TSTP Solution File: LCL509+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL509+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 : n009.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 17.35s 8.12s
% Output : CNFRefutation 17.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 112
% Syntax : Number of formulae : 237 ( 73 unt; 92 typ; 0 def)
% Number of atoms : 229 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 164 ( 80 ~; 70 |; 1 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 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 : 224 (; 224 !; 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_258,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_259,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_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
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',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_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_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_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_262,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_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_151,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_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_153,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_151,c_112]) ).
tff(c_12080,plain,
! [X_742,Y_743] : ( not(and(X_742,not(Y_743))) = implies(X_742,Y_743) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_12083,plain,
! [X_60,X_742,Y_743] : ( implies(X_60,and(X_742,not(Y_743))) = not(and(X_60,implies(X_742,Y_743))) ),
inference(superposition,[status(thm),theory(equality)],[c_12080,c_151]) ).
tff(c_12309,plain,
! [X_770,Y_771,Y_772] : ( or(and(X_770,not(Y_771)),Y_772) = implies(implies(X_770,Y_771),Y_772) ),
inference(superposition,[status(thm),theory(equality)],[c_12080,c_153]) ).
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_192,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_202,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_151,c_112]) ).
tff(c_130,plain,
kn1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_70,plain,
! [P_33] :
( is_a_theorem(implies(P_33,and(P_33,P_33)))
| ~ kn1 ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_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_209,plain,
! [X_71] : is_a_theorem(or(X_71,and(not(X_71),not(X_71)))),
inference(superposition,[status(thm),theory(equality)],[c_202,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_217,plain,
! [X_73,Y_74] : ( not(and(X_73,not(Y_74))) = implies(X_73,Y_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_226,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_217,c_153]) ).
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_702,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_153,c_78]) ).
tff(c_733,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_151,c_702]) ).
tff(c_742,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_153,c_733]) ).
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_184,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_779,plain,
! [Q_124,X_125,Y_126] :
( is_a_theorem(or(and(Q_124,X_125),implies(X_125,Y_126)))
| ~ is_a_theorem(or(Y_126,Q_124)) ),
inference(resolution,[status(thm)],[c_742,c_184]) ).
tff(c_795,plain,
! [X_73,Y_74,Y_126] :
( is_a_theorem(implies(implies(X_73,Y_74),implies(not(Y_74),Y_126)))
| ~ is_a_theorem(or(Y_126,X_73)) ),
inference(superposition,[status(thm),theory(equality)],[c_226,c_779]) ).
tff(c_826,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(demodulation,[status(thm),theory(equality)],[c_153,c_795]) ).
tff(c_873,plain,
! [Y_136,Y_137,X_138] :
( is_a_theorem(or(Y_136,Y_137))
| ~ is_a_theorem(implies(X_138,Y_136))
| ~ is_a_theorem(or(Y_137,X_138)) ),
inference(resolution,[status(thm)],[c_826,c_184]) ).
tff(c_926,plain,
! [P_141,Y_142,Q_143] :
( is_a_theorem(or(P_141,Y_142))
| ~ is_a_theorem(or(Y_142,and(P_141,Q_143))) ),
inference(resolution,[status(thm)],[c_163,c_873]) ).
tff(c_949,plain,
! [X_144] : is_a_theorem(or(not(X_144),X_144)),
inference(resolution,[status(thm)],[c_209,c_926]) ).
tff(c_911,plain,
! [P_34,Y_137,Q_35] :
( is_a_theorem(or(P_34,Y_137))
| ~ is_a_theorem(or(Y_137,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_873]) ).
tff(c_966,plain,
! [P_146,Q_147] : is_a_theorem(or(P_146,not(and(P_146,Q_147)))),
inference(resolution,[status(thm)],[c_949,c_911]) ).
tff(c_985,plain,
! [X_60,Y_61] : is_a_theorem(or(X_60,implies(X_60,Y_61))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_966]) ).
tff(c_768,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_742,c_184]) ).
