TSTP Solution File: LCL500+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL500+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 : n004.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 10:48:15 EDT 2023
% Result : Theorem 19.48s 8.69s
% Output : CNFRefutation 19.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 122
% Syntax : Number of formulae : 264 ( 111 unt; 92 typ; 0 def)
% Number of atoms : 243 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 133 ( 62 ~; 51 |; 1 &)
% ( 12 <=>; 7 =>; 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 : 245 (; 245 !; 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_263,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_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_243,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',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_262,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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_261,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_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_244,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',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_250,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
tff(f_155,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
tff(f_253,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
tff(f_164,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_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_249,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
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_251,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',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(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_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_257,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.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_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_254,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
tff(f_168,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
tff(f_88,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
tff(f_265,negated_conjecture,
~ kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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(c_146,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_263]) ).
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_151,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_146,c_120]) ).
tff(c_122,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_243]) ).
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_153,plain,
! [X_62,Y_63] : ( or(not(X_62),Y_63) = implies(X_62,Y_63) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_144,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_262]) ).
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_155,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
tff(c_5557,plain,
! [X_434,Y_435] : ( not(and(X_434,not(Y_435))) = implies(X_434,Y_435) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
tff(c_5581,plain,
! [X_434,X_60,Y_61] : ( implies(X_434,and(X_60,not(Y_61))) = not(and(X_434,implies(X_60,Y_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_5557]) ).
tff(c_142,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_261]) ).
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_159,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_5717,plain,
! [X_448,Y_449] : ( and(implies(X_448,Y_449),implies(Y_449,X_448)) = equiv(X_448,Y_449) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_120]) ).
tff(c_5740,plain,
! [X_56,Y_57] : ( and(or(X_56,Y_57),implies(Y_57,not(X_56))) = equiv(not(X_56),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_5717]) ).
tff(c_124,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_244]) ).
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_157,plain,
! [X_58,Y_59] : ( not(implies(X_58,not(Y_59))) = and(X_58,Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_5526,plain,
! [X_432,Y_433] : ( not(implies(X_432,not(Y_433))) = and(X_432,Y_433) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_12432,plain,
! [X_758,X_759,Y_760] : ( and(X_758,implies(X_759,not(Y_760))) = not(implies(X_758,and(X_759,Y_760))) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_5526]) ).
tff(c_25006,plain,
! [X_1280,Y_1281] : ( not(implies(or(X_1280,Y_1281),and(Y_1281,X_1280))) = equiv(not(X_1280),Y_1281) ),
inference(superposition,[status(thm),theory(equality)],[c_5740,c_12432]) ).
tff(c_25700,plain,
! [Y_61,X_60] : ( not(not(and(or(not(Y_61),X_60),implies(X_60,Y_61)))) = equiv(not(not(Y_61)),X_60) ),
inference(superposition,[status(thm),theory(equality)],[c_5581,c_25006]) ).
tff(c_25749,plain,
! [Y_1282,X_1283] : ( equiv(not(not(Y_1282)),X_1283) = not(not(equiv(Y_1282,X_1283))) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_153,c_25700]) ).
tff(c_4971,plain,
! [X_382,Y_383] : ( implies(not(X_382),Y_383) = or(X_382,Y_383) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_132,plain,
r2,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_98,plain,
! [Q_47,P_46] :
( is_a_theorem(implies(Q_47,or(P_46,Q_47)))
| ~ r2 ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_173,plain,
! [Q_47,P_46] : is_a_theorem(implies(Q_47,or(P_46,Q_47))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_98]) ).
tff(c_4982,plain,
! [X_382,P_46] : is_a_theorem(or(X_382,or(P_46,not(X_382)))),
inference(superposition,[status(thm),theory(equality)],[c_4971,c_173]) ).
tff(c_136,plain,
r4,
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_106,plain,
! [P_50,Q_51,R_52] :
( is_a_theorem(implies(or(P_50,or(Q_51,R_52)),or(Q_51,or(P_50,R_52))))
| ~ r4 ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_6646,plain,
! [P_507,Q_508,R_509] : is_a_theorem(implies(or(P_507,or(Q_508,R_509)),or(Q_508,or(P_507,R_509)))),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_106]) ).
