TSTP Solution File: LCL513+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL513+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 : n011.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 23.96s 13.67s
% Output : CNFRefutation 24.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 110
% Syntax : Number of formulae : 243 ( 79 unt; 92 typ; 0 def)
% Number of atoms : 237 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 169 ( 83 ~; 74 |; 1 &)
% ( 7 <=>; 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 : 252 (; 252 !; 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_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_258,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
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_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_262,negated_conjecture,
~ equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
tff(f_116,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
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_29633,plain,
! [X_1671,Y_1672] : ( not(and(X_1671,not(Y_1672))) = implies(X_1671,Y_1672) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_138,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_258]) ).
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_29645,plain,
! [X_1671,Y_1672,Y_57] : ( or(and(X_1671,not(Y_1672)),Y_57) = implies(implies(X_1671,Y_1672),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_29633,c_153]) ).
tff(c_29578,plain,
! [X_1659,Y_1660] : ( implies(not(X_1659),Y_1660) = or(X_1659,Y_1660) ),
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_29589,plain,
! [X_1659] : is_a_theorem(or(X_1659,and(not(X_1659),not(X_1659)))),
inference(superposition,[status(thm),theory(equality)],[c_29578,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_30400,plain,
! [P_1755,Q_1756,R_1757] : is_a_theorem(implies(implies(P_1755,Q_1756),or(and(Q_1756,R_1757),not(and(R_1757,P_1755))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_30431,plain,
! [Y_61,Q_1756,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_1756),or(and(Q_1756,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_30400]) ).
tff(c_30439,plain,
! [Y_1758,Q_1759,X_1760] : is_a_theorem(implies(or(Y_1758,Q_1759),or(and(Q_1759,X_1760),implies(X_1760,Y_1758)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_30431]) ).
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_30471,plain,
! [Q_1761,X_1762,Y_1763] :
( is_a_theorem(or(and(Q_1761,X_1762),implies(X_1762,Y_1763)))
| ~ is_a_theorem(or(Y_1763,Q_1761)) ),
inference(resolution,[status(thm)],[c_30439,c_184]) ).
tff(c_30493,plain,
! [Q_1761,X_56,Y_57] :
( is_a_theorem(or(and(Q_1761,not(X_56)),or(X_56,Y_57)))
| ~ is_a_theorem(or(Y_57,Q_1761)) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_30471]) ).
tff(c_30527,plain,
! [Q_1767,X_1768,Y_1769] :
( is_a_theorem(implies(implies(Q_1767,X_1768),or(X_1768,Y_1769)))
| ~ is_a_theorem(or(Y_1769,Q_1767)) ),
inference(demodulation,[status(thm),theory(equality)],[c_29645,c_30493]) ).
tff(c_30544,plain,
! [X_1770,Y_1771,Q_1772] :
( is_a_theorem(or(X_1770,Y_1771))
| ~ is_a_theorem(implies(Q_1772,X_1770))
| ~ is_a_theorem(or(Y_1771,Q_1772)) ),
inference(resolution,[status(thm)],[c_30527,c_184]) ).
tff(c_30602,plain,
! [P_1773,Y_1774,Q_1775] :
( is_a_theorem(or(P_1773,Y_1774))
| ~ is_a_theorem(or(Y_1774,and(P_1773,Q_1775))) ),
inference(resolution,[status(thm)],[c_163,c_30544]) ).
tff(c_30625,plain,
! [X_1776] : is_a_theorem(or(not(X_1776),X_1776)),
inference(resolution,[status(thm)],[c_29589,c_30602]) ).
tff(c_30600,plain,
! [P_34,Y_1771,Q_35] :
( is_a_theorem(or(P_34,Y_1771))
| ~ is_a_theorem(or(Y_1771,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_30544]) ).
tff(c_30673,plain,
! [P_1780,Q_1781] : is_a_theorem(or(P_1780,not(and(P_1780,Q_1781)))),
inference(resolution,[status(thm)],[c_30625,c_30600]) ).
tff(c_30694,plain,
! [X_1782,Y_1783] : is_a_theorem(or(X_1782,implies(X_1782,Y_1783))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_30673]) ).
