TSTP Solution File: LCL524+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL524+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 : n025.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 10:48:18 EDT 2023
% Result : Theorem 18.10s 7.94s
% Output : CNFRefutation 18.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 194
% Syntax : Number of formulae : 280 ( 67 unt; 162 typ; 0 def)
% Number of atoms : 178 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 108 ( 48 ~; 40 |; 1 &)
% ( 14 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 131 (; 131 !; 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_243,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
tff(f_244,axiom,
op_implies_and,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
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_470,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).
tff(f_429,axiom,
( op_possibly
=> ! [X] : ( possibly(X) = not(necessarily(not(X))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
tff(f_250,axiom,
implies_1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(f_251,axiom,
implies_2,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_258,axiom,
or_3,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
tff(f_146,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_475,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
tff(f_328,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
tff(f_252,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
tff(f_84,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
tff(f_249,axiom,
modus_tollens,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
tff(f_254,axiom,
and_2,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_476,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
tff(f_340,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
tff(f_261,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
tff(f_120,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
tff(f_264,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_480,negated_conjecture,
~ axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_B) ).
tff(f_336,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_B) ).
tff(c_122,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_243]) ).
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_303,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_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_305,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_303,c_112]) ).
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_282,plain,
! [X_105] : ( not(necessarily(not(X_105))) = possibly(X_105) ),
inference(demodulation,[status(thm),theory(equality)],[c_270,c_262]) ).
tff(c_13182,plain,
! [X_969,Y_970] : ( not(and(X_969,not(Y_970))) = implies(X_969,Y_970) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_13212,plain,
! [X_969,X_105] : ( implies(X_969,necessarily(not(X_105))) = not(and(X_969,possibly(X_105))) ),
inference(superposition,[status(thm),theory(equality)],[c_282,c_13182]) ).
tff(c_4035,plain,
! [X_450,Y_451] : ( implies(not(X_450),Y_451) = or(X_450,Y_451) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_303,c_112]) ).
tff(c_4059,plain,
! [X_105,Y_451] : ( or(necessarily(not(X_105)),Y_451) = implies(possibly(X_105),Y_451) ),
inference(superposition,[status(thm),theory(equality)],[c_282,c_4035]) ).
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_369,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_2062,plain,
! [X_311,Y_312] : is_a_theorem(implies(implies(X_311,implies(X_311,Y_312)),implies(X_311,Y_312))),
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_384,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_2624,plain,
! [X_379,Y_380] :
( is_a_theorem(implies(X_379,Y_380))
| ~ is_a_theorem(implies(X_379,implies(X_379,Y_380))) ),
inference(resolution,[status(thm)],[c_2062,c_384]) ).
tff(c_2680,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_369,c_2624]) ).
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_3224,plain,
! [X_401,Z_402,Y_403] : is_a_theorem(implies(implies(X_401,Z_402),implies(implies(Y_403,Z_402),implies(or(X_401,Y_403),Z_402)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_2076,plain,
! [X_311,Y_312] :
( is_a_theorem(implies(X_311,Y_312))
| ~ is_a_theorem(implies(X_311,implies(X_311,Y_312))) ),
inference(resolution,[status(thm)],[c_2062,c_384]) ).
tff(c_3730,plain,
! [Y_427,Z_428] : is_a_theorem(implies(implies(Y_427,Z_428),implies(or(Y_427,Y_427),Z_428))),
inference(resolution,[status(thm)],[c_3224,c_2076]) ).
tff(c_3985,plain,
! [Y_447,Z_448] :
( is_a_theorem(implies(or(Y_447,Y_447),Z_448))
| ~ is_a_theorem(implies(Y_447,Z_448)) ),
inference(resolution,[status(thm)],[c_3730,c_384]) ).
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_307,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_88]) ).
tff(c_1512,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(splitLeft,[status(thm)],[c_307]) ).
tff(c_3998,plain,
~ is_a_theorem(implies('#skF_44','#skF_44')),
inference(resolution,[status(thm)],[c_3985,c_1512]) ).
tff(c_4020,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2680,c_3998]) ).
tff(c_4021,plain,
cn3,
inference(splitRight,[status(thm)],[c_307]) ).
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_306,plain,
! [P_44] :
( is_a_theorem(implies(or(P_44,P_44),P_44))
| ~ cn3 ),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_90]) ).
tff(c_4025,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_4021,c_306]) ).
