TSTP Solution File: LCL516+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL516+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 : n024.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 10:48:16 EDT 2023
% Result : Theorem 16.74s 7.17s
% Output : CNFRefutation 16.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 113
% Syntax : Number of formulae : 245 ( 82 unt; 93 typ; 0 def)
% Number of atoms : 235 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 162 ( 79 ~; 69 |; 1 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 233 (; 233 !; 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_258,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
tff(f_244,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/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_146,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_249,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
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_250,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
tff(f_129,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
tff(f_251,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
tff(f_133,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
tff(f_60,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_260,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_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_112,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_1) ).
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_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(f_262,negated_conjecture,
~ cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
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(c_138,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_124,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_116,plain,
! [X_60,Y_61] :
( ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) )
| ~ op_implies_and ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_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_124,c_116]) ).
tff(c_112,plain,
! [X_56,Y_57] :
( ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) )
| ~ op_or ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_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_11671,plain,
! [X_732,Y_733] : ( not(and(X_732,not(Y_733))) = implies(X_732,Y_733) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_11976,plain,
! [X_763,X_764,Y_765] : ( implies(X_763,and(X_764,not(Y_765))) = not(and(X_763,implies(X_764,Y_765))) ),
inference(superposition,[status(thm),theory(equality)],[c_11671,c_150]) ).
tff(c_12028,plain,
! [X_56,X_764,Y_765] : ( not(and(not(X_56),implies(X_764,Y_765))) = or(X_56,and(X_764,not(Y_765))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_11976]) ).
tff(c_11674,plain,
! [X_60,X_732,Y_733] : ( implies(X_60,and(X_732,not(Y_733))) = not(and(X_60,implies(X_732,Y_733))) ),
inference(superposition,[status(thm),theory(equality)],[c_11671,c_150]) ).
tff(c_11680,plain,
! [X_732,Y_733,Y_57] : ( or(and(X_732,not(Y_733)),Y_57) = implies(implies(X_732,Y_733),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_11671,c_152]) ).
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_153,plain,
! [P_44] :
( is_a_theorem(implies(or(P_44,P_44),P_44))
| ~ cn3 ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_90]) ).
tff(c_11613,plain,
~ cn3,
inference(splitLeft,[status(thm)],[c_153]) ).
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_130,plain,
kn1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_70,plain,
! [P_33] :
( is_a_theorem(implies(P_33,and(P_33,P_33)))
| ~ kn1 ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_167,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_70]) ).
tff(c_208,plain,
! [X_71] : is_a_theorem(or(X_71,and(not(X_71),not(X_71)))),
inference(superposition,[status(thm),theory(equality)],[c_201,c_167]) ).
tff(c_132,plain,
kn2,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_74,plain,
! [P_34,Q_35] :
( is_a_theorem(implies(and(P_34,Q_35),P_34))
| ~ kn2 ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_163,plain,
! [P_34,Q_35] : is_a_theorem(implies(and(P_34,Q_35),P_34)),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_74]) ).
tff(c_215,plain,
! [X_73,Y_74] : ( not(and(X_73,not(Y_74))) = implies(X_73,Y_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_224,plain,
! [X_73,Y_74,Y_57] : ( or(and(X_73,not(Y_74)),Y_57) = implies(implies(X_73,Y_74),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_215,c_152]) ).
tff(c_134,plain,
kn3,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_78,plain,
! [P_36,Q_37,R_38] :
( is_a_theorem(implies(implies(P_36,Q_37),implies(not(and(Q_37,R_38)),not(and(R_38,P_36)))))
| ~ kn3 ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_683,plain,
! [P_118,Q_119,R_120] : is_a_theorem(implies(implies(P_118,Q_119),or(and(Q_119,R_120),not(and(R_120,P_118))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_152,c_78]) ).
tff(c_714,plain,
! [Y_61,Q_119,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_119),or(and(Q_119,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_150,c_683]) ).
tff(c_727,plain,
! [Y_121,Q_122,X_123] : is_a_theorem(implies(or(Y_121,Q_122),or(and(Q_122,X_123),implies(X_123,Y_121)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_714]) ).
tff(c_746,plain,
! [Y_121,X_73,Y_74] : is_a_theorem(implies(or(Y_121,X_73),implies(implies(X_73,Y_74),implies(not(Y_74),Y_121)))),
inference(superposition,[status(thm),theory(equality)],[c_224,c_727]) ).
tff(c_786,plain,
! [Y_127,X_128,Y_129] : is_a_theorem(implies(or(Y_127,X_128),implies(implies(X_128,Y_129),or(Y_129,Y_127)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_746]) ).
