TSTP Solution File: LCL463+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL463+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 : n022.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 10:48:11 EDT 2023
% Result : Theorem 53.57s 39.25s
% Output : CNFRefutation 53.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 111
% Syntax : Number of formulae : 239 ( 62 unt; 93 typ; 0 def)
% Number of atoms : 262 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 224 ( 108 ~; 104 |; 1 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 35 ( 33 usr; 33 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 289 (; 289 !; 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_implies > 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(op_implies,type,
op_implies: $o ).
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_250,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
tff(f_258,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_259,axiom,
op_implies_and,
file('/export/starexec/sandbox2/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/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_142,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn2) ).
tff(f_251,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn3) ).
tff(f_146,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_249,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn1) ).
tff(f_138,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn1) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_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_260,axiom,
op_equiv,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_254,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.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_262,negated_conjecture,
~ implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
tff(f_76,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(c_132,plain,
cn2,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_138,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_140,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_259]) ).
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_150,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,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_152,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_150,c_112]) ).
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_161,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_152,c_86]) ).
tff(c_134,plain,
cn3,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_90,plain,
! [P_44] :
( is_a_theorem(implies(implies(not(P_44),P_44),P_44))
| ~ cn3 ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_154,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_152,c_90]) ).
tff(c_130,plain,
cn1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_82,plain,
! [P_39,Q_40,R_41] :
( is_a_theorem(implies(implies(P_39,Q_40),implies(implies(Q_40,R_41),implies(P_39,R_41))))
| ~ cn1 ),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_304,plain,
! [P_89,Q_90,R_91] : is_a_theorem(implies(implies(P_89,Q_90),implies(implies(Q_90,R_91),implies(P_89,R_91)))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_82]) ).
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_187,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_418,plain,
! [Q_106,R_107,P_108] :
( is_a_theorem(implies(implies(Q_106,R_107),implies(P_108,R_107)))
| ~ is_a_theorem(implies(P_108,Q_106)) ),
inference(resolution,[status(thm)],[c_304,c_187]) ).
tff(c_545,plain,
! [P_117,R_118,Q_119] :
( is_a_theorem(implies(P_117,R_118))
| ~ is_a_theorem(implies(Q_119,R_118))
| ~ is_a_theorem(implies(P_117,Q_119)) ),
inference(resolution,[status(thm)],[c_418,c_187]) ).
tff(c_611,plain,
! [P_123,P_124] :
( is_a_theorem(implies(P_123,P_124))
| ~ is_a_theorem(implies(P_123,or(P_124,P_124))) ),
inference(resolution,[status(thm)],[c_154,c_545]) ).
tff(c_645,plain,
! [Q_43] : is_a_theorem(implies(Q_43,Q_43)),
inference(resolution,[status(thm)],[c_161,c_611]) ).
tff(c_142,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_260]) ).
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_148,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_142,c_120]) ).
tff(c_231,plain,
! [X_79,Y_80] : ( not(and(X_79,not(Y_80))) = implies(X_79,Y_80) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_432,plain,
! [X_109,X_110,Y_111] : ( implies(X_109,and(X_110,not(Y_111))) = not(and(X_109,implies(X_110,Y_111))) ),
inference(superposition,[status(thm),theory(equality)],[c_231,c_150]) ).
tff(c_494,plain,
! [X_56,X_110,Y_111] : ( not(and(not(X_56),implies(X_110,Y_111))) = or(X_56,and(X_110,not(Y_111))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_432]) ).
tff(c_234,plain,
! [X_60,X_79,Y_80] : ( implies(X_60,and(X_79,not(Y_80))) = not(and(X_60,implies(X_79,Y_80))) ),
inference(superposition,[status(thm),theory(equality)],[c_231,c_150]) ).
tff(c_243,plain,
! [X_79,Y_80,Y_57] : ( or(and(X_79,not(Y_80)),Y_57) = implies(implies(X_79,Y_80),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_231,c_152]) ).
tff(c_484,plain,
! [X_110,Y_111] : is_a_theorem(not(and(or(and(X_110,not(Y_111)),and(X_110,not(Y_111))),implies(X_110,Y_111)))),
inference(superposition,[status(thm),theory(equality)],[c_432,c_154]) ).