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_419,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_420,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(negUnitSimplification,[status(thm)],[c_419,c_92]) ).
tff(c_4029,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4025,c_420]) ).
tff(c_4030,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
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_289,plain,
! [X_75] : is_a_theorem(implies(necessarily(X_75),X_75)),
inference(demodulation,[status(thm),theory(equality)],[c_276,c_192]) ).
tff(c_136,plain,
implies_3,
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_30,plain,
! [X_11,Y_12,Z_13] :
( is_a_theorem(implies(implies(X_11,Y_12),implies(implies(Y_12,Z_13),implies(X_11,Z_13))))
| ~ implies_3 ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_14117,plain,
! [X_1065,Y_1066,Z_1067] : is_a_theorem(implies(implies(X_1065,Y_1066),implies(implies(Y_1066,Z_1067),implies(X_1065,Z_1067)))),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_30]) ).
tff(c_15718,plain,
! [Y_1168,Z_1169,X_1170] :
( is_a_theorem(implies(implies(Y_1168,Z_1169),implies(X_1170,Z_1169)))
| ~ is_a_theorem(implies(X_1170,Y_1168)) ),
inference(resolution,[status(thm)],[c_14117,c_384]) ).
tff(c_23618,plain,
! [X_1625,Z_1626,Y_1627] :
( is_a_theorem(implies(X_1625,Z_1626))
| ~ is_a_theorem(implies(Y_1627,Z_1626))
| ~ is_a_theorem(implies(X_1625,Y_1627)) ),
inference(resolution,[status(thm)],[c_15718,c_384]) ).
tff(c_23823,plain,
! [X_1628,X_1629] :
( is_a_theorem(implies(X_1628,X_1629))
| ~ is_a_theorem(implies(X_1628,necessarily(X_1629))) ),
inference(resolution,[status(thm)],[c_289,c_23618]) ).
tff(c_24224,plain,
! [X_1644] : is_a_theorem(implies(or(necessarily(X_1644),necessarily(X_1644)),X_1644)),
inference(resolution,[status(thm)],[c_4030,c_23823]) ).
tff(c_24259,plain,
! [X_105] : is_a_theorem(implies(implies(possibly(X_105),necessarily(not(X_105))),not(X_105))),
inference(superposition,[status(thm),theory(equality)],[c_4059,c_24224]) ).
tff(c_25378,plain,
! [X_1711] : is_a_theorem(or(and(possibly(X_1711),possibly(X_1711)),not(X_1711))),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_13212,c_24259]) ).
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_13415,plain,
! [Y_1002,X_1003] : is_a_theorem(implies(or(Y_1002,not(X_1003)),implies(X_1003,Y_1002))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_305,c_18]) ).
tff(c_13428,plain,
! [X_1003,Y_1002] :
( is_a_theorem(implies(X_1003,Y_1002))
| ~ is_a_theorem(or(Y_1002,not(X_1003))) ),
inference(resolution,[status(thm)],[c_13415,c_384]) ).
tff(c_25442,plain,
! [X_1712] : is_a_theorem(implies(X_1712,and(possibly(X_1712),possibly(X_1712)))),
inference(resolution,[status(thm)],[c_25378,c_13428]) ).
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_347,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_23817,plain,
! [X_1625,Y_17,X_16] :
( is_a_theorem(implies(X_1625,Y_17))
| ~ is_a_theorem(implies(X_1625,and(X_16,Y_17))) ),
inference(resolution,[status(thm)],[c_347,c_23618]) ).
tff(c_25481,plain,
! [X_1712] : is_a_theorem(implies(X_1712,possibly(X_1712))),
inference(resolution,[status(thm)],[c_25442,c_23817]) ).
tff(c_278,plain,
axiom_5,
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_204,plain,
! [X_78] :
( is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78))))
| ~ axiom_5 ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_284,plain,
! [X_78] : is_a_theorem(implies(possibly(X_78),necessarily(possibly(X_78)))),
inference(demodulation,[status(thm),theory(equality)],[c_278,c_204]) ).
tff(c_154,plain,
equivalence_3,
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_66,plain,
! [X_31,Y_32] :
( is_a_theorem(implies(implies(X_31,Y_32),implies(implies(Y_32,X_31),equiv(X_31,Y_32))))
| ~ equivalence_3 ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_14172,plain,
! [X_1077,Y_1078] : is_a_theorem(implies(implies(X_1077,Y_1078),implies(implies(Y_1078,X_1077),equiv(X_1077,Y_1078)))),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_66]) ).
