TSTP Solution File: LCL517+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL517+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 : n032.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 10:48:17 EDT 2023
% Result : Theorem 11.62s 4.23s
% Output : CNFRefutation 11.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 111
% Syntax : Number of formulae : 195 ( 54 unt; 93 typ; 0 def)
% Number of atoms : 157 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 104 ( 49 ~; 43 |; 1 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 33 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 148 (; 148 !; 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/sandbox2/benchmark/theBenchmark.p',luka_op_or) ).
tff(f_244,axiom,
op_implies_and,
file('/export/starexec/sandbox2/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/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_249,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
tff(f_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_250,axiom,
kn2,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
tff(f_251,axiom,
kn3,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_260,axiom,
op_equiv,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_1) ).
tff(f_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_262,negated_conjecture,
~ cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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(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_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_218,plain,
! [X_60,X_73,Y_74] : ( implies(X_60,and(X_73,not(Y_74))) = not(and(X_60,implies(X_73,Y_74))) ),
inference(superposition,[status(thm),theory(equality)],[c_215,c_150]) ).
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_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_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_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_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_538,plain,
! [P_107,Q_108,R_109] : is_a_theorem(implies(implies(P_107,Q_108),or(and(Q_108,R_109),not(and(R_109,P_107))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_152,c_78]) ).
tff(c_557,plain,
! [X_56,Y_57,R_109] : is_a_theorem(implies(or(X_56,Y_57),or(and(Y_57,R_109),not(and(R_109,not(X_56)))))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_538]) ).
tff(c_665,plain,
! [X_116,Y_117,R_118] : is_a_theorem(implies(or(X_116,Y_117),or(and(Y_117,R_118),implies(R_118,X_116)))),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_557]) ).
tff(c_687,plain,
! [Y_57,Y_117,X_56] : is_a_theorem(implies(or(Y_57,Y_117),or(and(Y_117,not(X_56)),or(X_56,Y_57)))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_665]) ).
tff(c_744,plain,
! [Y_124,Y_125,X_126] : is_a_theorem(implies(or(Y_124,Y_125),implies(implies(Y_125,X_126),or(X_126,Y_124)))),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_687]) ).
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_796,plain,
! [Y_130,X_131,Y_132] :
( is_a_theorem(implies(implies(Y_130,X_131),or(X_131,Y_132)))
| ~ is_a_theorem(or(Y_132,Y_130)) ),
inference(resolution,[status(thm)],[c_744,c_183]) ).
tff(c_818,plain,
! [X_133,Y_134,Y_135] :
( is_a_theorem(or(X_133,Y_134))
| ~ is_a_theorem(implies(Y_135,X_133))
| ~ is_a_theorem(or(Y_134,Y_135)) ),
inference(resolution,[status(thm)],[c_796,c_183]) ).
tff(c_871,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_818]) ).
tff(c_894,plain,
! [X_141] : is_a_theorem(or(not(X_141),X_141)),
inference(resolution,[status(thm)],[c_209,c_871]) ).
tff(c_856,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_818]) ).
tff(c_905,plain,
! [P_34,Q_35] : is_a_theorem(or(P_34,not(and(P_34,Q_35)))),
inference(resolution,[status(thm)],[c_894,c_856]) ).
tff(c_857,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_818]) ).
tff(c_864,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_857]) ).
tff(c_1578,plain,
! [Y_216,Y_217] :
( is_a_theorem(implies(or(Y_216,Y_216),Y_217))
| ~ is_a_theorem(or(Y_217,not(Y_216))) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_864]) ).
tff(c_1632,plain,
! [P_220,Q_221] : is_a_theorem(implies(or(and(P_220,Q_221),and(P_220,Q_221)),P_220)),
inference(resolution,[status(thm)],[c_905,c_1578]) ).
tff(c_1657,plain,
! [X_73,Y_74] : is_a_theorem(implies(implies(implies(X_73,Y_74),and(X_73,not(Y_74))),X_73)),
inference(superposition,[status(thm),theory(equality)],[c_224,c_1632]) ).
tff(c_1670,plain,
! [X_73,Y_74] : is_a_theorem(or(and(implies(X_73,Y_74),implies(X_73,Y_74)),X_73)),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_218,c_1657]) ).
tff(c_855,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_818]) ).
tff(c_6144,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_855,c_871]) ).
tff(c_6224,plain,
! [X_73,Y_74] : is_a_theorem(or(implies(X_73,Y_74),and(X_73,X_73))),
inference(resolution,[status(thm)],[c_1670,c_6144]) ).
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_6411,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_855,c_6144]) ).
tff(c_7930,plain,
! [P_572,Y_573] :
( is_a_theorem(or(P_572,equiv(Y_573,Y_573)))
| ~ is_a_theorem(or(implies(Y_573,Y_573),P_572)) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_6411]) ).
tff(c_8032,plain,
! [Y_574] : is_a_theorem(or(and(Y_574,Y_574),equiv(Y_574,Y_574))),
inference(resolution,[status(thm)],[c_6224,c_7930]) ).
tff(c_892,plain,
! [P_138,P_33,Q_140] :
( is_a_theorem(or(P_138,and(P_33,P_33)))
| ~ is_a_theorem(or(and(P_138,Q_140),P_33)) ),
inference(resolution,[status(thm)],[c_855,c_871]) ).
tff(c_8064,plain,
! [Y_574] : is_a_theorem(or(Y_574,and(equiv(Y_574,Y_574),equiv(Y_574,Y_574)))),
inference(resolution,[status(thm)],[c_8032,c_892]) ).