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_201,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_10763,plain,
! [Q_690,P_691,R_692] :
( is_a_theorem(or(Q_690,or(P_691,R_692)))
| ~ is_a_theorem(or(P_691,or(Q_690,R_692))) ),
inference(resolution,[status(thm)],[c_6646,c_201]) ).
tff(c_10807,plain,
! [P_693,X_694] : is_a_theorem(or(P_693,or(X_694,not(X_694)))),
inference(resolution,[status(thm)],[c_4982,c_10763]) ).
tff(c_130,plain,
r1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
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_177,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_94]) ).
tff(c_5051,plain,
! [Y_392,X_393] :
( is_a_theorem(Y_392)
| ~ is_a_theorem(implies(X_393,Y_392))
| ~ is_a_theorem(X_393) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_5074,plain,
! [P_45] :
( is_a_theorem(P_45)
| ~ is_a_theorem(or(P_45,P_45)) ),
inference(resolution,[status(thm)],[c_177,c_5051]) ).
tff(c_10872,plain,
! [X_695] : is_a_theorem(or(X_695,not(X_695))),
inference(resolution,[status(thm)],[c_10807,c_5074]) ).
tff(c_134,plain,
r3,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_102,plain,
! [P_48,Q_49] :
( is_a_theorem(implies(or(P_48,Q_49),or(Q_49,P_48)))
| ~ r3 ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_5590,plain,
! [P_436,Q_437] : is_a_theorem(implies(or(P_436,Q_437),or(Q_437,P_436))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_5599,plain,
! [Y_63,X_62] : is_a_theorem(implies(or(Y_63,not(X_62)),implies(X_62,Y_63))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_5590]) ).
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_191,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_159,c_18]) ).
tff(c_5766,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_191]) ).
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_192,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_159,c_16]) ).
tff(c_5834,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_5766,c_192]) ).
tff(c_6326,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5599,c_5834]) ).
tff(c_6338,plain,
! [Y_486,X_487] : is_a_theorem(implies(or(Y_486,not(X_487)),implies(X_487,Y_486))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_6355,plain,
! [X_487,Y_486] :
( is_a_theorem(implies(X_487,Y_486))
| ~ is_a_theorem(or(Y_486,not(X_487))) ),
inference(resolution,[status(thm)],[c_6338,c_201]) ).
tff(c_10902,plain,
! [X_695] : is_a_theorem(implies(X_695,X_695)),
inference(resolution,[status(thm)],[c_10872,c_6355]) ).
tff(c_297,plain,
! [X_85,Y_86] : ( not(implies(X_85,not(Y_86))) = and(X_85,Y_86) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_312,plain,
! [X_85,Y_86,Y_63] : ( implies(implies(X_85,not(Y_86)),Y_63) = or(and(X_85,Y_86),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_297,c_153]) ).
tff(c_228,plain,
! [X_73,Y_74] : ( or(not(X_73),Y_74) = implies(X_73,Y_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_238,plain,
! [X_73] : is_a_theorem(implies(implies(X_73,not(X_73)),not(X_73))),
inference(superposition,[status(thm),theory(equality)],[c_228,c_177]) ).
tff(c_2352,plain,
! [X_218] : is_a_theorem(or(and(X_218,X_218),not(X_218))),
inference(demodulation,[status(thm),theory(equality)],[c_312,c_238]) ).
tff(c_375,plain,
! [P_90,Q_91] : is_a_theorem(implies(or(P_90,Q_91),or(Q_91,P_90))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_384,plain,
! [Y_63,X_62] : is_a_theorem(implies(or(Y_63,not(X_62)),implies(X_62,Y_63))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_375]) ).
tff(c_555,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(splitLeft,[status(thm)],[c_192]) ).
tff(c_915,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_555]) ).
tff(c_916,plain,
modus_tollens,
inference(splitRight,[status(thm)],[c_192]) ).
tff(c_941,plain,
! [Y_130,X_131] : is_a_theorem(implies(or(Y_130,not(X_131)),implies(X_131,Y_130))),
inference(demodulation,[status(thm),theory(equality)],[c_916,c_191]) ).
tff(c_958,plain,
! [X_131,Y_130] :
( is_a_theorem(implies(X_131,Y_130))
| ~ is_a_theorem(or(Y_130,not(X_131))) ),
inference(resolution,[status(thm)],[c_941,c_201]) ).
tff(c_2378,plain,
! [X_218] : is_a_theorem(implies(X_218,and(X_218,X_218))),
inference(resolution,[status(thm)],[c_2352,c_958]) ).
