TSTP Solution File: LCL490+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL490+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 : n021.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 10:48:13 EDT 2023
% Result : Theorem 20.25s 10.02s
% Output : CNFRefutation 20.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 125
% Syntax : Number of formulae : 309 ( 145 unt; 92 typ; 0 def)
% Number of atoms : 299 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 160 ( 78 ~; 59 |; 1 &)
% ( 15 <=>; 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 : 287 (; 287 !; 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_261,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_262,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_243,axiom,
op_implies_or,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
tff(f_244,axiom,
op_and,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
tff(f_263,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
tff(f_214,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_250,axiom,
r2,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
tff(f_253,axiom,
r4,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',r4) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_249,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
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_251,axiom,
r3,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
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_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_257,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_254,axiom,
r5,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',r5) ).
tff(f_129,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
tff(f_88,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
tff(f_142,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn2) ).
tff(f_265,negated_conjecture,
~ or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
tff(f_100,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
tff(c_142,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_261]) ).
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_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_49162,plain,
! [X_2269,Y_2270] : ( not(and(X_2269,not(Y_2270))) = implies(X_2269,Y_2270) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
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_51013,plain,
! [X_2401,Y_2402,Y_2403] : ( implies(and(X_2401,not(Y_2402)),Y_2403) = or(implies(X_2401,Y_2402),Y_2403) ),
inference(superposition,[status(thm),theory(equality)],[c_49162,c_153]) ).
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_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_8061,plain,
! [X_619,Y_620] : ( not(and(X_619,not(Y_620))) = implies(X_619,Y_620) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
tff(c_8085,plain,
! [X_619,X_60,Y_61] : ( implies(X_619,and(X_60,not(Y_61))) = not(and(X_619,implies(X_60,Y_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_8061]) ).
tff(c_8018,plain,
! [X_615,Y_616] : ( not(implies(X_615,not(Y_616))) = and(X_615,Y_616) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_14742,plain,
! [X_946,X_947,Y_948] : ( and(X_946,implies(X_947,not(Y_948))) = not(implies(X_946,and(X_947,Y_948))) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_8018]) ).
tff(c_14857,plain,
! [Y_948,X_947] : ( not(implies(implies(not(Y_948),X_947),and(X_947,Y_948))) = equiv(not(Y_948),X_947) ),
inference(superposition,[status(thm),theory(equality)],[c_14742,c_151]) ).
tff(c_29221,plain,
! [Y_1535,X_1536] : ( not(implies(or(Y_1535,X_1536),and(X_1536,Y_1535))) = equiv(not(Y_1535),X_1536) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_14857]) ).
tff(c_29949,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_8085,c_29221]) ).
tff(c_30010,plain,
! [Y_1537,X_1538] : ( equiv(not(not(Y_1537)),X_1538) = not(not(equiv(Y_1537,X_1538))) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_153,c_29949]) ).
tff(c_7851,plain,
! [X_593,Y_594] : ( implies(not(X_593),Y_594) = or(X_593,Y_594) ),
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_7862,plain,
! [X_593,P_46] : is_a_theorem(or(X_593,or(P_46,not(X_593)))),
inference(superposition,[status(thm),theory(equality)],[c_7851,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_9730,plain,
! [P_720,Q_721,R_722] : is_a_theorem(implies(or(P_720,or(Q_721,R_722)),or(Q_721,or(P_720,R_722)))),
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_13095,plain,
! [Q_876,P_877,R_878] :
( is_a_theorem(or(Q_876,or(P_877,R_878)))
| ~ is_a_theorem(or(P_877,or(Q_876,R_878))) ),
inference(resolution,[status(thm)],[c_9730,c_201]) ).
tff(c_13139,plain,
! [P_879,X_880] : is_a_theorem(or(P_879,or(X_880,not(X_880)))),
inference(resolution,[status(thm)],[c_7862,c_13095]) ).