tff(c_688,plain,
! [Y_117,R_118,X_116] :
( is_a_theorem(or(and(Y_117,R_118),implies(R_118,X_116)))
| ~ is_a_theorem(or(X_116,Y_117)) ),
inference(resolution,[status(thm)],[c_665,c_183]) ).
tff(c_2324,plain,
! [Y_258,Y_259] :
( is_a_theorem(or(equiv(Y_258,Y_258),Y_259))
| ~ is_a_theorem(or(Y_259,implies(Y_258,Y_258))) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_857]) ).
tff(c_11491,plain,
! [X_729,Y_730] :
( is_a_theorem(or(equiv(X_729,X_729),and(Y_730,X_729)))
| ~ is_a_theorem(or(X_729,Y_730)) ),
inference(resolution,[status(thm)],[c_688,c_2324]) ).
tff(c_11531,plain,
! [Y_731,X_732] :
( is_a_theorem(or(Y_731,equiv(X_732,X_732)))
| ~ is_a_theorem(or(X_732,Y_731)) ),
inference(resolution,[status(thm)],[c_11491,c_856]) ).
tff(c_1673,plain,
! [P_222,Q_223] :
( is_a_theorem(P_222)
| ~ is_a_theorem(or(and(P_222,Q_223),and(P_222,Q_223))) ),
inference(resolution,[status(thm)],[c_1632,c_183]) ).
tff(c_1700,plain,
! [P_33] :
( is_a_theorem(P_33)
| ~ is_a_theorem(or(and(P_33,P_33),P_33)) ),
inference(resolution,[status(thm)],[c_855,c_1673]) ).
tff(c_11585,plain,
! [X_732] :
( is_a_theorem(equiv(X_732,X_732))
| ~ is_a_theorem(or(X_732,and(equiv(X_732,X_732),equiv(X_732,X_732)))) ),
inference(resolution,[status(thm)],[c_11531,c_1700]) ).
tff(c_11638,plain,
! [X_732] : is_a_theorem(equiv(X_732,X_732)),
inference(demodulation,[status(thm),theory(equality)],[c_8064,c_11585]) ).
tff(c_893,plain,
! [X_71] : is_a_theorem(or(not(X_71),X_71)),
inference(resolution,[status(thm)],[c_209,c_871]) ).
tff(c_277,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_294,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_277,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_265,plain,
~ is_a_theorem(implies(equiv('#skF_27','#skF_28'),implies('#skF_27','#skF_28'))),
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_317,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_294,c_265]) ).
tff(c_318,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_327,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_318,c_58]) ).
tff(c_334,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_327,c_183]) ).
tff(c_5094,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_334,c_818]) ).
tff(c_5199,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_893,c_5094]) ).
tff(c_870,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_864]) ).
tff(c_5310,plain,
! [X_433,Y_434] :
( is_a_theorem(implies(or(X_433,X_433),Y_434))
| ~ is_a_theorem(equiv(X_433,Y_434)) ),
inference(resolution,[status(thm)],[c_5199,c_870]) ).
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_5347,plain,
~ is_a_theorem(equiv('#skF_45','#skF_45')),
inference(resolution,[status(thm)],[c_5310,c_187]) ).
tff(c_11697,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11638,c_5347]) ).
tff(c_11698,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_11708,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_11698,c_94]) ).
tff(c_144,plain,
~ cn3,
inference(cnfTransformation,[status(thm)],[f_262]) ).
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_155,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_144,c_154]) ).
tff(c_11712,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11708,c_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL517+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % 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
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 3 13:31:36 EDT 2023
% 0.10/0.30 % CPUTime :
% 11.62/4.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.62/4.24
% 11.62/4.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.62/4.28
% 11.62/4.28 Inference rules
% 11.62/4.28 ----------------------
% 11.62/4.28 #Ref : 0
% 11.62/4.28 #Sup : 2806
% 11.62/4.28 #Fact : 0
% 11.62/4.28 #Define : 0
% 11.62/4.28 #Split : 44
% 11.62/4.28 #Chain : 0
% 11.62/4.28 #Close : 0
% 11.62/4.28
% 11.62/4.28 Ordering : KBO
% 11.62/4.28
% 11.62/4.28 Simplification rules
% 11.62/4.28 ----------------------
% 11.62/4.28 #Subsume : 925
% 11.62/4.28 #Demod : 1123
% 11.62/4.28 #Tautology : 258
% 11.62/4.28 #SimpNegUnit : 13
% 11.62/4.28 #BackRed : 9
% 11.62/4.28
% 11.62/4.28 #Partial instantiations: 0
% 11.62/4.28 #Strategies tried : 1
% 11.62/4.28
% 11.62/4.28 Timing (in seconds)
% 11.62/4.28 ----------------------
% 11.62/4.29 Preprocessing : 0.60
% 11.62/4.29 Parsing : 0.29
% 11.62/4.29 CNF conversion : 0.05
% 11.62/4.29 Main loop : 2.67
% 11.62/4.29 Inferencing : 0.74
% 11.62/4.29 Reduction : 1.00
% 11.62/4.29 Demodulation : 0.72
% 11.62/4.29 BG Simplification : 0.06
% 11.62/4.29 Subsumption : 0.71
% 11.62/4.29 Abstraction : 0.06
% 11.62/4.29 MUC search : 0.00
% 11.62/4.29 Cooper : 0.00
% 11.62/4.29 Total : 3.34
% 11.62/4.29 Index Insertion : 0.00
% 11.62/4.29 Index Deletion : 0.00
% 11.62/4.29 Index Matching : 0.00
% 11.62/4.29 BG Taut test : 0.00
%------------------------------------------------------------------------------