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_149,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_912,plain,
! [P_139,Y_140] :
( is_a_theorem(or(and(P_139,P_139),Y_140))
| ~ is_a_theorem(or(Y_140,P_139)) ),
inference(resolution,[status(thm)],[c_167,c_873]) ).
tff(c_2255,plain,
! [Y_245,Y_246] :
( is_a_theorem(or(equiv(Y_245,Y_245),Y_246))
| ~ is_a_theorem(or(Y_246,implies(Y_245,Y_245))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_912]) ).
tff(c_11758,plain,
! [Y_730,Q_731] :
( is_a_theorem(or(equiv(Y_730,Y_730),and(Q_731,Y_730)))
| ~ is_a_theorem(or(Y_730,Q_731)) ),
inference(resolution,[status(thm)],[c_768,c_2255]) ).
tff(c_11801,plain,
! [Q_732,Y_733] :
( is_a_theorem(or(Q_732,equiv(Y_733,Y_733)))
| ~ is_a_theorem(or(Y_733,Q_732)) ),
inference(resolution,[status(thm)],[c_11758,c_911]) ).
tff(c_910,plain,
! [P_33,Y_137] :
( is_a_theorem(or(and(P_33,P_33),Y_137))
| ~ is_a_theorem(or(Y_137,P_33)) ),
inference(resolution,[status(thm)],[c_167,c_873]) ).
tff(c_6183,plain,
! [P_506,P_507,Q_508] :
( is_a_theorem(or(P_506,and(P_507,P_507)))
| ~ is_a_theorem(or(and(P_506,Q_508),P_507)) ),
inference(resolution,[status(thm)],[c_910,c_926]) ).
tff(c_6456,plain,
! [P_520,Y_521] :
( is_a_theorem(or(P_520,and(Y_521,Y_521)))
| ~ is_a_theorem(or(Y_521,P_520)) ),
inference(resolution,[status(thm)],[c_910,c_6183]) ).
tff(c_960,plain,
! [P_34,Q_35] : is_a_theorem(or(P_34,not(and(P_34,Q_35)))),
inference(resolution,[status(thm)],[c_949,c_911]) ).
tff(c_919,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_226,c_912]) ).
tff(c_1733,plain,
! [Y_219,Y_220] :
( is_a_theorem(implies(or(Y_219,Y_219),Y_220))
| ~ is_a_theorem(or(Y_220,not(Y_219))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_919]) ).
tff(c_1830,plain,
! [P_226,Q_227] : is_a_theorem(implies(or(and(P_226,Q_227),and(P_226,Q_227)),P_226)),
inference(resolution,[status(thm)],[c_960,c_1733]) ).
tff(c_1863,plain,
! [P_226,Q_227] :
( is_a_theorem(P_226)
| ~ is_a_theorem(or(and(P_226,Q_227),and(P_226,Q_227))) ),
inference(resolution,[status(thm)],[c_1830,c_184]) ).
tff(c_6549,plain,
! [Y_522] :
( is_a_theorem(Y_522)
| ~ is_a_theorem(or(Y_522,and(Y_522,Y_522))) ),
inference(resolution,[status(thm)],[c_6456,c_1863]) ).
tff(c_6601,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_149,c_6549]) ).
tff(c_11809,plain,
! [Y_733] :
( is_a_theorem(implies(Y_733,Y_733))
| ~ is_a_theorem(or(Y_733,implies(Y_733,Y_733))) ),
inference(resolution,[status(thm)],[c_11801,c_6601]) ).
tff(c_11888,plain,
! [Y_733] : is_a_theorem(implies(Y_733,Y_733)),
inference(demodulation,[status(thm),theory(equality)],[c_985,c_11809]) ).