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_183,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_811,plain,
! [X_130,Y_131,Y_132] :
( is_a_theorem(implies(implies(X_130,Y_131),or(Y_131,Y_132)))
| ~ is_a_theorem(or(Y_132,X_130)) ),
inference(resolution,[status(thm)],[c_786,c_183]) ).
tff(c_828,plain,
! [Y_133,Y_134,X_135] :
( is_a_theorem(or(Y_133,Y_134))
| ~ is_a_theorem(implies(X_135,Y_133))
| ~ is_a_theorem(or(Y_134,X_135)) ),
inference(resolution,[status(thm)],[c_811,c_183]) ).
tff(c_886,plain,
! [P_138,Y_139,Q_140] :
( is_a_theorem(or(P_138,Y_139))
| ~ is_a_theorem(or(Y_139,and(P_138,Q_140))) ),
inference(resolution,[status(thm)],[c_163,c_828]) ).
tff(c_909,plain,
! [X_141] : is_a_theorem(or(not(X_141),X_141)),
inference(resolution,[status(thm)],[c_208,c_886]) ).
tff(c_926,plain,
! [X_143,Y_144] : is_a_theorem(or(implies(X_143,Y_144),and(X_143,not(Y_144)))),
inference(superposition,[status(thm),theory(equality)],[c_150,c_909]) ).
tff(c_866,plain,
! [P_34,Y_134,Q_35] :
( is_a_theorem(or(P_34,Y_134))
| ~ is_a_theorem(or(Y_134,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_828]) ).
tff(c_942,plain,
! [X_143,Y_144] : is_a_theorem(or(X_143,implies(X_143,Y_144))),
inference(resolution,[status(thm)],[c_926,c_866]) ).
tff(c_753,plain,
! [Q_122,X_123,Y_121] :
( is_a_theorem(or(and(Q_122,X_123),implies(X_123,Y_121)))
| ~ is_a_theorem(or(Y_121,Q_122)) ),
inference(resolution,[status(thm)],[c_727,c_183]) ).
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_867,plain,
! [P_136,Y_137] :
( is_a_theorem(or(and(P_136,P_136),Y_137))
| ~ is_a_theorem(or(Y_137,P_136)) ),
inference(resolution,[status(thm)],[c_167,c_828]) ).
tff(c_3854,plain,
! [Y_350,Y_351] :
( is_a_theorem(or(equiv(Y_350,Y_350),Y_351))
| ~ is_a_theorem(or(Y_351,implies(Y_350,Y_350))) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_867]) ).
tff(c_11327,plain,
! [Y_718,Q_719] :
( is_a_theorem(or(equiv(Y_718,Y_718),and(Q_719,Y_718)))
| ~ is_a_theorem(or(Y_718,Q_719)) ),
inference(resolution,[status(thm)],[c_753,c_3854]) ).
tff(c_11367,plain,
! [Q_720,Y_721] :
( is_a_theorem(or(Q_720,equiv(Y_721,Y_721)))
| ~ is_a_theorem(or(Y_721,Q_720)) ),
inference(resolution,[status(thm)],[c_11327,c_866]) ).
tff(c_865,plain,
! [P_33,Y_134] :
( is_a_theorem(or(and(P_33,P_33),Y_134))
| ~ is_a_theorem(or(Y_134,P_33)) ),
inference(resolution,[status(thm)],[c_167,c_828]) ).
tff(c_6123,plain,
! [P_496,P_497,Q_498] :
( is_a_theorem(or(P_496,and(P_497,P_497)))
| ~ is_a_theorem(or(and(P_496,Q_498),P_497)) ),
inference(resolution,[status(thm)],[c_865,c_886]) ).