tff(c_504,plain,
! [X_110,Y_111] : is_a_theorem(not(and(not(and(implies(X_110,Y_111),implies(X_110,Y_111))),implies(X_110,Y_111)))),
inference(demodulation,[status(thm),theory(equality)],[c_234,c_243,c_484]) ).
tff(c_3206,plain,
! [X_309,Y_310] : is_a_theorem(or(and(implies(X_309,Y_310),implies(X_309,Y_310)),and(X_309,not(Y_310)))),
inference(demodulation,[status(thm),theory(equality)],[c_494,c_504]) ).
tff(c_3234,plain,
! [Y_65] : is_a_theorem(or(equiv(Y_65,Y_65),and(Y_65,not(Y_65)))),
inference(superposition,[status(thm),theory(equality)],[c_148,c_3206]) ).
tff(c_574,plain,
! [P_117,P_42,Q_43] :
( is_a_theorem(implies(P_117,or(P_42,Q_43)))
| ~ is_a_theorem(implies(P_117,P_42)) ),
inference(resolution,[status(thm)],[c_161,c_545]) ).
tff(c_201,plain,
! [X_71,Y_72] : ( implies(not(X_71),Y_72) = or(X_71,Y_72) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_150,c_112]) ).
tff(c_208,plain,
! [X_71,Q_43] : is_a_theorem(or(X_71,or(not(X_71),Q_43))),
inference(superposition,[status(thm),theory(equality)],[c_201,c_161]) ).
tff(c_218,plain,
! [Y_75,X_76] :
( is_a_theorem(Y_75)
| ~ is_a_theorem(implies(X_76,Y_75))
| ~ is_a_theorem(X_76) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_228,plain,
! [P_42,Q_43] :
( is_a_theorem(or(P_42,Q_43))
| ~ is_a_theorem(P_42) ),
inference(resolution,[status(thm)],[c_161,c_218]) ).
tff(c_427,plain,
! [Q_106,Y_57,X_56] :
( is_a_theorem(implies(implies(Q_106,Y_57),or(X_56,Y_57)))
| ~ is_a_theorem(implies(not(X_56),Q_106)) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_418]) ).
tff(c_429,plain,
! [Q_106,Y_57,X_56] :
( is_a_theorem(implies(implies(Q_106,Y_57),or(X_56,Y_57)))
| ~ is_a_theorem(or(X_56,Q_106)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_427]) ).
tff(c_846,plain,
! [Q_143,Y_144] :
( is_a_theorem(implies(implies(Q_143,Y_144),Y_144))
| ~ is_a_theorem(or(Y_144,Q_143)) ),
inference(resolution,[status(thm)],[c_429,c_611]) ).
tff(c_1066,plain,
! [X_162,Y_163] :
( is_a_theorem(implies(or(X_162,Y_163),Y_163))
| ~ is_a_theorem(or(Y_163,not(X_162))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_846]) ).
tff(c_1085,plain,
! [X_162,P_42] :
( is_a_theorem(implies(or(X_162,P_42),P_42))
| ~ is_a_theorem(P_42) ),
inference(resolution,[status(thm)],[c_228,c_1066]) ).
tff(c_529,plain,
! [Q_114,Y_115,X_116] :
( is_a_theorem(implies(implies(Q_114,Y_115),or(X_116,Y_115)))
| ~ is_a_theorem(or(X_116,Q_114)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_427]) ).
tff(c_1251,plain,
! [X_180,Y_181,Q_182] :
( is_a_theorem(or(X_180,Y_181))
| ~ is_a_theorem(implies(Q_182,Y_181))
| ~ is_a_theorem(or(X_180,Q_182)) ),
inference(resolution,[status(thm)],[c_529,c_187]) ).
tff(c_1928,plain,
! [X_233,P_234,X_235] :
( is_a_theorem(or(X_233,P_234))
| ~ is_a_theorem(or(X_233,or(X_235,P_234)))
| ~ is_a_theorem(P_234) ),
inference(resolution,[status(thm)],[c_1085,c_1251]) ).
tff(c_1965,plain,
! [X_236,Q_237] :
( is_a_theorem(or(X_236,Q_237))
| ~ is_a_theorem(Q_237) ),
inference(resolution,[status(thm)],[c_208,c_1928]) ).
tff(c_870,plain,
! [X_56,Y_57] :
( is_a_theorem(implies(or(X_56,Y_57),Y_57))
| ~ is_a_theorem(or(Y_57,not(X_56))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_846]) ).