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_7942,plain,
! [Y_605,X_606] :
( is_a_theorem(Y_605)
| ~ is_a_theorem(implies(X_606,Y_605))
| ~ is_a_theorem(X_606) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_7965,plain,
! [P_45] :
( is_a_theorem(P_45)
| ~ is_a_theorem(or(P_45,P_45)) ),
inference(resolution,[status(thm)],[c_177,c_7942]) ).
tff(c_13254,plain,
! [X_883] : is_a_theorem(or(X_883,not(X_883))),
inference(resolution,[status(thm)],[c_13139,c_7965]) ).
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_8050,plain,
! [P_617,Q_618] : is_a_theorem(implies(or(P_617,Q_618),or(Q_618,P_617))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_8059,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_8050]) ).
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_8518,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_8521,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_8518,c_192]) ).
tff(c_9354,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8059,c_8521]) ).
tff(c_9358,plain,
! [Y_696,X_697] : is_a_theorem(implies(or(Y_696,not(X_697)),implies(X_697,Y_696))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_9375,plain,
! [X_697,Y_696] :
( is_a_theorem(implies(X_697,Y_696))
| ~ is_a_theorem(or(Y_696,not(X_697))) ),
inference(resolution,[status(thm)],[c_9358,c_201]) ).
tff(c_13285,plain,
! [X_883] : is_a_theorem(implies(X_883,X_883)),
inference(resolution,[status(thm)],[c_13254,c_9375]) ).
tff(c_9426,plain,
! [X_701,Y_702] : ( and(implies(X_701,Y_702),implies(Y_702,X_701)) = equiv(X_701,Y_702) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_120]) ).
tff(c_5033,plain,
! [X_399,Y_400] : ( or(not(X_399),Y_400) = implies(X_399,Y_400) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_5043,plain,
! [X_399] : is_a_theorem(implies(implies(X_399,not(X_399)),not(X_399))),
inference(superposition,[status(thm),theory(equality)],[c_5033,c_177]) ).
tff(c_5486,plain,
! [P_439,Q_440] : is_a_theorem(implies(or(P_439,Q_440),or(Q_440,P_439))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_5495,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_5486]) ).
tff(c_5711,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_5737,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_5711,c_192]) ).
tff(c_6231,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5495,c_5737]) ).
tff(c_6234,plain,
! [Y_487,X_488] : is_a_theorem(implies(or(Y_487,not(X_488)),implies(X_488,Y_487))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_7181,plain,
! [X_553,X_554] : is_a_theorem(implies(implies(X_553,not(X_554)),implies(X_554,not(X_553)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_6234]) ).
tff(c_7791,plain,
! [X_588,X_589] :
( is_a_theorem(implies(X_588,not(X_589)))
| ~ is_a_theorem(implies(X_589,not(X_588))) ),
inference(resolution,[status(thm)],[c_7181,c_201]) ).
tff(c_7800,plain,
! [X_399] : is_a_theorem(implies(X_399,not(implies(X_399,not(X_399))))),
inference(resolution,[status(thm)],[c_5043,c_7791]) ).
tff(c_7827,plain,
! [X_399] : is_a_theorem(implies(X_399,and(X_399,X_399))),
inference(demodulation,[status(thm),theory(equality)],[c_157,c_7800]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_4977,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_7838,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7827,c_4977]) ).
tff(c_7839,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_7846,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_7839,c_70]) ).
tff(c_7962,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_7846,c_7942]) ).
tff(c_9436,plain,
! [Y_702] :
( is_a_theorem(equiv(Y_702,Y_702))
| ~ is_a_theorem(implies(Y_702,Y_702)) ),
inference(superposition,[status(thm),theory(equality)],[c_9426,c_7962]) ).
tff(c_13293,plain,
! [Y_702] : is_a_theorem(equiv(Y_702,Y_702)),
inference(demodulation,[status(thm),theory(equality)],[c_13285,c_9436]) ).
tff(c_30173,plain,
! [Y_1539] : is_a_theorem(not(not(equiv(Y_1539,not(not(Y_1539)))))),
inference(superposition,[status(thm),theory(equality)],[c_30010,c_13293]) ).
tff(c_7871,plain,
! [X_595,Y_596] : ( or(not(X_595),Y_596) = implies(X_595,Y_596) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_7877,plain,
! [Y_596,X_595] : is_a_theorem(implies(Y_596,implies(X_595,Y_596))),
inference(superposition,[status(thm),theory(equality)],[c_7871,c_173]) ).