tff(c_391,plain,
! [X_90,Y_91] : ( and(implies(X_90,Y_91),implies(Y_91,X_90)) = equiv(X_90,Y_91) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_421,plain,
! [Y_92] : is_a_theorem(implies(implies(Y_92,Y_92),equiv(Y_92,Y_92))),
inference(superposition,[status(thm),theory(equality)],[c_391,c_167]) ).
tff(c_429,plain,
! [Y_92] :
( is_a_theorem(equiv(Y_92,Y_92))
| ~ is_a_theorem(implies(Y_92,Y_92)) ),
inference(resolution,[status(thm)],[c_421,c_184]) ).
tff(c_11933,plain,
! [Y_92] : is_a_theorem(equiv(Y_92,Y_92)),
inference(demodulation,[status(thm),theory(equality)],[c_11888,c_429]) ).
tff(c_948,plain,
! [X_71] : is_a_theorem(or(not(X_71),X_71)),
inference(resolution,[status(thm)],[c_209,c_926]) ).
tff(c_275,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_292,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_275,c_163]) ).
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_263,plain,
~ is_a_theorem(implies(equiv('#skF_27','#skF_28'),implies('#skF_27','#skF_28'))),
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_292,c_263]) ).
tff(c_316,plain,
equivalence_1,
inference(splitRight,[status(thm)],[c_56]) ).
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_329,plain,
! [X_86,Y_87] : is_a_theorem(implies(equiv(X_86,Y_87),implies(X_86,Y_87))),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_58]) ).
tff(c_336,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_329,c_184]) ).
tff(c_5208,plain,
! [Y_438,Y_439,X_440] :
( is_a_theorem(or(Y_438,Y_439))
| ~ is_a_theorem(or(Y_439,X_440))
| ~ is_a_theorem(equiv(X_440,Y_438)) ),
inference(resolution,[status(thm)],[c_336,c_873]) ).
tff(c_5319,plain,
! [Y_441,X_442] :
( is_a_theorem(or(Y_441,not(X_442)))
| ~ is_a_theorem(equiv(X_442,Y_441)) ),
inference(resolution,[status(thm)],[c_948,c_5208]) ).
tff(c_925,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_153,c_919]) ).
tff(c_5430,plain,
! [X_446,Y_447] :
( is_a_theorem(implies(or(X_446,X_446),Y_447))
| ~ is_a_theorem(equiv(X_446,Y_447)) ),
inference(resolution,[status(thm)],[c_5319,c_925]) ).
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))
| ~ cn3 ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_90]) ).
tff(c_194,plain,
~ cn3,
inference(splitLeft,[status(thm)],[c_154]) ).
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_155,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_88]) ).
tff(c_201,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_194,c_155]) ).
tff(c_5467,plain,
~ is_a_theorem(equiv('#skF_44','#skF_44')),
inference(resolution,[status(thm)],[c_5430,c_201]) ).
tff(c_12027,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11933,c_5467]) ).
tff(c_12028,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_12033,plain,
r1,
inference(demodulation,[status(thm),theory(equality)],[c_12028,c_92]) ).
tff(c_12034,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_192,c_12033]) ).
tff(c_12035,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_12330,plain,
! [X_770,Y_771] : is_a_theorem(implies(implies(implies(X_770,Y_771),and(X_770,not(Y_771))),and(X_770,not(Y_771)))),
inference(superposition,[status(thm),theory(equality)],[c_12309,c_12035]) ).
tff(c_15433,plain,
! [X_997,Y_998] : is_a_theorem(or(and(implies(X_997,Y_998),implies(X_997,Y_998)),and(X_997,not(Y_998)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_12083,c_12330]) ).
tff(c_12089,plain,
! [X_742,Y_743,Y_57] : ( or(and(X_742,not(Y_743)),Y_57) = implies(implies(X_742,Y_743),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_12080,c_153]) ).
tff(c_12531,plain,
! [P_786,Q_787,R_788] : is_a_theorem(implies(implies(P_786,Q_787),or(and(Q_787,R_788),not(and(R_788,P_786))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_12562,plain,
! [Y_61,Q_787,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_787),or(and(Q_787,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_12531]) ).