tff(c_2392,plain,
! [X_252,X_253] :
( is_a_theorem(implies(or(X_252,X_253),X_253))
| ~ is_a_theorem(not(X_252)) ),
inference(resolution,[status(thm)],[c_1965,c_870]) ).
tff(c_428,plain,
! [P_108,R_107,Q_106] :
( is_a_theorem(implies(P_108,R_107))
| ~ is_a_theorem(implies(Q_106,R_107))
| ~ is_a_theorem(implies(P_108,Q_106)) ),
inference(resolution,[status(thm)],[c_418,c_187]) ).
tff(c_11185,plain,
! [P_813,X_814,X_815] :
( is_a_theorem(implies(P_813,X_814))
| ~ is_a_theorem(implies(P_813,or(X_815,X_814)))
| ~ is_a_theorem(not(X_815)) ),
inference(resolution,[status(thm)],[c_2392,c_428]) ).
tff(c_13387,plain,
! [P_904,Q_905,P_906] :
( is_a_theorem(implies(P_904,Q_905))
| ~ is_a_theorem(not(P_906))
| ~ is_a_theorem(implies(P_904,P_906)) ),
inference(resolution,[status(thm)],[c_574,c_11185]) ).
tff(c_13489,plain,
! [X_56,Q_905,Y_57] :
( is_a_theorem(implies(not(X_56),Q_905))
| ~ is_a_theorem(not(Y_57))
| ~ is_a_theorem(or(X_56,Y_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_13387]) ).
tff(c_14014,plain,
! [X_924,Q_925,Y_926] :
( is_a_theorem(or(X_924,Q_925))
| ~ is_a_theorem(not(Y_926))
| ~ is_a_theorem(or(X_924,Y_926)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_13489]) ).
tff(c_14060,plain,
! [Y_65,Q_925] :
( is_a_theorem(or(equiv(Y_65,Y_65),Q_925))
| ~ is_a_theorem(not(and(Y_65,not(Y_65)))) ),
inference(resolution,[status(thm)],[c_3234,c_14014]) ).
tff(c_14124,plain,
! [Y_927,Q_928] : is_a_theorem(or(equiv(Y_927,Y_927),Q_928)),
inference(demodulation,[status(thm),theory(equality)],[c_645,c_150,c_14060]) ).
tff(c_1964,plain,
! [X_71,Q_43] :
( is_a_theorem(or(X_71,Q_43))
| ~ is_a_theorem(Q_43) ),
inference(resolution,[status(thm)],[c_208,c_1928]) ).
tff(c_2443,plain,
! [P_254,Y_255,X_256] :
( is_a_theorem(implies(P_254,Y_255))
| ~ is_a_theorem(or(X_256,Y_255))
| ~ is_a_theorem(implies(P_254,not(X_256))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_545]) ).
tff(c_3401,plain,
! [P_320,Q_321,X_322] :
( is_a_theorem(implies(P_320,Q_321))
| ~ is_a_theorem(implies(P_320,not(X_322)))
| ~ is_a_theorem(Q_321) ),
inference(resolution,[status(thm)],[c_1964,c_2443]) ).
tff(c_3641,plain,
! [P_333,Q_334,X_335,Y_336] :
( is_a_theorem(implies(P_333,Q_334))
| ~ is_a_theorem(implies(P_333,implies(X_335,Y_336)))
| ~ is_a_theorem(Q_334) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_3401]) ).
tff(c_3896,plain,
! [P_351,Q_352,X_353,Y_354] :
( is_a_theorem(implies(P_351,Q_352))
| ~ is_a_theorem(implies(P_351,or(X_353,Y_354)))
| ~ is_a_theorem(Q_352) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_3641]) ).
tff(c_3980,plain,
! [P_355,Q_356] :
( is_a_theorem(implies(P_355,Q_356))
| ~ is_a_theorem(Q_356) ),
inference(resolution,[status(thm)],[c_161,c_3896]) ).
tff(c_575,plain,
! [P_117,P_44] :
( is_a_theorem(implies(P_117,P_44))
| ~ is_a_theorem(implies(P_117,or(P_44,P_44))) ),
inference(resolution,[status(thm)],[c_154,c_545]) ).