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_206,plain,
~ kn1,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_210,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(negUnitSimplification,[status(thm)],[c_206,c_68]) ).
tff(c_2384,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2378,c_210]) ).
tff(c_2385,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_5072,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_2385,c_5051]) ).
tff(c_5724,plain,
! [Y_449] :
( is_a_theorem(equiv(Y_449,Y_449))
| ~ is_a_theorem(implies(Y_449,Y_449)) ),
inference(superposition,[status(thm),theory(equality)],[c_5717,c_5072]) ).
tff(c_10911,plain,
! [Y_449] : is_a_theorem(equiv(Y_449,Y_449)),
inference(demodulation,[status(thm),theory(equality)],[c_10902,c_5724]) ).
tff(c_25895,plain,
! [Y_1284] : is_a_theorem(not(not(equiv(Y_1284,not(not(Y_1284)))))),
inference(superposition,[status(thm),theory(equality)],[c_25749,c_10911]) ).
tff(c_5042,plain,
! [X_390,P_391] : is_a_theorem(or(X_390,or(P_391,not(X_390)))),
inference(superposition,[status(thm),theory(equality)],[c_4971,c_173]) ).
tff(c_6529,plain,
! [X_498,P_499] : is_a_theorem(implies(X_498,or(P_499,not(not(X_498))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_5042]) ).
tff(c_7358,plain,
! [X_543,P_544] : is_a_theorem(or(X_543,or(P_544,not(not(not(X_543)))))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_6529]) ).
tff(c_7428,plain,
! [X_547,X_548] : is_a_theorem(or(X_547,implies(X_548,not(not(not(X_547)))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_7358]) ).
tff(c_5600,plain,
! [Q_437,P_436] :
( is_a_theorem(or(Q_437,P_436))
| ~ is_a_theorem(or(P_436,Q_437)) ),
inference(resolution,[status(thm)],[c_5590,c_201]) ).
tff(c_7483,plain,
! [X_551,X_552] : is_a_theorem(or(implies(X_551,not(not(not(X_552)))),X_552)),
inference(resolution,[status(thm)],[c_7428,c_5600]) ).
tff(c_5057,plain,
! [Y_57,X_56] :
( is_a_theorem(Y_57)
| ~ is_a_theorem(or(X_56,Y_57))
| ~ is_a_theorem(not(X_56)) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_5051]) ).
tff(c_7490,plain,
! [X_552,X_551] :
( is_a_theorem(X_552)
| ~ is_a_theorem(not(implies(X_551,not(not(not(X_552)))))) ),
inference(resolution,[status(thm)],[c_7483,c_5057]) ).
tff(c_7512,plain,
! [X_553,X_554] :
( is_a_theorem(X_553)
| ~ is_a_theorem(and(X_554,not(not(X_553)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_157,c_7490]) ).
tff(c_7534,plain,
! [X_553] :
( is_a_theorem(X_553)
| ~ is_a_theorem(not(not(X_553))) ),
inference(resolution,[status(thm)],[c_5072,c_7512]) ).
tff(c_26107,plain,
! [Y_1286] : is_a_theorem(equiv(Y_1286,not(not(Y_1286)))),
inference(resolution,[status(thm)],[c_25895,c_7534]) ).
tff(c_140,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_257]) ).
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_196,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_10]) ).
tff(c_26300,plain,
! [Y_1287] : ( not(not(Y_1287)) = Y_1287 ),
inference(resolution,[status(thm)],[c_26107,c_196]) ).
tff(c_26728,plain,
! [X_60,Y_1287] : ( implies(X_60,not(Y_1287)) = not(and(X_60,Y_1287)) ),
inference(superposition,[status(thm),theory(equality)],[c_26300,c_155]) ).
tff(c_5541,plain,
! [X_432,Y_433,Y_63] : ( implies(implies(X_432,not(Y_433)),Y_63) = or(and(X_432,Y_433),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_5526,c_153]) ).
tff(c_6351,plain,
! [X_62,X_487] : is_a_theorem(implies(implies(X_62,not(X_487)),implies(X_487,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_6338]) ).
tff(c_8591,plain,
! [X_62,X_487] : is_a_theorem(or(and(X_62,X_487),implies(X_487,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_5541,c_6351]) ).
tff(c_27069,plain,
! [X_62,X_487] : is_a_theorem(or(and(X_62,X_487),not(and(X_487,X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_26728,c_8591]) ).