tff(c_17218,plain,
! [Y_1289,X_1290] :
( is_a_theorem(implies(implies(Y_1289,X_1290),equiv(X_1290,Y_1289)))
| ~ is_a_theorem(implies(X_1290,Y_1289)) ),
inference(resolution,[status(thm)],[c_14172,c_384]) ).
tff(c_28034,plain,
! [X_1851,Y_1852] :
( is_a_theorem(equiv(X_1851,Y_1852))
| ~ is_a_theorem(implies(Y_1852,X_1851))
| ~ is_a_theorem(implies(X_1851,Y_1852)) ),
inference(resolution,[status(thm)],[c_17218,c_384]) ).
tff(c_28222,plain,
! [X_78] :
( is_a_theorem(equiv(necessarily(possibly(X_78)),possibly(X_78)))
| ~ is_a_theorem(implies(necessarily(possibly(X_78)),possibly(X_78))) ),
inference(resolution,[status(thm)],[c_284,c_28034]) ).
tff(c_34515,plain,
! [X_1897] : is_a_theorem(equiv(necessarily(possibly(X_1897)),possibly(X_1897))),
inference(demodulation,[status(thm),theory(equality)],[c_289,c_28222]) ).
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_379,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_34588,plain,
! [X_1897] : ( necessarily(possibly(X_1897)) = possibly(X_1897) ),
inference(resolution,[status(thm)],[c_34515,c_379]) ).
tff(c_280,plain,
~ axiom_B,
inference(cnfTransformation,[status(thm)],[f_480]) ).
tff(c_198,plain,
( axiom_B
| ~ is_a_theorem(implies('#skF_67',necessarily(possibly('#skF_67')))) ),
inference(cnfTransformation,[status(thm)],[f_336]) ).
tff(c_287,plain,
~ is_a_theorem(implies('#skF_67',necessarily(possibly('#skF_67')))),
inference(negUnitSimplification,[status(thm)],[c_280,c_198]) ).
tff(c_34615,plain,
~ is_a_theorem(implies('#skF_67',possibly('#skF_67'))),
inference(demodulation,[status(thm),theory(equality)],[c_34588,c_287]) ).
tff(c_34623,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25481,c_34615]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LCL524+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % 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
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 13:52:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 18.10/7.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.10/7.95
% 18.10/7.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.22/8.00
% 18.22/8.00 Inference rules
% 18.22/8.00 ----------------------
% 18.22/8.00 #Ref : 0
% 18.22/8.00 #Sup : 8534
% 18.22/8.00 #Fact : 0
% 18.22/8.00 #Define : 0
% 18.22/8.00 #Split : 160
% 18.22/8.00 #Chain : 0
% 18.22/8.00 #Close : 0
% 18.22/8.00
% 18.22/8.00 Ordering : KBO
% 18.22/8.00
% 18.22/8.00 Simplification rules
% 18.22/8.00 ----------------------
% 18.22/8.00 #Subsume : 2434
% 18.22/8.00 #Demod : 4896
% 18.22/8.00 #Tautology : 1470
% 18.22/8.00 #SimpNegUnit : 48
% 18.22/8.00 #BackRed : 165
% 18.22/8.00
% 18.22/8.00 #Partial instantiations: 0
% 18.22/8.00 #Strategies tried : 1
% 18.22/8.00
% 18.22/8.00 Timing (in seconds)
% 18.22/8.00 ----------------------
% 18.22/8.00 Preprocessing : 0.73
% 18.22/8.00 Parsing : 0.36
% 18.22/8.00 CNF conversion : 0.07
% 18.22/8.00 Main loop : 6.18
% 18.22/8.00 Inferencing : 1.36
% 18.22/8.00 Reduction : 2.79
% 18.22/8.00 Demodulation : 2.08
% 18.22/8.00 BG Simplification : 0.09
% 18.22/8.00 Subsumption : 1.58
% 18.22/8.00 Abstraction : 0.09
% 18.22/8.00 MUC search : 0.00
% 18.22/8.00 Cooper : 0.00
% 18.22/8.00 Total : 6.98
% 18.22/8.00 Index Insertion : 0.00
% 18.22/8.00 Index Deletion : 0.00
% 18.22/8.00 Index Matching : 0.00
% 18.22/8.00 BG Taut test : 0.00
%------------------------------------------------------------------------------