_264) = or(X_263,Y_264) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_309,c_112]) ).
tff(c_1623,plain,
! [X_105,Y_264] : ( or(necessarily(not(X_105)),Y_264) = implies(possibly(X_105),Y_264) ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_1595]) ).
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_335,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_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_375,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_1995,plain,
! [X_320,Y_321] : is_a_theorem(implies(implies(X_320,implies(X_320,Y_321)),implies(X_320,Y_321))),
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_390,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_2949,plain,
! [X_408,Y_409] :
( is_a_theorem(implies(X_408,Y_409))
| ~ is_a_theorem(implies(X_408,implies(X_408,Y_409))) ),
inference(resolution,[status(thm)],[c_1995,c_390]) ).
tff(c_3005,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_375,c_2949]) ).
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_3575,plain,
! [X_435,Z_436,Y_437] : is_a_theorem(implies(implies(X_435,Z_436),implies(implies(Y_437,Z_436),implies(or(X_435,Y_437),Z_436)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_2009,plain,
! [X_320,Y_321] :
( is_a_theorem(implies(X_320,Y_321))
| ~ is_a_theorem(implies(X_320,implies(X_320,Y_321))) ),
inference(resolution,[status(thm)],[c_1995,c_390]) ).
tff(c_3939,plain,
! [Y_458,Z_459] : is_a_theorem(implies(implies(Y_458,Z_459),implies(or(Y_458,Y_458),Z_459))),
inference(resolution,[status(thm)],[c_3575,c_2009]) ).
tff(c_4233,plain,
! [Y_472,Z_473] :
( is_a_theorem(implies(or(Y_472,Y_472),Z_473))
| ~ is_a_theorem(implies(Y_472,Z_473)) ),
inference(resolution,[status(thm)],[c_3939,c_390]) ).
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_1638,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_1644,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(negUnitSimplification,[status(thm)],[c_1638,c_92]) ).
tff(c_4246,plain,
~ is_a_theorem(implies('#skF_45','#skF_45')),
inference(resolution,[status(thm)],[c_4233,c_1644]) ).
tff(c_4268,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3005,c_4246]) ).
tff(c_4269,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_9172,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_4269,c_9088]) ).
tff(c_9264,plain,
! [P_823] : is_a_theorem(equiv(P_823,or(P_823,P_823))),
inference(demodulation,[status(thm),theory(equality)],[c_335,c_9172]) ).
tff(c_9303,plain,
! [P_823] : ( or(P_823,P_823) = P_823 ),
inference(resolution,[status(thm)],[c_9264,c_385]) ).
tff(c_311,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_309,c_112]) ).
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_353,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_349,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_1010,plain,
! [X_195,Y_196] : is_a_theorem(implies(implies(X_195,implies(X_195,Y_196)),implies(X_195,Y_196))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_1500,plain,
! [X_259,Y_260] :
( is_a_theorem(implies(X_259,Y_260))
| ~ is_a_theorem(implies(X_259,implies(X_259,Y_260))) ),
inference(resolution,[status(thm)],[c_1010,c_390]) ).
tff(c_1550,plain,
! [Y_19] : is_a_theorem(implies(Y_19,and(Y_19,Y_19))),
inference(resolution,[status(thm)],[c_349,c_1500]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_428,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_1592,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1550,c_428]) ).
tff(c_1593,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_1631,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_1593,c_70]) ).
tff(c_9174,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_1631,c_9088]) ).
tff(c_9537,plain,
! [P_827] : is_a_theorem(equiv(and(P_827,P_827),P_827)),
inference(demodulation,[status(thm),theory(equality)],[c_353,c_9174]) ).
tff(c_9583,plain,
! [P_828] : ( and(P_828,P_828) = P_828 ),
inference(resolution,[status(thm)],[c_9537,c_385]) ).
tff(c_4331,plain,
! [X_483,Y_484] : ( possibly(and(X_483,not(Y_484))) = not(necessarily(implies(X_483,Y_484))) ),
inference(superposition,[status(thm),theory(equality)],[c_4307,c_284]) ).
tff(c_9694,plain,
! [Y_484] : ( not(necessarily(implies(not(Y_484),Y_484))) = possibly(not(Y_484)) ),
inference(superposition,[status(thm),theory(equality)],[c_9583,c_4331]) ).
tff(c_9780,plain,
! [Y_484] : ( possibly(not(Y_484)) = not(necessarily(Y_484)) ),
inference(demodulation,[status(thm),theory(equality)],[c_9303,c_311,c_9694]) ).