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_7868,plain,
~ implies_1,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_20,plain,
( implies_1
| ~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_7869,plain,
~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))),
inference(negUnitSimplification,[status(thm)],[c_7868,c_20]) ).
tff(c_7889,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7877,c_7869]) ).
tff(c_7892,plain,
! [X_597,Y_598] : is_a_theorem(implies(X_597,implies(Y_598,X_597))),
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_7931,plain,
! [X_603,Y_604] : is_a_theorem(or(X_603,implies(Y_604,not(X_603)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_7892]) ).
tff(c_9555,plain,
! [X_709,Y_710] : is_a_theorem(implies(X_709,implies(Y_710,not(not(X_709))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_7931]) ).
tff(c_10388,plain,
! [X_753,Y_754] : is_a_theorem(or(X_753,implies(Y_754,not(not(not(X_753)))))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_9555]) ).
tff(c_8060,plain,
! [Q_618,P_617] :
( is_a_theorem(or(Q_618,P_617))
| ~ is_a_theorem(or(P_617,Q_618)) ),
inference(resolution,[status(thm)],[c_8050,c_201]) ).
tff(c_10511,plain,
! [Y_760,X_761] : is_a_theorem(or(implies(Y_760,not(not(not(X_761)))),X_761)),
inference(resolution,[status(thm)],[c_10388,c_8060]) ).
tff(c_7948,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_7942]) ).
tff(c_10514,plain,
! [X_761,Y_760] :
( is_a_theorem(X_761)
| ~ is_a_theorem(not(implies(Y_760,not(not(not(X_761)))))) ),
inference(resolution,[status(thm)],[c_10511,c_7948]) ).
tff(c_10540,plain,
! [X_762,Y_763] :
( is_a_theorem(X_762)
| ~ is_a_theorem(and(Y_763,not(not(X_762)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_157,c_10514]) ).
tff(c_10562,plain,
! [X_762] :
( is_a_theorem(X_762)
| ~ is_a_theorem(not(not(X_762))) ),
inference(resolution,[status(thm)],[c_7962,c_10540]) ).
tff(c_30235,plain,
! [Y_1542] : is_a_theorem(equiv(Y_1542,not(not(Y_1542)))),
inference(resolution,[status(thm)],[c_30173,c_10562]) ).
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_30439,plain,
! [Y_1543] : ( not(not(Y_1543)) = Y_1543 ),
inference(resolution,[status(thm)],[c_30235,c_196]) ).
tff(c_30924,plain,
! [X_58,Y_59] : ( implies(X_58,not(Y_59)) = not(and(X_58,Y_59)) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_30439]) ).
tff(c_8033,plain,
! [X_615,Y_616,Y_63] : ( implies(implies(X_615,not(Y_616)),Y_63) = or(and(X_615,Y_616),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_8018,c_153]) ).
tff(c_9371,plain,
! [X_62,X_697] : is_a_theorem(implies(implies(X_62,not(X_697)),implies(X_697,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_9358]) ).
tff(c_11069,plain,
! [X_62,X_697] : is_a_theorem(or(and(X_62,X_697),implies(X_697,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_8033,c_9371]) ).
tff(c_31610,plain,
! [X_62,X_697] : is_a_theorem(or(and(X_62,X_697),not(and(X_697,X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_30924,c_11069]) ).