tff(c_7831,plain,
! [X_571,Y_572,Y_573] : ( or(implies(X_571,not(Y_572)),Y_573) = implies(and(X_571,Y_572),Y_573) ),
inference(superposition,[status(thm),theory(equality)],[c_5526,c_159]) ).
tff(c_7549,plain,
! [X_556,Y_557,Y_558] : ( implies(and(X_556,not(Y_557)),Y_558) = or(implies(X_556,Y_557),Y_558) ),
inference(superposition,[status(thm),theory(equality)],[c_5557,c_153]) ).
tff(c_2489,plain,
! [X_235,Y_236] : ( not(implies(X_235,not(Y_236))) = and(X_235,Y_236) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_2507,plain,
! [X_235,Y_236,Y_57] : ( or(implies(X_235,not(Y_236)),Y_57) = implies(and(X_235,Y_236),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_2489,c_159]) ).
tff(c_2396,plain,
! [X_220,Y_221] : ( implies(not(X_220),Y_221) = or(X_220,Y_221) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_2407,plain,
! [X_220,P_46] : is_a_theorem(or(X_220,or(P_46,not(X_220)))),
inference(superposition,[status(thm),theory(equality)],[c_2396,c_173]) ).
tff(c_2601,plain,
! [P_242,Q_243] : is_a_theorem(implies(or(P_242,Q_243),or(Q_243,P_242))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_2646,plain,
! [Q_245,P_246] :
( is_a_theorem(or(Q_245,P_246))
| ~ is_a_theorem(or(P_246,Q_245)) ),
inference(resolution,[status(thm)],[c_2601,c_201]) ).
tff(c_2696,plain,
! [P_249,X_250] : is_a_theorem(or(or(P_249,not(X_250)),X_250)),
inference(resolution,[status(thm)],[c_2407,c_2646]) ).
tff(c_2708,plain,
! [X_62,X_250] : is_a_theorem(or(implies(X_62,not(X_250)),X_250)),
inference(superposition,[status(thm),theory(equality)],[c_153,c_2696]) ).
tff(c_4776,plain,
! [X_62,X_250] : is_a_theorem(implies(and(X_62,X_250),X_250)),
inference(demodulation,[status(thm),theory(equality)],[c_2507,c_2708]) ).
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_2387,plain,
~ and_2,
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_36,plain,
( and_2
| ~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_2393,plain,
~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')),
inference(negUnitSimplification,[status(thm)],[c_2387,c_36]) ).
tff(c_4960,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4776,c_2393]) ).
tff(c_4961,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_7657,plain,
! [X_556,Y_557] : is_a_theorem(or(implies(X_556,Y_557),not(Y_557))),
inference(superposition,[status(thm),theory(equality)],[c_7549,c_4961]) ).
tff(c_7844,plain,
! [X_571,Y_572] : is_a_theorem(implies(and(X_571,Y_572),not(not(Y_572)))),
inference(superposition,[status(thm),theory(equality)],[c_7831,c_7657]) ).
tff(c_6980,plain,
! [X_528,Y_529] :
( is_a_theorem(implies(X_528,Y_529))
| ~ is_a_theorem(or(Y_529,not(X_528))) ),
inference(resolution,[status(thm)],[c_6338,c_201]) ).
tff(c_10183,plain,
! [X_667,X_668] :
( is_a_theorem(implies(X_667,not(X_668)))
| ~ is_a_theorem(implies(X_668,not(X_667))) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_6980]) ).
tff(c_10190,plain,
! [Y_572,X_571] : is_a_theorem(implies(not(Y_572),not(and(X_571,Y_572)))),
inference(resolution,[status(thm)],[c_7844,c_10183]) ).
tff(c_10224,plain,
! [Y_572,X_571] : is_a_theorem(or(Y_572,not(and(X_571,Y_572)))),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_10190]) ).
tff(c_138,plain,
r5,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_110,plain,
! [Q_54,R_55,P_53] :
( is_a_theorem(implies(implies(Q_54,R_55),implies(or(P_53,Q_54),or(P_53,R_55))))
| ~ r5 ),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_6548,plain,
! [Q_500,R_501,P_502] : is_a_theorem(implies(implies(Q_500,R_501),implies(or(P_502,Q_500),or(P_502,R_501)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_9465,plain,
! [P_635,Q_636,R_637] :
( is_a_theorem(implies(or(P_635,Q_636),or(P_635,R_637)))
| ~ is_a_theorem(implies(Q_636,R_637)) ),
inference(resolution,[status(thm)],[c_6548,c_201]) ).