tff(c_30707,plain,
! [X_56,Y_57] : is_a_theorem(or(not(X_56),or(X_56,Y_57))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_30694]) ).
tff(c_230,plain,
! [X_75,Y_76] : ( not(and(X_75,not(Y_76))) = implies(X_75,Y_76) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_233,plain,
! [X_60,X_75,Y_76] : ( implies(X_60,and(X_75,not(Y_76))) = not(and(X_60,implies(X_75,Y_76))) ),
inference(superposition,[status(thm),theory(equality)],[c_230,c_151]) ).
tff(c_239,plain,
! [X_75,Y_76,Y_57] : ( or(and(X_75,not(Y_76)),Y_57) = implies(implies(X_75,Y_76),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_230,c_153]) ).
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_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_509,plain,
! [P_106,Q_107,R_108] : is_a_theorem(implies(implies(P_106,Q_107),or(and(Q_107,R_108),not(and(R_108,P_106))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_525,plain,
! [Y_61,Q_107,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_107),or(and(Q_107,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_509]) ).
tff(c_661,plain,
! [Y_116,Q_117,X_118] : is_a_theorem(implies(or(Y_116,Q_117),or(and(Q_117,X_118),implies(X_118,Y_116)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_525]) ).
tff(c_734,plain,
! [Q_121,X_122,Y_123] :
( is_a_theorem(or(and(Q_121,X_122),implies(X_122,Y_123)))
| ~ is_a_theorem(or(Y_123,Q_121)) ),
inference(resolution,[status(thm)],[c_661,c_184]) ).
tff(c_750,plain,
! [X_75,Y_76,Y_123] :
( is_a_theorem(implies(implies(X_75,Y_76),implies(not(Y_76),Y_123)))
| ~ is_a_theorem(or(Y_123,X_75)) ),
inference(superposition,[status(thm),theory(equality)],[c_239,c_734]) ).
tff(c_799,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_750]) ).
tff(c_820,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_799,c_184]) ).
tff(c_874,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_820]) ).
tff(c_897,plain,
! [X_141] : is_a_theorem(or(not(X_141),X_141)),
inference(resolution,[status(thm)],[c_209,c_874]) ).
tff(c_858,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_820]) ).
tff(c_908,plain,
! [P_34,Q_35] : is_a_theorem(or(P_34,not(and(P_34,Q_35)))),
inference(resolution,[status(thm)],[c_897,c_858]) ).
tff(c_860,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_820]) ).
tff(c_867,plain,
! [Y_76,Y_57] :
( is_a_theorem(implies(implies(not(Y_76),Y_76),Y_57))
| ~ is_a_theorem(or(Y_57,not(Y_76))) ),
inference(superposition,[status(thm),theory(equality)],[c_239,c_860]) ).
tff(c_1444,plain,
! [Y_205,Y_206] :
( is_a_theorem(implies(or(Y_205,Y_205),Y_206))
| ~ is_a_theorem(or(Y_206,not(Y_205))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_867]) ).
tff(c_1644,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_908,c_1444]) ).
tff(c_1669,plain,
! [X_75,Y_76] : is_a_theorem(implies(implies(implies(X_75,Y_76),and(X_75,not(Y_76))),X_75)),
inference(superposition,[status(thm),theory(equality)],[c_239,c_1644]) ).
tff(c_1682,plain,
! [X_75,Y_76] : is_a_theorem(or(and(implies(X_75,Y_76),implies(X_75,Y_76)),X_75)),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_233,c_1669]) ).
tff(c_857,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_820]) ).
tff(c_5987,plain,
! [P_487,P_488,Q_489] :
( is_a_theorem(or(P_487,and(P_488,P_488)))
| ~ is_a_theorem(or(and(P_487,Q_489),P_488)) ),
inference(resolution,[status(thm)],[c_857,c_874]) ).
tff(c_6067,plain,
! [X_75,Y_76] : is_a_theorem(or(implies(X_75,Y_76),and(X_75,X_75))),
inference(resolution,[status(thm)],[c_1682,c_5987]) ).