tff(c_6386,plain,
! [P_509,Y_510] :
( is_a_theorem(or(P_509,and(Y_510,Y_510)))
| ~ is_a_theorem(or(Y_510,P_509)) ),
inference(resolution,[status(thm)],[c_865,c_6123]) ).
tff(c_920,plain,
! [P_34,Q_35] : is_a_theorem(or(P_34,not(and(P_34,Q_35)))),
inference(resolution,[status(thm)],[c_909,c_866]) ).
tff(c_874,plain,
! [Y_74,Y_57] :
( is_a_theorem(implies(implies(not(Y_74),Y_74),Y_57))
| ~ is_a_theorem(or(Y_57,not(Y_74))) ),
inference(superposition,[status(thm),theory(equality)],[c_224,c_867]) ).
tff(c_1586,plain,
! [Y_208,Y_209] :
( is_a_theorem(implies(or(Y_208,Y_208),Y_209))
| ~ is_a_theorem(or(Y_209,not(Y_208))) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_874]) ).
tff(c_1646,plain,
! [P_212,Q_213] : is_a_theorem(implies(or(and(P_212,Q_213),and(P_212,Q_213)),P_212)),
inference(resolution,[status(thm)],[c_920,c_1586]) ).
tff(c_1679,plain,
! [P_212,Q_213] :
( is_a_theorem(P_212)
| ~ is_a_theorem(or(and(P_212,Q_213),and(P_212,Q_213))) ),
inference(resolution,[status(thm)],[c_1646,c_183]) ).
tff(c_6479,plain,
! [Y_511] :
( is_a_theorem(Y_511)
| ~ is_a_theorem(or(Y_511,and(Y_511,Y_511))) ),
inference(resolution,[status(thm)],[c_6386,c_1679]) ).
tff(c_6531,plain,
! [Y_65] :
( is_a_theorem(implies(Y_65,Y_65))
| ~ is_a_theorem(or(implies(Y_65,Y_65),equiv(Y_65,Y_65))) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_6479]) ).
tff(c_11375,plain,
! [Y_721] :
( is_a_theorem(implies(Y_721,Y_721))
| ~ is_a_theorem(or(Y_721,implies(Y_721,Y_721))) ),
inference(resolution,[status(thm)],[c_11367,c_6531]) ).
tff(c_11454,plain,
! [Y_721] : is_a_theorem(implies(Y_721,Y_721)),
inference(demodulation,[status(thm),theory(equality)],[c_942,c_11375]) ).
tff(c_407,plain,
! [X_98,Y_99] : ( and(implies(X_98,Y_99),implies(Y_99,X_98)) = equiv(X_98,Y_99) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_233,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_243,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_167,c_233]) ).
tff(c_417,plain,
! [Y_99] :
( is_a_theorem(equiv(Y_99,Y_99))
| ~ is_a_theorem(implies(Y_99,Y_99)) ),
inference(superposition,[status(thm),theory(equality)],[c_407,c_243]) ).
tff(c_11499,plain,
! [Y_99] : is_a_theorem(equiv(Y_99,Y_99)),
inference(demodulation,[status(thm),theory(equality)],[c_11454,c_417]) ).
tff(c_908,plain,
! [X_71] : is_a_theorem(or(not(X_71),X_71)),
inference(resolution,[status(thm)],[c_208,c_886]) ).
tff(c_274,plain,
! [X_83,Y_84] : ( and(implies(X_83,Y_84),implies(Y_84,X_83)) = equiv(X_83,Y_84) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_291,plain,
! [X_83,Y_84] : is_a_theorem(implies(equiv(X_83,Y_84),implies(X_83,Y_84))),
inference(superposition,[status(thm),theory(equality)],[c_274,c_163]) ).
tff(c_58,plain,
! [X_27,Y_28] :
( is_a_theorem(implies(equiv(X_27,Y_28),implies(X_27,Y_28)))
| ~ equivalence_1 ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_265,plain,
~ equivalence_1,
inference(splitLeft,[status(thm)],[c_58]) ).