tff(c_33244,plain,
! [P_1503,R_1504,Q_1505] :
( is_a_theorem(or(P_1503,R_1504))
| ~ is_a_theorem(or(P_1503,Q_1505))
| ~ is_a_theorem(implies(Q_1505,R_1504)) ),
inference(resolution,[status(thm)],[c_9465,c_201]) ).
tff(c_33372,plain,
! [Y_572,R_1504,X_571] :
( is_a_theorem(or(Y_572,R_1504))
| ~ is_a_theorem(implies(not(and(X_571,Y_572)),R_1504)) ),
inference(resolution,[status(thm)],[c_10224,c_33244]) ).
tff(c_41018,plain,
! [Y_1738,R_1739,X_1740] :
( is_a_theorem(or(Y_1738,R_1739))
| ~ is_a_theorem(or(and(X_1740,Y_1738),R_1739)) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_33372]) ).
tff(c_41305,plain,
! [X_1741,X_1742] : is_a_theorem(or(X_1741,not(and(X_1741,X_1742)))),
inference(resolution,[status(thm)],[c_27069,c_41018]) ).
tff(c_41368,plain,
! [X_1741,X_1742] : is_a_theorem(implies(and(X_1741,X_1742),X_1741)),
inference(resolution,[status(thm)],[c_41305,c_6355]) ).
tff(c_32,plain,
( and_1
| ~ is_a_theorem(implies(and('#skF_14','#skF_15'),'#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_205,plain,
~ is_a_theorem(implies(and('#skF_14','#skF_15'),'#skF_14')),
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_41383,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41368,c_205]) ).
tff(c_41384,plain,
and_1,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_34,plain,
! [X_14,Y_15] :
( is_a_theorem(implies(and(X_14,Y_15),X_14))
| ~ and_1 ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_41387,plain,
! [X_14,Y_15] : is_a_theorem(implies(and(X_14,Y_15),X_14)),
inference(demodulation,[status(thm),theory(equality)],[c_41384,c_34]) ).
tff(c_148,plain,
~ kn2,
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_72,plain,
( kn2
| ~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_187,plain,
~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')),
inference(negUnitSimplification,[status(thm)],[c_148,c_72]) ).
tff(c_41390,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41387,c_187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 13:59:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 19.48/8.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.56/8.71
% 19.56/8.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.56/8.75
% 19.56/8.75 Inference rules
% 19.56/8.75 ----------------------
% 19.56/8.75 #Ref : 0
% 19.56/8.75 #Sup : 9750
% 19.56/8.75 #Fact : 0
% 19.56/8.75 #Define : 0
% 19.56/8.75 #Split : 88
% 19.56/8.75 #Chain : 0
% 19.56/8.75 #Close : 0
% 19.56/8.75
% 19.56/8.75 Ordering : KBO
% 19.56/8.75
% 19.56/8.75 Simplification rules
% 19.56/8.75 ----------------------
% 19.56/8.75 #Subsume : 2251
% 19.56/8.75 #Demod : 7178
% 19.56/8.75 #Tautology : 2527
% 19.56/8.75 #SimpNegUnit : 34
% 19.56/8.75 #BackRed : 209
% 19.56/8.75
% 19.56/8.75 #Partial instantiations: 0
% 19.56/8.75 #Strategies tried : 1
% 19.56/8.75
% 19.56/8.75 Timing (in seconds)
% 19.56/8.76 ----------------------
% 19.56/8.76 Preprocessing : 0.66
% 19.56/8.76 Parsing : 0.33
% 19.56/8.76 CNF conversion : 0.05
% 19.56/8.76 Main loop : 7.03
% 19.56/8.76 Inferencing : 1.52
% 19.56/8.76 Reduction : 3.27
% 19.56/8.76 Demodulation : 2.36
% 19.56/8.76 BG Simplification : 0.08
% 19.56/8.76 Subsumption : 1.69
% 19.56/8.76 Abstraction : 0.10
% 19.56/8.76 MUC search : 0.00
% 19.56/8.76 Cooper : 0.00
% 19.56/8.76 Total : 7.77
% 19.56/8.76 Index Insertion : 0.00
% 19.56/8.76 Index Deletion : 0.00
% 19.56/8.76 Index Matching : 0.00
% 19.56/8.76 BG Taut test : 0.00
%------------------------------------------------------------------------------