tff(c_4142,plain,
! [P_355,P_44] :
( is_a_theorem(implies(P_355,P_44))
| ~ is_a_theorem(or(P_44,P_44)) ),
inference(resolution,[status(thm)],[c_3980,c_575]) ).
tff(c_14234,plain,
! [P_355,Y_927] : is_a_theorem(implies(P_355,equiv(Y_927,Y_927))),
inference(resolution,[status(thm)],[c_14124,c_4142]) ).
tff(c_3258,plain,
! [Y_311] : is_a_theorem(or(equiv(Y_311,Y_311),and(Y_311,not(Y_311)))),
inference(superposition,[status(thm),theory(equality)],[c_148,c_3206]) ).
tff(c_577,plain,
! [P_120,P_121,Q_122] :
( is_a_theorem(implies(P_120,or(P_121,Q_122)))
| ~ is_a_theorem(implies(P_120,P_121)) ),
inference(resolution,[status(thm)],[c_161,c_545]) ).
tff(c_601,plain,
! [X_56,P_121,Q_122] :
( is_a_theorem(or(X_56,or(P_121,Q_122)))
| ~ is_a_theorem(implies(not(X_56),P_121)) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_577]) ).
tff(c_609,plain,
! [X_56,P_121,Q_122] :
( is_a_theorem(or(X_56,or(P_121,Q_122)))
| ~ is_a_theorem(or(X_56,P_121)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_601]) ).
tff(c_989,plain,
! [Y_153,Q_154] :
( is_a_theorem(Y_153)
| ~ is_a_theorem(implies(Q_154,Y_153))
| ~ is_a_theorem(or(Y_153,Q_154)) ),
inference(resolution,[status(thm)],[c_846,c_187]) ).
tff(c_1009,plain,
! [X_56,P_121,Q_122] :
( is_a_theorem(X_56)
| ~ is_a_theorem(implies(or(P_121,Q_122),X_56))
| ~ is_a_theorem(or(X_56,P_121)) ),
inference(resolution,[status(thm)],[c_609,c_989]) ).
tff(c_2432,plain,
! [X_253,X_252] :
( is_a_theorem(X_253)
| ~ is_a_theorem(or(X_253,X_252))
| ~ is_a_theorem(not(X_252)) ),
inference(resolution,[status(thm)],[c_2392,c_1009]) ).
tff(c_3261,plain,
! [Y_311] :
( is_a_theorem(equiv(Y_311,Y_311))
| ~ is_a_theorem(not(and(Y_311,not(Y_311)))) ),
inference(resolution,[status(thm)],[c_3258,c_2432]) ).
tff(c_3282,plain,
! [Y_311] : is_a_theorem(equiv(Y_311,Y_311)),
inference(demodulation,[status(thm),theory(equality)],[c_645,c_150,c_3261]) ).
tff(c_3978,plain,
! [P_42,Q_352] :
( is_a_theorem(implies(P_42,Q_352))
| ~ is_a_theorem(Q_352) ),
inference(resolution,[status(thm)],[c_161,c_3896]) ).
tff(c_44844,plain,
! [Q_1754,Y_1755,X_1756] :
( is_a_theorem(implies(implies(Q_1754,Y_1755),Y_1755))
| ~ is_a_theorem(not(X_1756))
| ~ is_a_theorem(or(X_1756,Q_1754)) ),
inference(resolution,[status(thm)],[c_429,c_11185]) ).
tff(c_45121,plain,
! [Q_43,Y_1755,X_71] :
( is_a_theorem(implies(implies(Q_43,Y_1755),Y_1755))
| ~ is_a_theorem(not(X_71))
| ~ is_a_theorem(Q_43) ),
inference(resolution,[status(thm)],[c_1964,c_44844]) ).
tff(c_45132,plain,
! [X_71] : ~ is_a_theorem(not(X_71)),
inference(splitLeft,[status(thm)],[c_45121]) ).
tff(c_288,plain,
! [X_87,Y_88] : ( and(implies(X_87,Y_88),implies(Y_88,X_87)) = equiv(X_87,Y_88) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_297,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_152,c_288]) ).
tff(c_2040,plain,
! [X_238,Y_239,P_240] :
( is_a_theorem(implies(or(X_238,Y_239),implies(P_240,Y_239)))
| ~ is_a_theorem(implies(P_240,not(X_238))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_418]) ).