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_6216,plain,
! [P_498,Y_499] :
( is_a_theorem(or(P_498,and(Y_499,Y_499)))
| ~ is_a_theorem(or(Y_499,P_498)) ),
inference(resolution,[status(thm)],[c_857,c_5987]) ).
tff(c_8487,plain,
! [P_589,Y_590] :
( is_a_theorem(or(P_589,equiv(Y_590,Y_590)))
| ~ is_a_theorem(or(implies(Y_590,Y_590),P_589)) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_6216]) ).
tff(c_8598,plain,
! [Y_591] : is_a_theorem(or(and(Y_591,Y_591),equiv(Y_591,Y_591))),
inference(resolution,[status(thm)],[c_6067,c_8487]) ).
tff(c_895,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_857,c_874]) ).
tff(c_8630,plain,
! [Y_591] : is_a_theorem(or(Y_591,and(equiv(Y_591,Y_591),equiv(Y_591,Y_591)))),
inference(resolution,[status(thm)],[c_8598,c_895]) ).
tff(c_684,plain,
! [Q_117,X_118,Y_116] :
( is_a_theorem(or(and(Q_117,X_118),implies(X_118,Y_116)))
| ~ is_a_theorem(or(Y_116,Q_117)) ),
inference(resolution,[status(thm)],[c_661,c_184]) ).
tff(c_4156,plain,
! [Y_367,Y_368] :
( is_a_theorem(or(equiv(Y_367,Y_367),Y_368))
| ~ is_a_theorem(or(Y_368,implies(Y_367,Y_367))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_860]) ).
tff(c_11044,plain,
! [Y_706,Q_707] :
( is_a_theorem(or(equiv(Y_706,Y_706),and(Q_707,Y_706)))
| ~ is_a_theorem(or(Y_706,Q_707)) ),
inference(resolution,[status(thm)],[c_684,c_4156]) ).
tff(c_11081,plain,
! [Q_708,Y_709] :
( is_a_theorem(or(Q_708,equiv(Y_709,Y_709)))
| ~ is_a_theorem(or(Y_709,Q_708)) ),
inference(resolution,[status(thm)],[c_11044,c_858]) ).
tff(c_1685,plain,
! [P_214,Q_215] :
( is_a_theorem(P_214)
| ~ is_a_theorem(or(and(P_214,Q_215),and(P_214,Q_215))) ),
inference(resolution,[status(thm)],[c_1644,c_184]) ).
tff(c_1712,plain,
! [P_33] :
( is_a_theorem(P_33)
| ~ is_a_theorem(or(and(P_33,P_33),P_33)) ),
inference(resolution,[status(thm)],[c_857,c_1685]) ).
tff(c_11150,plain,
! [Y_709] :
( is_a_theorem(equiv(Y_709,Y_709))
| ~ is_a_theorem(or(Y_709,and(equiv(Y_709,Y_709),equiv(Y_709,Y_709)))) ),
inference(resolution,[status(thm)],[c_11081,c_1712]) ).
tff(c_11194,plain,
! [Y_709] : is_a_theorem(equiv(Y_709,Y_709)),
inference(demodulation,[status(thm),theory(equality)],[c_8630,c_11150]) ).
tff(c_896,plain,
! [X_71] : is_a_theorem(or(not(X_71),X_71)),
inference(resolution,[status(thm)],[c_209,c_874]) ).
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_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_266,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_292,c_266]) ).
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_184]) ).
tff(c_5018,plain,
! [Y_420,Y_421,X_422] :
( is_a_theorem(or(Y_420,Y_421))
| ~ is_a_theorem(or(Y_421,X_422))
| ~ is_a_theorem(equiv(X_422,Y_420)) ),
inference(resolution,[status(thm)],[c_325,c_820]) ).
tff(c_5123,plain,
! [Y_423,X_424] :
( is_a_theorem(or(Y_423,not(X_424)))
| ~ is_a_theorem(equiv(X_424,Y_423)) ),
inference(resolution,[status(thm)],[c_896,c_5018]) ).
tff(c_873,plain,
! [Y_76,Y_57] :
( is_a_theorem(implies(or(Y_76,Y_76),Y_57))
| ~ is_a_theorem(or(Y_57,not(Y_76))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_867]) ).
tff(c_5293,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_5123,c_873]) ).