tff(c_56,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv('#skF_27','#skF_28'),implies('#skF_27','#skF_28'))) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_267,plain,
~ is_a_theorem(implies(equiv('#skF_27','#skF_28'),implies('#skF_27','#skF_28'))),
inference(negUnitSimplification,[status(thm)],[c_265,c_56]) ).
tff(c_315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_291,c_267]) ).
tff(c_318,plain,
! [X_86,Y_87] : is_a_theorem(implies(equiv(X_86,Y_87),implies(X_86,Y_87))),
inference(splitRight,[status(thm)],[c_58]) ).
tff(c_325,plain,
! [X_86,Y_87] :
( is_a_theorem(implies(X_86,Y_87))
| ~ is_a_theorem(equiv(X_86,Y_87)) ),
inference(resolution,[status(thm)],[c_318,c_183]) ).
tff(c_5073,plain,
! [Y_425,Y_426,X_427] :
( is_a_theorem(or(Y_425,Y_426))
| ~ is_a_theorem(or(Y_426,X_427))
| ~ is_a_theorem(equiv(X_427,Y_425)) ),
inference(resolution,[status(thm)],[c_325,c_828]) ).
tff(c_5178,plain,
! [Y_428,X_429] :
( is_a_theorem(or(Y_428,not(X_429)))
| ~ is_a_theorem(equiv(X_429,Y_428)) ),
inference(resolution,[status(thm)],[c_908,c_5073]) ).
tff(c_880,plain,
! [Y_74,Y_57] :
( is_a_theorem(implies(or(Y_74,Y_74),Y_57))
| ~ is_a_theorem(or(Y_57,not(Y_74))) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_874]) ).
tff(c_5327,plain,
! [X_436,Y_437] :
( is_a_theorem(implies(or(X_436,X_436),Y_437))
| ~ is_a_theorem(equiv(X_436,Y_437)) ),
inference(resolution,[status(thm)],[c_5178,c_880]) ).
tff(c_88,plain,
( cn3
| ~ is_a_theorem(implies(implies(not('#skF_44'),'#skF_44'),'#skF_44')) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_154,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_88]) ).
tff(c_195,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(splitLeft,[status(thm)],[c_154]) ).
tff(c_5364,plain,
~ is_a_theorem(equiv('#skF_44','#skF_44')),
inference(resolution,[status(thm)],[c_5327,c_195]) ).
tff(c_11597,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11499,c_5364]) ).
tff(c_11598,plain,
cn3,
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_11601,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_11598,c_153]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_187,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_11605,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11601,c_187]) ).
tff(c_11606,plain,
r1,
inference(splitRight,[status(thm)],[c_92]) ).
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_11616,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_11606,c_94]) ).
tff(c_11624,plain,
cn3,
inference(demodulation,[status(thm),theory(equality)],[c_11616,c_154]) ).
tff(c_11625,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11613,c_11624]) ).
tff(c_11626,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(splitRight,[status(thm)],[c_153]) ).
tff(c_12010,plain,
! [X_764,Y_765] : is_a_theorem(not(and(or(and(X_764,not(Y_765)),and(X_764,not(Y_765))),implies(X_764,Y_765)))),
inference(superposition,[status(thm),theory(equality)],[c_11976,c_11626]) ).
tff(c_12031,plain,
! [X_764,Y_765] : is_a_theorem(not(and(not(and(implies(X_764,Y_765),implies(X_764,Y_765))),implies(X_764,Y_765)))),
inference(demodulation,[status(thm),theory(equality)],[c_11674,c_11680,c_12010]) ).
tff(c_15130,plain,
! [X_998,Y_999] : is_a_theorem(or(and(implies(X_998,Y_999),implies(X_998,Y_999)),and(X_998,not(Y_999)))),
inference(demodulation,[status(thm),theory(equality)],[c_12028,c_12031]) ).
tff(c_12126,plain,
! [P_774,Q_775,R_776] : is_a_theorem(implies(implies(P_774,Q_775),or(and(Q_775,R_776),not(and(R_776,P_774))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_152,c_78]) ).
