TSTP Solution File: LCL520+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL520+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 : n020.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 10:48:17 EDT 2023
% Result : Theorem 103.83s 86.70s
% Output : CNFRefutation 103.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 111
% Syntax : Number of formulae : 198 ( 68 unt; 92 typ; 0 def)
% Number of atoms : 153 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 41 ~; 35 |; 1 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 169 (; 169 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > or > implies > equiv > and > #nlpp > not > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_or > op_implies_or > op_implies_and > op_equiv > op_and > modus_tollens > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > and_3 > and_2 > and_1 > #skF_33 > #skF_41 > #skF_52 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_31 > #skF_15 > #skF_25 > #skF_55 > #skF_38 > #skF_36 > #skF_54 > #skF_43 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_10 > #skF_16 > #skF_47 > #skF_26 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_21 > #skF_9 > #skF_32 > #skF_50 > #skF_8 > #skF_30 > #skF_42 > #skF_4 > #skF_22 > #skF_29 > #skF_28 > #skF_35 > #skF_24 > #skF_27 > #skF_23 > #skF_44 > #skF_12 > #skF_34
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $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_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $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(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(cn2,type,
cn2: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_54',type,
'#skF_54': $i ).
tff('#skF_43',type,
'#skF_43': $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(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(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
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('#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(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_2',type,
'#skF_2': $i ).
tff(modus_ponens,type,
modus_ponens: $o ).
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('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(or_3,type,
or_3: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(kn1,type,
kn1: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $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(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff(f_243,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
tff(f_244,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_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_258,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
tff(f_210,axiom,
( op_implies_or
=> ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
tff(f_259,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
tff(f_202,axiom,
( op_and
=> ! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
tff(f_249,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
tff(f_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_250,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
tff(f_129,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
tff(f_251,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
tff(f_133,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_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_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_262,negated_conjecture,
~ r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
tff(f_159,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
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_151,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_155,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_151,c_112]) ).
tff(c_27221,plain,
! [X_929,Y_930] : ( not(and(X_929,not(Y_930))) = implies(X_929,Y_930) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_27236,plain,
! [X_929,Y_930,Y_57] : ( or(and(X_929,not(Y_930)),Y_57) = implies(implies(X_929,Y_930),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_27221,c_155]) ).
tff(c_138,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_118,plain,
! [X_62,Y_63] :
( ( or(not(X_62),Y_63) = implies(X_62,Y_63) )
| ~ op_implies_or ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_149,plain,
! [X_62,Y_63] : ( or(not(X_62),Y_63) = implies(X_62,Y_63) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_118]) ).
tff(c_27233,plain,
! [X_929,Y_930,Y_63] : ( implies(and(X_929,not(Y_930)),Y_63) = or(implies(X_929,Y_930),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_27221,c_149]) ).
tff(c_140,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_114,plain,
! [X_58,Y_59] :
( ( not(or(not(X_58),not(Y_59))) = and(X_58,Y_59) )
| ~ op_and ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_27196,plain,
! [X_927,Y_928] : ( not(implies(X_927,not(Y_928))) = and(X_927,Y_928) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_149,c_114]) ).
tff(c_27208,plain,
! [X_927,Y_928,Y_57] : ( or(implies(X_927,not(Y_928)),Y_57) = implies(and(X_927,Y_928),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_27196,c_155]) ).
tff(c_27205,plain,
! [X_927,Y_928,Y_63] : ( implies(implies(X_927,not(Y_928)),Y_63) = or(and(X_927,Y_928),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_27196,c_149]) ).
tff(c_153,plain,
! [X_58,Y_59] : ( not(implies(X_58,not(Y_59))) = and(X_58,Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_149,c_114]) ).
tff(c_27677,plain,
! [X_972,Y_973] : ( not(or(X_972,not(Y_973))) = and(not(X_972),Y_973) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_27196]) ).
tff(c_27737,plain,
! [X_62,Y_973] : ( and(not(not(X_62)),Y_973) = not(implies(X_62,not(Y_973))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_27677]) ).
tff(c_27747,plain,
! [X_974,Y_975] : ( and(not(not(X_974)),Y_975) = and(X_974,Y_975) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_27737]) ).
tff(c_10638,plain,
! [X_425,Y_426] : ( implies(not(X_425),Y_426) = or(X_425,Y_426) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_151,c_112]) ).
tff(c_130,plain,
kn1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
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_170,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_70]) ).
tff(c_10645,plain,
! [X_425] : is_a_theorem(or(X_425,and(not(X_425),not(X_425)))),
inference(superposition,[status(thm),theory(equality)],[c_10638,c_170]) ).