tff(c_11788,plain,
! [X_819,Y_820,Y_821] : ( or(implies(X_819,not(Y_820)),Y_821) = implies(and(X_819,Y_820),Y_821) ),
inference(superposition,[status(thm),theory(equality)],[c_8018,c_159]) ).
tff(c_10798,plain,
! [X_780,Y_781,Y_782] : ( implies(and(X_780,not(Y_781)),Y_782) = or(implies(X_780,Y_781),Y_782) ),
inference(superposition,[status(thm),theory(equality)],[c_8061,c_153]) ).
tff(c_2857,plain,
! [X_265,Y_266] : ( not(implies(X_265,not(Y_266))) = and(X_265,Y_266) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_2878,plain,
! [X_265,Y_266,Y_57] : ( or(implies(X_265,not(Y_266)),Y_57) = implies(and(X_265,Y_266),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_2857,c_159]) ).
tff(c_2683,plain,
! [X_245,Y_246] : ( or(not(X_245),Y_246) = implies(X_245,Y_246) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_2689,plain,
! [Y_246,X_245] : is_a_theorem(implies(Y_246,implies(X_245,Y_246))),
inference(superposition,[status(thm),theory(equality)],[c_2683,c_173]) ).
tff(c_2680,plain,
~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_2701,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2689,c_2680]) ).
tff(c_2702,plain,
implies_1,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_2704,plain,
~ implies_1,
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_2706,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2702,c_2704]) ).
tff(c_2711,plain,
! [X_247,Y_248] : is_a_theorem(implies(X_247,implies(Y_248,X_247))),
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_2718,plain,
! [X_56,Y_248] : is_a_theorem(or(X_56,implies(Y_248,not(X_56)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_2711]) ).
tff(c_2895,plain,
! [P_267,Q_268] : is_a_theorem(implies(or(P_267,Q_268),or(Q_268,P_267))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_2952,plain,
! [Q_271,P_272] :
( is_a_theorem(or(Q_271,P_272))
| ~ is_a_theorem(or(P_272,Q_271)) ),
inference(resolution,[status(thm)],[c_2895,c_201]) ).
tff(c_2966,plain,
! [Y_248,X_56] : is_a_theorem(or(implies(Y_248,not(X_56)),X_56)),
inference(resolution,[status(thm)],[c_2718,c_2952]) ).
tff(c_4795,plain,
! [Y_248,X_56] : is_a_theorem(implies(and(Y_248,X_56),X_56)),
inference(demodulation,[status(thm),theory(equality)],[c_2878,c_2966]) ).
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_208,plain,
~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')),
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_4974,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4795,c_208]) ).
tff(c_4975,plain,
and_2,
inference(splitRight,[status(thm)],[c_36]) ).
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_7842,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_4975,c_38]) ).
tff(c_10922,plain,
! [X_780,Y_781] : is_a_theorem(or(implies(X_780,Y_781),not(Y_781))),
inference(superposition,[status(thm),theory(equality)],[c_10798,c_7842]) ).
tff(c_11812,plain,
! [X_819,Y_820] : is_a_theorem(implies(and(X_819,Y_820),not(not(Y_820)))),
inference(superposition,[status(thm),theory(equality)],[c_11788,c_10922]) ).
tff(c_10352,plain,
! [X_751,X_752] : is_a_theorem(implies(implies(X_751,not(X_752)),implies(X_752,not(X_751)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_9358]) ).
tff(c_12877,plain,
! [X_868,X_869] :
( is_a_theorem(implies(X_868,not(X_869)))
| ~ is_a_theorem(implies(X_869,not(X_868))) ),
inference(resolution,[status(thm)],[c_10352,c_201]) ).
tff(c_12879,plain,
! [Y_820,X_819] : is_a_theorem(implies(not(Y_820),not(and(X_819,Y_820)))),
inference(resolution,[status(thm)],[c_11812,c_12877]) ).
tff(c_12915,plain,
! [Y_820,X_819] : is_a_theorem(or(Y_820,not(and(X_819,Y_820)))),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_12879]) ).