tff(c_11666,plain,
! [P_822,P_823,Y_824,X_825] :
( is_a_theorem(implies(P_822,implies(P_823,Y_824)))
| ~ is_a_theorem(implies(P_822,or(X_825,Y_824)))
| ~ is_a_theorem(implies(P_823,not(X_825))) ),
inference(resolution,[status(thm)],[c_2040,c_428]) ).
tff(c_11960,plain,
! [P_842,P_843,Q_844] :
( is_a_theorem(implies(P_842,implies(P_843,Q_844)))
| ~ is_a_theorem(implies(P_843,not(P_842))) ),
inference(resolution,[status(thm)],[c_161,c_11666]) ).
tff(c_12510,plain,
! [P_864,Q_865] : is_a_theorem(implies(P_864,implies(or(not(P_864),not(P_864)),Q_865))),
inference(resolution,[status(thm)],[c_154,c_11960]) ).
tff(c_38874,plain,
! [P_1620,X_1621,Y_1622] : is_a_theorem(implies(P_1620,not(and(or(not(P_1620),not(P_1620)),implies(X_1621,Y_1622))))),
inference(superposition,[status(thm),theory(equality)],[c_234,c_12510]) ).
tff(c_39019,plain,
! [P_1623] : is_a_theorem(implies(P_1623,not(equiv(not(not(P_1623)),not(P_1623))))),
inference(superposition,[status(thm),theory(equality)],[c_297,c_38874]) ).
tff(c_631,plain,
! [X_56,P_124] :
( is_a_theorem(implies(not(X_56),P_124))
| ~ is_a_theorem(or(X_56,or(P_124,P_124))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_611]) ).
tff(c_644,plain,
! [X_56,P_124] :
( is_a_theorem(or(X_56,P_124))
| ~ is_a_theorem(or(X_56,or(P_124,P_124))) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_631]) ).
tff(c_2036,plain,
! [X_236,P_124] :
( is_a_theorem(or(X_236,P_124))
| ~ is_a_theorem(or(P_124,P_124)) ),
inference(resolution,[status(thm)],[c_1965,c_644]) ).
tff(c_14328,plain,
! [X_931,Y_932] : is_a_theorem(or(X_931,equiv(Y_932,Y_932))),
inference(resolution,[status(thm)],[c_14124,c_2036]) ).
tff(c_875,plain,
! [Y_144,Q_143] :
( is_a_theorem(Y_144)
| ~ is_a_theorem(implies(Q_143,Y_144))
| ~ is_a_theorem(or(Y_144,Q_143)) ),
inference(resolution,[status(thm)],[c_846,c_187]) ).
tff(c_14425,plain,
! [X_931,Y_932] :
( is_a_theorem(X_931)
| ~ is_a_theorem(implies(equiv(Y_932,Y_932),X_931)) ),
inference(resolution,[status(thm)],[c_14328,c_875]) ).
tff(c_39126,plain,
! [Y_932] : is_a_theorem(not(equiv(not(not(equiv(Y_932,Y_932))),not(equiv(Y_932,Y_932))))),
inference(resolution,[status(thm)],[c_39019,c_14425]) ).
tff(c_45167,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_45132,c_39126]) ).
tff(c_45169,plain,
! [Q_1757,Y_1758] :
( is_a_theorem(implies(implies(Q_1757,Y_1758),Y_1758))
| ~ is_a_theorem(Q_1757) ),
inference(splitRight,[status(thm)],[c_45121]) ).
tff(c_45234,plain,
! [X_60,X_79,Y_80] :
( is_a_theorem(implies(not(and(X_60,implies(X_79,Y_80))),and(X_79,not(Y_80))))
| ~ is_a_theorem(X_60) ),
inference(superposition,[status(thm),theory(equality)],[c_234,c_45169]) ).
tff(c_124942,plain,
! [X_3023,X_3024,Y_3025] :
( is_a_theorem(or(and(X_3023,implies(X_3024,Y_3025)),and(X_3024,not(Y_3025))))
| ~ is_a_theorem(X_3023) ),
inference(demodulation,[status(thm),theory(equality)],[c_494,c_234,c_45234]) ).
tff(c_124987,plain,
! [X_3023,X_3024,Y_3025] :
( is_a_theorem(and(X_3023,implies(X_3024,Y_3025)))
| ~ is_a_theorem(not(and(X_3024,not(Y_3025))))
| ~ is_a_theorem(X_3023) ),
inference(resolution,[status(thm)],[c_124942,c_2432]) ).