tff(c_27754,plain,
! [X_974] : is_a_theorem(or(not(X_974),and(X_974,not(not(X_974))))),
inference(superposition,[status(thm),theory(equality)],[c_27747,c_10645]) ).
tff(c_27790,plain,
! [X_976] : is_a_theorem(implies(X_976,and(X_976,not(not(X_976))))),
inference(demodulation,[status(thm),theory(equality)],[c_149,c_27754]) ).
tff(c_27810,plain,
! [X_56] : is_a_theorem(or(X_56,and(not(X_56),not(not(not(X_56)))))),
inference(superposition,[status(thm),theory(equality)],[c_155,c_27790]) ).
tff(c_27746,plain,
! [X_62,Y_973] : ( and(not(not(X_62)),Y_973) = and(X_62,Y_973) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_27737]) ).
tff(c_132,plain,
kn2,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_74,plain,
! [P_34,Q_35] :
( is_a_theorem(implies(and(P_34,Q_35),P_34))
| ~ kn2 ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_166,plain,
! [P_34,Q_35] : is_a_theorem(implies(and(P_34,Q_35),P_34)),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_74]) ).
tff(c_27903,plain,
! [X_985,Y_986] : is_a_theorem(implies(and(X_985,Y_986),not(not(X_985)))),
inference(superposition,[status(thm),theory(equality)],[c_27747,c_166]) ).
tff(c_27912,plain,
! [X_62,Y_973] : is_a_theorem(implies(and(X_62,Y_973),not(not(not(not(X_62)))))),
inference(superposition,[status(thm),theory(equality)],[c_27746,c_27903]) ).
tff(c_134,plain,
kn3,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_78,plain,
! [P_36,Q_37,R_38] :
( is_a_theorem(implies(implies(P_36,Q_37),implies(not(and(Q_37,R_38)),not(and(R_38,P_36)))))
| ~ kn3 ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_28632,plain,
! [P_1042,Q_1043,R_1044] : is_a_theorem(implies(implies(P_1042,Q_1043),or(and(Q_1043,R_1044),not(and(R_1044,P_1042))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_155,c_78]) ).
tff(c_28652,plain,
! [Y_61,Q_1043,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_1043),or(and(Q_1043,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_28632]) ).
tff(c_31183,plain,
! [Y_1169,Q_1170,X_1171] : is_a_theorem(implies(or(Y_1169,Q_1170),or(and(Q_1170,X_1171),implies(X_1171,Y_1169)))),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_28652]) ).
tff(c_31204,plain,
! [Y_1169,X_929,Y_930] : is_a_theorem(implies(or(Y_1169,X_929),implies(implies(X_929,Y_930),implies(not(Y_930),Y_1169)))),
inference(superposition,[status(thm),theory(equality)],[c_27236,c_31183]) ).
tff(c_38376,plain,
! [Y_1424,X_1425,Y_1426] : is_a_theorem(implies(or(Y_1424,X_1425),implies(implies(X_1425,Y_1426),or(Y_1426,Y_1424)))),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_31204]) ).
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_186,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_116922,plain,
! [X_2388,Y_2389,Y_2390] :
( is_a_theorem(implies(implies(X_2388,Y_2389),or(Y_2389,Y_2390)))
| ~ is_a_theorem(or(Y_2390,X_2388)) ),
inference(resolution,[status(thm)],[c_38376,c_186]) ).
tff(c_121795,plain,
! [Y_2429,Y_2430,X_2431] :
( is_a_theorem(or(Y_2429,Y_2430))
| ~ is_a_theorem(implies(X_2431,Y_2429))
| ~ is_a_theorem(or(Y_2430,X_2431)) ),
inference(resolution,[status(thm)],[c_116922,c_186]) ).
tff(c_121921,plain,
! [X_62,Y_2430,Y_973] :
( is_a_theorem(or(not(not(not(not(X_62)))),Y_2430))
| ~ is_a_theorem(or(Y_2430,and(X_62,Y_973))) ),
inference(resolution,[status(thm)],[c_27912,c_121795]) ).
tff(c_138114,plain,
! [X_2548,Y_2549,Y_2550] :
( is_a_theorem(or(X_2548,Y_2549))
| ~ is_a_theorem(or(Y_2549,and(X_2548,Y_2550))) ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_149,c_155,c_149,c_121921]) ).
tff(c_138348,plain,
! [X_56] : is_a_theorem(or(not(X_56),X_56)),
inference(resolution,[status(thm)],[c_27810,c_138114]) ).