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_9689,plain,
! [Q_717,R_718,P_719] : is_a_theorem(implies(implies(Q_717,R_718),implies(or(P_719,Q_717),or(P_719,R_718)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_13377,plain,
! [P_887,Q_888,R_889] :
( is_a_theorem(implies(or(P_887,Q_888),or(P_887,R_889)))
| ~ is_a_theorem(implies(Q_888,R_889)) ),
inference(resolution,[status(thm)],[c_9689,c_201]) ).
tff(c_37410,plain,
! [P_1727,R_1728,Q_1729] :
( is_a_theorem(or(P_1727,R_1728))
| ~ is_a_theorem(or(P_1727,Q_1729))
| ~ is_a_theorem(implies(Q_1729,R_1728)) ),
inference(resolution,[status(thm)],[c_13377,c_201]) ).
tff(c_37536,plain,
! [Y_820,R_1728,X_819] :
( is_a_theorem(or(Y_820,R_1728))
| ~ is_a_theorem(implies(not(and(X_819,Y_820)),R_1728)) ),
inference(resolution,[status(thm)],[c_12915,c_37410]) ).
tff(c_45410,plain,
! [Y_2003,R_2004,X_2005] :
( is_a_theorem(or(Y_2003,R_2004))
| ~ is_a_theorem(or(and(X_2005,Y_2003),R_2004)) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_37536]) ).
tff(c_45703,plain,
! [X_2006,X_2007] : is_a_theorem(or(X_2006,not(and(X_2006,X_2007)))),
inference(resolution,[status(thm)],[c_31610,c_45410]) ).
tff(c_45764,plain,
! [X_2006,X_2007] : is_a_theorem(implies(and(X_2006,X_2007),X_2006)),
inference(resolution,[status(thm)],[c_45703,c_9375]) ).
tff(c_72,plain,
( kn2
| ~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_206,plain,
~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')),
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_45778,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_45764,c_206]) ).
tff(c_45779,plain,
kn2,
inference(splitRight,[status(thm)],[c_72]) ).
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_45798,plain,
! [P_34,Q_35] : is_a_theorem(implies(and(P_34,Q_35),P_34)),
inference(demodulation,[status(thm),theory(equality)],[c_45779,c_74]) ).
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_45802,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_45798,c_205]) ).
tff(c_45803,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_48657,plain,
! [X_14,Y_15] : is_a_theorem(implies(and(X_14,Y_15),X_14)),
inference(demodulation,[status(thm),theory(equality)],[c_45803,c_34]) ).
tff(c_48635,plain,
~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')),
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_48661,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48657,c_48635]) ).
tff(c_48662,plain,
kn2,
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_48681,plain,
! [P_34,Q_35] : is_a_theorem(implies(and(P_34,Q_35),P_34)),
inference(demodulation,[status(thm),theory(equality)],[c_48662,c_74]) ).
tff(c_51162,plain,
! [Y_2404,Y_2405] : is_a_theorem(or(implies(Y_2404,Y_2405),Y_2404)),
inference(superposition,[status(thm),theory(equality)],[c_51013,c_48681]) ).
tff(c_48828,plain,
! [P_2233,Q_2234] : is_a_theorem(implies(or(P_2233,Q_2234),or(Q_2234,P_2233))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_48837,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_48828]) ).
tff(c_49643,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(splitLeft,[status(thm)],[c_192]) ).
tff(c_49975,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48837,c_49643]) ).
tff(c_49976,plain,
modus_tollens,
inference(splitRight,[status(thm)],[c_192]) ).
tff(c_50126,plain,
! [Y_2345,X_2346] : is_a_theorem(implies(or(Y_2345,not(X_2346)),implies(X_2346,Y_2345))),
inference(demodulation,[status(thm),theory(equality)],[c_49976,c_191]) ).