tff(c_129445,plain,
! [X_3096,X_3097,Y_3098] :
( is_a_theorem(and(X_3096,implies(X_3097,Y_3098)))
| ~ is_a_theorem(implies(X_3097,Y_3098))
| ~ is_a_theorem(X_3096) ),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_124987]) ).
tff(c_129607,plain,
! [X_3099,Y_3100] :
( is_a_theorem(equiv(X_3099,Y_3100))
| ~ is_a_theorem(implies(Y_3100,X_3099))
| ~ is_a_theorem(implies(X_3099,Y_3100)) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_129445]) ).
tff(c_133564,plain,
! [P_3110,Q_3111] :
( is_a_theorem(equiv(or(P_3110,Q_3111),P_3110))
| ~ is_a_theorem(implies(or(P_3110,Q_3111),P_3110)) ),
inference(resolution,[status(thm)],[c_161,c_129607]) ).
tff(c_134575,plain,
! [Q_3131,Q_3132] :
( is_a_theorem(equiv(or(Q_3131,Q_3132),Q_3131))
| ~ is_a_theorem(Q_3131) ),
inference(resolution,[status(thm)],[c_3978,c_133564]) ).
tff(c_136,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_254]) ).
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_182,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_10]) ).
tff(c_134622,plain,
! [Q_3133,Q_3134] :
( ( or(Q_3133,Q_3134) = Q_3133 )
| ~ is_a_theorem(Q_3133) ),
inference(resolution,[status(thm)],[c_134575,c_182]) ).
tff(c_144987,plain,
! [Y_3212,Q_3213] : ( or(equiv(Y_3212,Y_3212),Q_3213) = equiv(Y_3212,Y_3212) ),
inference(resolution,[status(thm)],[c_3282,c_134622]) ).
tff(c_130043,plain,
! [P_44] :
( is_a_theorem(equiv(P_44,or(P_44,P_44)))
| ~ is_a_theorem(implies(P_44,or(P_44,P_44))) ),
inference(resolution,[status(thm)],[c_154,c_129607]) ).
tff(c_130300,plain,
! [P_3101] : is_a_theorem(equiv(P_3101,or(P_3101,P_3101))),
inference(demodulation,[status(thm),theory(equality)],[c_161,c_130043]) ).
tff(c_130529,plain,
! [P_3102] : ( or(P_3102,P_3102) = P_3102 ),
inference(resolution,[status(thm)],[c_130300,c_182]) ).
tff(c_1118,plain,
! [P_166,X_167,Y_168] : is_a_theorem(implies(implies(P_166,not(X_167)),implies(or(X_167,Y_168),implies(P_166,Y_168)))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_304]) ).
tff(c_1141,plain,
! [X_56,X_167,Y_57] : is_a_theorem(implies(implies(not(X_56),not(X_167)),implies(or(X_167,Y_57),or(X_56,Y_57)))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_1118]) ).
tff(c_1148,plain,
! [X_56,X_167,Y_57] : is_a_theorem(implies(or(X_56,not(X_167)),implies(or(X_167,Y_57),or(X_56,Y_57)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_1141]) ).
tff(c_91642,plain,
! [P_2479,P_2480,Q_2481,P_2482] :
( is_a_theorem(implies(P_2479,or(P_2480,Q_2481)))
| ~ is_a_theorem(implies(P_2479,P_2482))
| ~ is_a_theorem(implies(P_2482,P_2480)) ),
inference(resolution,[status(thm)],[c_577,c_428]) ).
tff(c_92175,plain,
! [P_2483,P_2484,Q_2485,Q_2486] :
( is_a_theorem(implies(P_2483,or(P_2484,Q_2485)))
| ~ is_a_theorem(implies(or(P_2483,Q_2486),P_2484)) ),
inference(resolution,[status(thm)],[c_161,c_91642]) ).
tff(c_96334,plain,
! [X_2536,X_2537,Y_2538,Q_2539] : is_a_theorem(implies(X_2536,or(implies(or(X_2537,Y_2538),or(X_2536,Y_2538)),Q_2539))),
inference(resolution,[status(thm)],[c_1148,c_92175]) ).