tff(c_138439,plain,
! [X_2551] : is_a_theorem(implies(X_2551,X_2551)),
inference(demodulation,[status(thm),theory(equality)],[c_149,c_138348]) ).
tff(c_138500,plain,
! [X_56] : is_a_theorem(or(X_56,not(X_56))),
inference(superposition,[status(thm),theory(equality)],[c_155,c_138439]) ).
tff(c_29145,plain,
! [X_1077,Y_1078,Y_1079] : ( implies(implies(X_1077,not(Y_1078)),Y_1079) = or(and(X_1077,Y_1078),Y_1079) ),
inference(superposition,[status(thm),theory(equality)],[c_27196,c_149]) ).
tff(c_38931,plain,
! [X_1453,Y_1454,Y_1455] : ( or(and(not(X_1453),Y_1454),Y_1455) = implies(or(X_1453,not(Y_1454)),Y_1455) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_29145]) ).
tff(c_33567,plain,
! [Q_1282,R_1283,P_1284] :
( is_a_theorem(or(and(Q_1282,R_1283),not(and(R_1283,P_1284))))
| ~ is_a_theorem(implies(P_1284,Q_1282)) ),
inference(resolution,[status(thm)],[c_28632,c_186]) ).
tff(c_33616,plain,
! [Q_1282,X_60,Y_61] :
( is_a_theorem(or(and(Q_1282,X_60),implies(X_60,Y_61)))
| ~ is_a_theorem(implies(not(Y_61),Q_1282)) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_33567]) ).
tff(c_33627,plain,
! [Q_1282,X_60,Y_61] :
( is_a_theorem(or(and(Q_1282,X_60),implies(X_60,Y_61)))
| ~ is_a_theorem(or(Y_61,Q_1282)) ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_33616]) ).
tff(c_398722,plain,
! [X_4411,Y_4412,Y_4413] :
( is_a_theorem(implies(or(X_4411,not(Y_4412)),implies(Y_4412,Y_4413)))
| ~ is_a_theorem(or(Y_4413,not(X_4411))) ),
inference(superposition,[status(thm),theory(equality)],[c_38931,c_33627]) ).
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_176,plain,
! [Y_6,X_5] :
( is_a_theorem(implies(or(Y_6,not(X_5)),implies(X_5,Y_6)))
| ~ modus_tollens ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_18]) ).
tff(c_27653,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_176]) ).
tff(c_16,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not('#skF_6'),not('#skF_5')),implies('#skF_5','#skF_6'))) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_177,plain,
( modus_tollens
| ~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_16]) ).
tff(c_27924,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_27653,c_177]) ).
tff(c_398808,plain,
~ is_a_theorem(or('#skF_6',not('#skF_6'))),
inference(resolution,[status(thm)],[c_398722,c_27924]) ).
tff(c_399196,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_138500,c_398808]) ).
tff(c_399208,plain,
! [Y_4415,X_4416] : is_a_theorem(implies(or(Y_4415,not(X_4416)),implies(X_4416,Y_4415))),
inference(splitRight,[status(thm)],[c_176]) ).
tff(c_399221,plain,
! [X_62,X_4416] : is_a_theorem(implies(implies(X_62,not(X_4416)),implies(X_4416,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_149,c_399208]) ).
tff(c_400826,plain,
! [X_62,X_4416] : is_a_theorem(or(and(X_62,X_4416),implies(X_4416,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_27205,c_399221]) ).
tff(c_27218,plain,
! [X_56,Y_928] : ( not(or(X_56,not(Y_928))) = and(not(X_56),Y_928) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_27196]) ).
tff(c_399224,plain,
! [Y_57,X_56] : is_a_theorem(implies(or(Y_57,not(not(X_56))),or(X_56,Y_57))),
inference(superposition,[status(thm),theory(equality)],[c_155,c_399208]) ).
tff(c_27248,plain,
! [Y_931,X_932] :
( is_a_theorem(Y_931)
| ~ is_a_theorem(implies(X_932,Y_931))
| ~ is_a_theorem(X_932) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_27637,plain,
! [Y_967,X_968] :
( is_a_theorem(Y_967)
| ~ is_a_theorem(or(X_968,Y_967))
| ~ is_a_theorem(not(X_968)) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_27248]) ).
tff(c_401964,plain,
! [Y_4562,X_4563] :
( is_a_theorem(Y_4562)
| ~ is_a_theorem(implies(X_4563,Y_4562))
| ~ is_a_theorem(not(not(X_4563))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_27637]) ).