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_287,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_1602,plain,
! [X_263] : is_a_theorem(or(X_263,necessarily(possibly(not(X_263))))),
inference(superposition,[status(thm),theory(equality)],[c_1595,c_287]) ).
tff(c_12233,plain,
! [X_866] : is_a_theorem(or(X_866,necessarily(not(necessarily(X_866))))),
inference(demodulation,[status(thm),theory(equality)],[c_9780,c_1602]) ).
tff(c_12253,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(not(necessarily(necessarily(not(X_105))))))),
inference(superposition,[status(thm),theory(equality)],[c_1623,c_12233]) ).
tff(c_12263,plain,
! [X_105] : is_a_theorem(implies(possibly(X_105),necessarily(possibly(X_105)))),
inference(demodulation,[status(thm),theory(equality)],[c_309,c_418,c_12023,c_4340,c_12253]) ).
tff(c_282,plain,
~ axiom_5,
inference(cnfTransformation,[status(thm)],[f_481]) ).
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_285,plain,
~ is_a_theorem(implies(possibly('#skF_68'),necessarily(possibly('#skF_68')))),
inference(negUnitSimplification,[status(thm)],[c_282,c_202]) ).
tff(c_12742,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12263,c_285]) ).
tff(c_12743,plain,
is_a_theorem('#skF_59'),
inference(splitRight,[status(thm)],[c_178]) ).
tff(c_12744,plain,
~ adjunction,
inference(splitRight,[status(thm)],[c_178]) ).
tff(c_176,plain,
( is_a_theorem('#skF_60')
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_12747,plain,
is_a_theorem('#skF_60'),
inference(negUnitSimplification,[status(thm)],[c_12744,c_176]) ).
tff(c_12994,plain,
! [X_924,Y_925] : is_a_theorem(implies(X_924,implies(Y_925,and(X_924,Y_925)))),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_42]) ).
tff(c_13103,plain,
! [Y_931,X_932] :
( is_a_theorem(implies(Y_931,and(X_932,Y_931)))
| ~ is_a_theorem(X_932) ),
inference(resolution,[status(thm)],[c_12994,c_390]) ).
tff(c_13122,plain,
! [X_939,Y_940] :
( is_a_theorem(and(X_939,Y_940))
| ~ is_a_theorem(Y_940)
| ~ is_a_theorem(X_939) ),
inference(resolution,[status(thm)],[c_13103,c_390]) ).
tff(c_174,plain,
( ~ is_a_theorem(and('#skF_59','#skF_60'))
| adjunction ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_12748,plain,
~ is_a_theorem(and('#skF_59','#skF_60')),
inference(negUnitSimplification,[status(thm)],[c_12744,c_174]) ).
tff(c_13134,plain,
( ~ is_a_theorem('#skF_60')
| ~ is_a_theorem('#skF_59') ),
inference(resolution,[status(thm)],[c_13122,c_12748]) ).
tff(c_13141,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12743,c_12747,c_13134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL537+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % 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
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 14:21:26 EDT 2023
% 0.15/0.36 % CPUTime :
% 14.42/4.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.42/4.66
% 14.42/4.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.62/4.70
% 14.62/4.70 Inference rules
% 14.62/4.70 ----------------------
% 14.62/4.70 #Ref : 0
% 14.62/4.70 #Sup : 3110
% 14.62/4.70 #Fact : 0
% 14.62/4.70 #Define : 0
% 14.62/4.70 #Split : 125
% 14.62/4.70 #Chain : 0
% 14.62/4.70 #Close : 0
% 14.62/4.70
% 14.62/4.70 Ordering : KBO
% 14.62/4.70
% 14.62/4.70 Simplification rules
% 14.62/4.70 ----------------------
% 14.62/4.70 #Subsume : 691
% 14.62/4.70 #Demod : 2196
% 14.62/4.70 #Tautology : 732
% 14.62/4.70 #SimpNegUnit : 31
% 14.62/4.70 #BackRed : 54
% 14.62/4.70
% 14.62/4.70 #Partial instantiations: 0
% 14.62/4.70 #Strategies tried : 1
% 14.62/4.70
% 14.62/4.70 Timing (in seconds)
% 14.62/4.70 ----------------------
% 14.62/4.71 Preprocessing : 0.75
% 14.62/4.71 Parsing : 0.38
% 14.62/4.71 CNF conversion : 0.07
% 14.62/4.71 Main loop : 2.78
% 14.62/4.71 Inferencing : 0.80
% 14.62/4.71 Reduction : 1.12
% 14.62/4.71 Demodulation : 0.83
% 14.62/4.71 BG Simplification : 0.09
% 14.62/4.71 Subsumption : 0.56
% 14.62/4.71 Abstraction : 0.07
% 14.62/4.71 MUC search : 0.00
% 14.62/4.71 Cooper : 0.00
% 14.62/4.71 Total : 3.61
% 14.62/4.71 Index Insertion : 0.00
% 14.62/4.71 Index Deletion : 0.00
% 14.62/4.71 Index Matching : 0.00
% 14.62/4.71 BG Taut test : 0.00
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