tff(c_12570,plain,
! [Y_789,Q_790,X_791] : is_a_theorem(implies(or(Y_789,Q_790),or(and(Q_790,X_791),implies(X_791,Y_789)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_12562]) ).
tff(c_12602,plain,
! [Q_792,X_793,Y_794] :
( is_a_theorem(or(and(Q_792,X_793),implies(X_793,Y_794)))
| ~ is_a_theorem(or(Y_794,Q_792)) ),
inference(resolution,[status(thm)],[c_12570,c_184]) ).
tff(c_12624,plain,
! [Q_792,X_56,Y_57] :
( is_a_theorem(or(and(Q_792,not(X_56)),or(X_56,Y_57)))
| ~ is_a_theorem(or(Y_57,Q_792)) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_12602]) ).
tff(c_12654,plain,
! [Q_798,X_799,Y_800] :
( is_a_theorem(implies(implies(Q_798,X_799),or(X_799,Y_800)))
| ~ is_a_theorem(or(Y_800,Q_798)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12089,c_12624]) ).
tff(c_12680,plain,
! [X_801,Y_802,Q_803] :
( is_a_theorem(or(X_801,Y_802))
| ~ is_a_theorem(implies(Q_803,X_801))
| ~ is_a_theorem(or(Y_802,Q_803)) ),
inference(resolution,[status(thm)],[c_12654,c_184]) ).
tff(c_12721,plain,
! [P_34,Y_802,Q_35] :
( is_a_theorem(or(P_34,Y_802))
| ~ is_a_theorem(or(Y_802,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_12680]) ).
tff(c_15844,plain,
! [X_1020,Y_1021] : is_a_theorem(or(X_1020,and(implies(X_1020,Y_1021),implies(X_1020,Y_1021)))),
inference(resolution,[status(thm)],[c_15433,c_12721]) ).
tff(c_15881,plain,
! [X_1020,Y_1021] : is_a_theorem(or(implies(X_1020,Y_1021),X_1020)),
inference(resolution,[status(thm)],[c_15844,c_12721]) ).
tff(c_13040,plain,
! [Q_826,R_827,P_828] :
( is_a_theorem(or(and(Q_826,R_827),not(and(R_827,P_828))))
| ~ is_a_theorem(implies(P_828,Q_826)) ),
inference(resolution,[status(thm)],[c_12531,c_184]) ).
tff(c_14497,plain,
! [X_947,Y_948,P_949] :
( is_a_theorem(implies(implies(X_947,Y_948),not(and(not(Y_948),P_949))))
| ~ is_a_theorem(implies(P_949,X_947)) ),
inference(superposition,[status(thm),theory(equality)],[c_12089,c_13040]) ).
tff(c_30906,plain,
! [Y_1706,P_1707,X_1708] :
( is_a_theorem(not(and(not(Y_1706),P_1707)))
| ~ is_a_theorem(implies(X_1708,Y_1706))
| ~ is_a_theorem(implies(P_1707,X_1708)) ),
inference(resolution,[status(thm)],[c_14497,c_184]) ).
tff(c_32386,plain,
! [P_1772,P_1773,Q_1774] :
( is_a_theorem(not(and(not(P_1772),P_1773)))
| ~ is_a_theorem(implies(P_1773,and(P_1772,Q_1774))) ),
inference(resolution,[status(thm)],[c_163,c_30906]) ).
tff(c_32462,plain,
! [P_1775] : is_a_theorem(not(and(not(P_1775),P_1775))),
inference(resolution,[status(thm)],[c_167,c_32386]) ).
tff(c_12064,plain,
! [Y_740,X_741] :
( is_a_theorem(Y_740)
| ~ is_a_theorem(implies(X_741,Y_740))
| ~ is_a_theorem(X_741) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_12067,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_153,c_12064]) ).