tff(c_12157,plain,
! [Y_61,Q_775,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_775),or(and(Q_775,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_150,c_12126]) ).
tff(c_12166,plain,
! [Y_777,Q_778,X_779] : is_a_theorem(implies(or(Y_777,Q_778),or(and(Q_778,X_779),implies(X_779,Y_777)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_12157]) ).
tff(c_12185,plain,
! [Y_777,X_732,Y_733] : is_a_theorem(implies(or(Y_777,X_732),implies(implies(X_732,Y_733),implies(not(Y_733),Y_777)))),
inference(superposition,[status(thm),theory(equality)],[c_11680,c_12166]) ).
tff(c_12225,plain,
! [Y_783,X_784,Y_785] : is_a_theorem(implies(or(Y_783,X_784),implies(implies(X_784,Y_785),or(Y_785,Y_783)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_12185]) ).
tff(c_12250,plain,
! [X_786,Y_787,Y_788] :
( is_a_theorem(implies(implies(X_786,Y_787),or(Y_787,Y_788)))
| ~ is_a_theorem(or(Y_788,X_786)) ),
inference(resolution,[status(thm)],[c_12225,c_183]) ).
tff(c_12271,plain,
! [Y_789,Y_790,X_791] :
( is_a_theorem(or(Y_789,Y_790))
| ~ is_a_theorem(implies(X_791,Y_789))
| ~ is_a_theorem(or(Y_790,X_791)) ),
inference(resolution,[status(thm)],[c_12250,c_183]) ).
tff(c_12312,plain,
! [P_34,Y_790,Q_35] :
( is_a_theorem(or(P_34,Y_790))
| ~ is_a_theorem(or(Y_790,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_12271]) ).
tff(c_15325,plain,
! [X_1005,Y_1006] : is_a_theorem(or(X_1005,and(implies(X_1005,Y_1006),implies(X_1005,Y_1006)))),
inference(resolution,[status(thm)],[c_15130,c_12312]) ).
tff(c_15359,plain,
! [X_1005,Y_1006] : is_a_theorem(or(implies(X_1005,Y_1006),X_1005)),
inference(resolution,[status(thm)],[c_15325,c_12312]) ).
tff(c_12514,plain,
! [Q_806,R_807,P_808] :
( is_a_theorem(or(and(Q_806,R_807),not(and(R_807,P_808))))
| ~ is_a_theorem(implies(P_808,Q_806)) ),
inference(resolution,[status(thm)],[c_12126,c_183]) ).
tff(c_13670,plain,
! [X_908,Y_909,P_910] :
( is_a_theorem(implies(implies(X_908,Y_909),not(and(not(Y_909),P_910))))
| ~ is_a_theorem(implies(P_910,X_908)) ),
inference(superposition,[status(thm),theory(equality)],[c_11680,c_12514]) ).
tff(c_27860,plain,
! [Y_1628,P_1629,X_1630] :
( is_a_theorem(not(and(not(Y_1628),P_1629)))
| ~ is_a_theorem(implies(X_1630,Y_1628))
| ~ is_a_theorem(implies(P_1629,X_1630)) ),
inference(resolution,[status(thm)],[c_13670,c_183]) ).
tff(c_28566,plain,
! [P_1655,P_1656,Q_1657] :
( is_a_theorem(not(and(not(P_1655),P_1656)))
| ~ is_a_theorem(implies(P_1656,and(P_1655,Q_1657))) ),
inference(resolution,[status(thm)],[c_163,c_27860]) ).
tff(c_28642,plain,
! [P_1658] : is_a_theorem(not(and(not(P_1658),P_1658))),
inference(resolution,[status(thm)],[c_167,c_28566]) ).
tff(c_12198,plain,
! [Q_780,X_781,Y_782] :
( is_a_theorem(or(and(Q_780,X_781),implies(X_781,Y_782)))
| ~ is_a_theorem(or(Y_782,Q_780)) ),
inference(resolution,[status(thm)],[c_12166,c_183]) ).