tff(c_96644,plain,
! [X_2536,X_2537,Y_2538] : is_a_theorem(implies(X_2536,implies(or(X_2537,Y_2538),or(X_2536,Y_2538)))),
inference(resolution,[status(thm)],[c_96334,c_575]) ).
tff(c_131012,plain,
! [P_3102,X_2537] : is_a_theorem(implies(P_3102,implies(or(X_2537,P_3102),P_3102))),
inference(superposition,[status(thm),theory(equality)],[c_130529,c_96644]) ).
tff(c_147293,plain,
! [Q_3227,Y_3228] : is_a_theorem(implies(Q_3227,implies(equiv(Y_3228,Y_3228),Q_3227))),
inference(superposition,[status(thm),theory(equality)],[c_144987,c_131012]) ).
tff(c_317,plain,
! [Q_90,R_91,P_89] :
( is_a_theorem(implies(implies(Q_90,R_91),implies(P_89,R_91)))
| ~ is_a_theorem(implies(P_89,Q_90)) ),
inference(resolution,[status(thm)],[c_304,c_187]) ).
tff(c_568,plain,
! [P_117,P_89,R_91,Q_90] :
( is_a_theorem(implies(P_117,implies(P_89,R_91)))
| ~ is_a_theorem(implies(P_117,implies(Q_90,R_91)))
| ~ is_a_theorem(implies(P_89,Q_90)) ),
inference(resolution,[status(thm)],[c_317,c_545]) ).
tff(c_147419,plain,
! [Q_3227,P_89,Y_3228] :
( is_a_theorem(implies(Q_3227,implies(P_89,Q_3227)))
| ~ is_a_theorem(implies(P_89,equiv(Y_3228,Y_3228))) ),
inference(resolution,[status(thm)],[c_147293,c_568]) ).
tff(c_147512,plain,
! [Q_3227,P_89] : is_a_theorem(implies(Q_3227,implies(P_89,Q_3227))),
inference(demodulation,[status(thm),theory(equality)],[c_14234,c_147419]) ).
tff(c_144,plain,
~ implies_1,
inference(cnfTransformation,[status(thm)],[f_262]) ).
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_176,plain,
~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_20]) ).
tff(c_148104,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147512,c_176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL463+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 : n022.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 14:14:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 53.57/39.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.57/39.27
% 53.57/39.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.57/39.31
% 53.57/39.31 Inference rules
% 53.57/39.31 ----------------------
% 53.57/39.31 #Ref : 0
% 53.57/39.31 #Sup : 36995
% 53.57/39.31 #Fact : 0
% 53.57/39.31 #Define : 0
% 53.57/39.31 #Split : 63
% 53.57/39.31 #Chain : 0
% 53.57/39.31 #Close : 0
% 53.57/39.31
% 53.57/39.31 Ordering : KBO
% 53.57/39.31
% 53.57/39.31 Simplification rules
% 53.57/39.31 ----------------------
% 53.57/39.31 #Subsume : 13187
% 53.57/39.31 #Demod : 13899
% 53.57/39.31 #Tautology : 4053
% 53.57/39.31 #SimpNegUnit : 89
% 53.57/39.31 #BackRed : 239
% 53.57/39.31
% 53.57/39.31 #Partial instantiations: 0
% 53.57/39.31 #Strategies tried : 1
% 53.57/39.31
% 53.57/39.31 Timing (in seconds)
% 53.57/39.31 ----------------------
% 53.57/39.32 Preprocessing : 0.60
% 53.57/39.32 Parsing : 0.29
% 53.57/39.32 CNF conversion : 0.05
% 53.57/39.32 Main loop : 37.62
% 53.57/39.32 Inferencing : 3.74
% 53.57/39.32 Reduction : 15.64
% 53.57/39.32 Demodulation : 11.64
% 53.57/39.32 BG Simplification : 0.18
% 53.57/39.32 Subsumption : 16.11
% 53.57/39.32 Abstraction : 0.29
% 53.57/39.32 MUC search : 0.00
% 53.57/39.32 Cooper : 0.00
% 53.57/39.32 Total : 38.31
% 53.57/39.32 Index Insertion : 0.00
% 53.57/39.32 Index Deletion : 0.00
% 53.57/39.32 Index Matching : 0.00
% 53.57/39.32 BG Taut test : 0.00
%------------------------------------------------------------------------------