tff(c_12625,plain,
! [X_793,Y_794,Q_792] :
( is_a_theorem(implies(X_793,Y_794))
| ~ is_a_theorem(not(and(Q_792,X_793)))
| ~ is_a_theorem(or(Y_794,Q_792)) ),
inference(resolution,[status(thm)],[c_12602,c_12067]) ).
tff(c_32533,plain,
! [P_1778,Y_1779] :
( is_a_theorem(implies(P_1778,Y_1779))
| ~ is_a_theorem(or(Y_1779,not(P_1778))) ),
inference(resolution,[status(thm)],[c_32462,c_12625]) ).
tff(c_32690,plain,
! [P_1778,Y_1021] : is_a_theorem(implies(P_1778,implies(not(P_1778),Y_1021))),
inference(resolution,[status(thm)],[c_15881,c_32533]) ).
tff(c_32809,plain,
! [P_1778,Y_1021] : is_a_theorem(implies(P_1778,or(P_1778,Y_1021))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_32690]) ).
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_156,plain,
! [P_42,Q_43] :
( is_a_theorem(implies(P_42,or(P_42,Q_43)))
| ~ cn2 ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_86]) ).
tff(c_189,plain,
~ cn2,
inference(splitLeft,[status(thm)],[c_156]) ).
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_157,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_84]) ).
tff(c_12043,plain,
~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))),
inference(negUnitSimplification,[status(thm)],[c_189,c_157]) ).
tff(c_33083,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32809,c_12043]) ).
tff(c_33084,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(splitRight,[status(thm)],[c_156]) ).
tff(c_144,plain,
~ or_1,
inference(cnfTransformation,[status(thm)],[f_262]) ).
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_170,plain,
~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_44]) ).
tff(c_33088,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_33084,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL509+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
% 0.13/0.34 % Computer : n009.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 13:32:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 17.35/8.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.35/8.13
% 17.35/8.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.35/8.18
% 17.35/8.18 Inference rules
% 17.35/8.18 ----------------------
% 17.35/8.18 #Ref : 0
% 17.35/8.18 #Sup : 8111
% 17.35/8.18 #Fact : 0
% 17.35/8.18 #Define : 0
% 17.35/8.18 #Split : 70
% 17.35/8.18 #Chain : 0
% 17.35/8.18 #Close : 0
% 17.35/8.18
% 17.35/8.18 Ordering : KBO
% 17.35/8.18
% 17.35/8.18 Simplification rules
% 17.35/8.18 ----------------------
% 17.35/8.18 #Subsume : 2435
% 17.35/8.18 #Demod : 3792
% 17.35/8.18 #Tautology : 860
% 17.35/8.18 #SimpNegUnit : 25
% 17.35/8.18 #BackRed : 25
% 17.35/8.18
% 17.35/8.18 #Partial instantiations: 0
% 17.35/8.18 #Strategies tried : 1
% 17.35/8.18
% 17.35/8.18 Timing (in seconds)
% 17.35/8.18 ----------------------
% 17.35/8.19 Preprocessing : 0.61
% 17.35/8.19 Parsing : 0.32
% 17.35/8.19 CNF conversion : 0.05
% 17.35/8.19 Main loop : 6.42
% 17.35/8.19 Inferencing : 1.44
% 17.35/8.19 Reduction : 2.57
% 17.35/8.19 Demodulation : 1.91
% 17.35/8.19 BG Simplification : 0.08
% 17.35/8.19 Subsumption : 1.96
% 17.35/8.19 Abstraction : 0.09
% 17.35/8.19 MUC search : 0.00
% 17.35/8.19 Cooper : 0.00
% 17.35/8.19 Total : 7.11
% 17.35/8.19 Index Insertion : 0.00
% 17.35/8.19 Index Deletion : 0.00
% 17.35/8.19 Index Matching : 0.00
% 17.35/8.19 BG Taut test : 0.00
%------------------------------------------------------------------------------