tff(c_11653,plain,
! [Y_728,X_729] :
( is_a_theorem(Y_728)
| ~ is_a_theorem(implies(X_729,Y_728))
| ~ is_a_theorem(X_729) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_11656,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_152,c_11653]) ).
tff(c_12221,plain,
! [X_781,Y_782,Q_780] :
( is_a_theorem(implies(X_781,Y_782))
| ~ is_a_theorem(not(and(Q_780,X_781)))
| ~ is_a_theorem(or(Y_782,Q_780)) ),
inference(resolution,[status(thm)],[c_12198,c_11656]) ).
tff(c_28713,plain,
! [P_1661,Y_1662] :
( is_a_theorem(implies(P_1661,Y_1662))
| ~ is_a_theorem(or(Y_1662,not(P_1661))) ),
inference(resolution,[status(thm)],[c_28642,c_12221]) ).
tff(c_28860,plain,
! [P_1661,Y_1006] : is_a_theorem(implies(P_1661,implies(not(P_1661),Y_1006))),
inference(resolution,[status(thm)],[c_15359,c_28713]) ).
tff(c_28969,plain,
! [P_1661,Y_1006] : is_a_theorem(implies(P_1661,or(P_1661,Y_1006))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_28860]) ).
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_11609,plain,
~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))),
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_29223,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28969,c_11609]) ).
tff(c_29224,plain,
or_1,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_46,plain,
! [X_20,Y_21] :
( is_a_theorem(implies(X_20,or(X_20,Y_21)))
| ~ or_1 ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_29249,plain,
! [X_20,Y_21] : is_a_theorem(implies(X_20,or(X_20,Y_21))),
inference(demodulation,[status(thm),theory(equality)],[c_29224,c_46]) ).
tff(c_144,plain,
~ cn2,
inference(cnfTransformation,[status(thm)],[f_262]) ).
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_156,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_84]) ).
tff(c_157,plain,
~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_156]) ).
tff(c_29253,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29249,c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : LCL516+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.15 % 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
% 0.16/0.37 % Computer : n024.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 13:55:45 EDT 2023
% 0.16/0.37 % CPUTime :
% 16.74/7.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.74/7.18
% 16.74/7.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.74/7.23
% 16.74/7.23 Inference rules
% 16.74/7.23 ----------------------
% 16.74/7.23 #Ref : 0
% 16.74/7.23 #Sup : 7103
% 16.74/7.23 #Fact : 0
% 16.74/7.23 #Define : 0
% 16.74/7.23 #Split : 79
% 16.74/7.23 #Chain : 0
% 16.74/7.23 #Close : 0
% 16.74/7.23
% 16.74/7.23 Ordering : KBO
% 16.74/7.23
% 16.74/7.23 Simplification rules
% 16.74/7.23 ----------------------
% 16.74/7.23 #Subsume : 1921
% 16.74/7.23 #Demod : 3627
% 16.74/7.23 #Tautology : 1060
% 16.74/7.23 #SimpNegUnit : 32
% 16.74/7.23 #BackRed : 24
% 16.74/7.23
% 16.74/7.23 #Partial instantiations: 0
% 16.74/7.23 #Strategies tried : 1
% 16.74/7.23
% 16.74/7.23 Timing (in seconds)
% 16.74/7.23 ----------------------
% 16.74/7.24 Preprocessing : 0.61
% 16.74/7.24 Parsing : 0.31
% 16.74/7.24 CNF conversion : 0.05
% 16.74/7.24 Main loop : 5.49
% 16.74/7.24 Inferencing : 1.28
% 16.74/7.24 Reduction : 2.26
% 16.74/7.24 Demodulation : 1.65
% 16.74/7.24 BG Simplification : 0.08
% 16.74/7.24 Subsumption : 1.55
% 16.74/7.24 Abstraction : 0.09
% 16.74/7.24 MUC search : 0.00
% 16.74/7.24 Cooper : 0.00
% 16.74/7.24 Total : 6.19
% 16.74/7.24 Index Insertion : 0.00
% 16.74/7.24 Index Deletion : 0.00
% 16.74/7.24 Index Matching : 0.00
% 16.74/7.24 BG Taut test : 0.00
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