tff(c_401982,plain,
! [X_56,Y_57] :
( is_a_theorem(or(X_56,Y_57))
| ~ is_a_theorem(not(not(or(Y_57,not(not(X_56)))))) ),
inference(resolution,[status(thm)],[c_399224,c_401964]) ).
tff(c_402039,plain,
! [X_4564,Y_4565] :
( is_a_theorem(or(X_4564,Y_4565))
| ~ is_a_theorem(or(Y_4565,X_4564)) ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_151,c_27218,c_401982]) ).
tff(c_402057,plain,
! [X_4416,X_62] : is_a_theorem(or(implies(X_4416,not(X_62)),and(X_62,X_4416))),
inference(resolution,[status(thm)],[c_400826,c_402039]) ).
tff(c_402372,plain,
! [X_4576,X_4577] : is_a_theorem(implies(and(X_4576,X_4577),and(X_4577,X_4576))),
inference(demodulation,[status(thm),theory(equality)],[c_27208,c_402057]) ).
tff(c_402508,plain,
! [X_4586,Y_4587] : is_a_theorem(or(implies(X_4586,Y_4587),and(not(Y_4587),X_4586))),
inference(superposition,[status(thm),theory(equality)],[c_27233,c_402372]) ).
tff(c_402023,plain,
! [X_56,Y_57] :
( is_a_theorem(or(X_56,Y_57))
| ~ is_a_theorem(or(Y_57,X_56)) ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_151,c_27218,c_401982]) ).
tff(c_403791,plain,
! [Y_4626,X_4627] : is_a_theorem(or(and(not(Y_4626),X_4627),implies(X_4627,Y_4626))),
inference(resolution,[status(thm)],[c_402508,c_402023]) ).
tff(c_403817,plain,
! [Y_4626,Y_930] : is_a_theorem(implies(implies(not(Y_4626),Y_930),implies(not(Y_930),Y_4626))),
inference(superposition,[status(thm),theory(equality)],[c_27236,c_403791]) ).
tff(c_403841,plain,
! [Y_4626,Y_930] : is_a_theorem(implies(or(Y_4626,Y_930),or(Y_930,Y_4626))),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_155,c_403817]) ).
tff(c_144,plain,
~ r3,
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_100,plain,
( r3
| ~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_156,plain,
~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_100]) ).
tff(c_403847,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_403841,c_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL520+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/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 : n020.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 14:12:22 EDT 2023
% 0.15/0.37 % CPUTime :
% 103.83/86.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.83/86.71
% 103.83/86.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 103.83/86.75
% 103.83/86.75 Inference rules
% 103.83/86.75 ----------------------
% 103.83/86.75 #Ref : 0
% 103.83/86.75 #Sup : 107835
% 103.83/86.75 #Fact : 0
% 103.83/86.75 #Define : 0
% 103.83/86.75 #Split : 123
% 103.83/86.75 #Chain : 0
% 103.83/86.75 #Close : 0
% 103.83/86.75
% 103.83/86.75 Ordering : KBO
% 103.83/86.75
% 103.83/86.75 Simplification rules
% 103.83/86.75 ----------------------
% 103.83/86.75 #Subsume : 29199
% 103.83/86.75 #Demod : 81105
% 103.83/86.75 #Tautology : 26445
% 103.83/86.75 #SimpNegUnit : 402
% 103.83/86.75 #BackRed : 705
% 103.83/86.75
% 103.83/86.75 #Partial instantiations: 0
% 103.83/86.75 #Strategies tried : 1
% 103.83/86.75
% 103.83/86.75 Timing (in seconds)
% 103.83/86.75 ----------------------
% 103.83/86.76 Preprocessing : 0.61
% 103.83/86.76 Parsing : 0.30
% 103.83/86.76 CNF conversion : 0.05
% 103.83/86.76 Main loop : 85.02
% 103.83/86.76 Inferencing : 6.35
% 103.83/86.76 Reduction : 45.16
% 103.83/86.76 Demodulation : 34.10
% 103.83/86.76 BG Simplification : 0.47
% 103.83/86.76 Subsumption : 26.09
% 103.83/86.76 Abstraction : 0.80
% 103.83/86.76 MUC search : 0.00
% 103.83/86.76 Cooper : 0.00
% 103.83/86.76 Total : 85.70
% 103.83/86.76 Index Insertion : 0.00
% 103.83/86.76 Index Deletion : 0.00
% 103.83/86.76 Index Matching : 0.00
% 103.83/86.76 BG Taut test : 0.00
%------------------------------------------------------------------------------