tff(c_50143,plain,
! [X_2346,Y_2345] :
( is_a_theorem(implies(X_2346,Y_2345))
| ~ is_a_theorem(or(Y_2345,not(X_2346))) ),
inference(resolution,[status(thm)],[c_50126,c_201]) ).
tff(c_51166,plain,
! [X_2346,Y_2405] : is_a_theorem(implies(X_2346,implies(not(X_2346),Y_2405))),
inference(resolution,[status(thm)],[c_51162,c_50143]) ).
tff(c_51179,plain,
! [X_2346,Y_2405] : is_a_theorem(implies(X_2346,or(X_2346,Y_2405))),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_51166]) ).
tff(c_86,plain,
! [P_42,Q_43] :
( is_a_theorem(implies(P_42,implies(not(P_42),Q_43)))
| ~ cn2 ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_183,plain,
! [P_42,Q_43] :
( is_a_theorem(implies(P_42,or(P_42,Q_43)))
| ~ cn2 ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_86]) ).
tff(c_48664,plain,
~ cn2,
inference(splitLeft,[status(thm)],[c_183]) ).
tff(c_84,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',implies(not('#skF_42'),'#skF_43'))) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_184,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_84]) ).
tff(c_48685,plain,
~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))),
inference(negUnitSimplification,[status(thm)],[c_48664,c_184]) ).
tff(c_51186,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_51179,c_48685]) ).
tff(c_51187,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_148,plain,
~ or_1,
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_44,plain,
( or_1
| ~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_190,plain,
~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))),
inference(negUnitSimplification,[status(thm)],[c_148,c_44]) ).
tff(c_51192,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_51187,c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL490+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/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
% 0.18/0.35 % Computer : n021.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 14:03:36 EDT 2023
% 0.18/0.35 % CPUTime :
% 20.25/10.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.25/10.04
% 20.25/10.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.25/10.09
% 20.25/10.09 Inference rules
% 20.25/10.09 ----------------------
% 20.25/10.09 #Ref : 0
% 20.25/10.09 #Sup : 12133
% 20.25/10.09 #Fact : 0
% 20.25/10.09 #Define : 0
% 20.25/10.09 #Split : 216
% 20.25/10.09 #Chain : 0
% 20.25/10.09 #Close : 0
% 20.25/10.09
% 20.25/10.09 Ordering : KBO
% 20.25/10.09
% 20.25/10.09 Simplification rules
% 20.25/10.09 ----------------------
% 20.25/10.09 #Subsume : 2626
% 20.25/10.09 #Demod : 7923
% 20.25/10.09 #Tautology : 2911
% 20.25/10.09 #SimpNegUnit : 73
% 20.25/10.09 #BackRed : 240
% 20.25/10.09
% 20.25/10.09 #Partial instantiations: 0
% 20.25/10.09 #Strategies tried : 1
% 20.25/10.09
% 20.25/10.09 Timing (in seconds)
% 20.25/10.09 ----------------------
% 20.68/10.10 Preprocessing : 0.61
% 20.68/10.10 Parsing : 0.30
% 20.68/10.10 CNF conversion : 0.05
% 20.68/10.10 Main loop : 8.37
% 20.68/10.10 Inferencing : 1.74
% 20.68/10.10 Reduction : 4.01
% 20.68/10.10 Demodulation : 2.88
% 20.68/10.10 BG Simplification : 0.09
% 20.68/10.10 Subsumption : 1.98
% 20.68/10.10 Abstraction : 0.11
% 20.68/10.10 MUC search : 0.00
% 20.68/10.10 Cooper : 0.00
% 20.68/10.10 Total : 9.08
% 20.68/10.10 Index Insertion : 0.00
% 20.68/10.10 Index Deletion : 0.00
% 20.68/10.10 Index Matching : 0.00
% 20.68/10.10 BG Taut test : 0.00
%------------------------------------------------------------------------------