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_189,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_192,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_189,c_155]) ).
tff(c_5331,plain,
~ is_a_theorem(equiv('#skF_44','#skF_44')),
inference(resolution,[status(thm)],[c_5293,c_192]) ).
tff(c_11362,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11194,c_5331]) ).
tff(c_11363,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_31368,plain,
! [P_1822,Y_1823] :
( is_a_theorem(or(P_1822,Y_1823))
| ~ is_a_theorem(or(Y_1823,or(P_1822,P_1822))) ),
inference(resolution,[status(thm)],[c_11363,c_30544]) ).
tff(c_31406,plain,
! [Y_1824] : is_a_theorem(or(Y_1824,not(Y_1824))),
inference(resolution,[status(thm)],[c_30707,c_31368]) ).
tff(c_31419,plain,
! [X_60,Y_61] : is_a_theorem(or(and(X_60,not(Y_61)),implies(X_60,Y_61))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_31406]) ).
tff(c_31422,plain,
! [X_60,Y_61] : is_a_theorem(implies(implies(X_60,Y_61),implies(X_60,Y_61))),
inference(demodulation,[status(thm),theory(equality)],[c_29645,c_31419]) ).
tff(c_30802,plain,
! [Q_1788,R_1789,P_1790] :
( is_a_theorem(or(and(Q_1788,R_1789),not(and(R_1789,P_1790))))
| ~ is_a_theorem(implies(P_1790,Q_1788)) ),
inference(resolution,[status(thm)],[c_30400,c_184]) ).
tff(c_34787,plain,
! [X_2072,Y_2073,P_2074] :
( is_a_theorem(or(equiv(X_2072,Y_2073),not(and(implies(Y_2073,X_2072),P_2074))))
| ~ is_a_theorem(implies(P_2074,implies(X_2072,Y_2073))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_30802]) ).
tff(c_34807,plain,
! [Y_65,X_64] :
( is_a_theorem(or(equiv(Y_65,X_64),not(equiv(X_64,Y_65))))
| ~ is_a_theorem(implies(implies(Y_65,X_64),implies(Y_65,X_64))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_34787]) ).
tff(c_34822,plain,
! [Y_65,X_64] : is_a_theorem(or(equiv(Y_65,X_64),not(equiv(X_64,Y_65)))),
inference(demodulation,[status(thm),theory(equality)],[c_31422,c_34807]) ).
tff(c_31397,plain,
! [Y_57] : is_a_theorem(or(Y_57,not(Y_57))),
inference(resolution,[status(thm)],[c_30707,c_31368]) ).
tff(c_29599,plain,
! [Y_1663,X_1664] :
( is_a_theorem(Y_1663)
| ~ is_a_theorem(implies(X_1664,Y_1663))
| ~ is_a_theorem(X_1664) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_29602,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_29599]) ).
tff(c_31584,plain,
! [R_1836,P_1837,Q_1838] :
( is_a_theorem(not(and(R_1836,P_1837)))
| ~ is_a_theorem(not(and(Q_1838,R_1836)))
| ~ is_a_theorem(implies(P_1837,Q_1838)) ),
inference(resolution,[status(thm)],[c_30802,c_29602]) ).
tff(c_49466,plain,
! [Y_2727,P_2728,X_2729] :
( is_a_theorem(not(and(not(Y_2727),P_2728)))
| ~ is_a_theorem(implies(X_2729,Y_2727))
| ~ is_a_theorem(implies(P_2728,X_2729)) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_31584]) ).
tff(c_52190,plain,
! [P_2828,P_2829,Q_2830] :
( is_a_theorem(not(and(not(P_2828),P_2829)))
| ~ is_a_theorem(implies(P_2829,and(P_2828,Q_2830))) ),
inference(resolution,[status(thm)],[c_163,c_49466]) ).
tff(c_52288,plain,
! [P_2831] : is_a_theorem(not(and(not(P_2831),P_2831))),
inference(resolution,[status(thm)],[c_167,c_52190]) ).
tff(c_30494,plain,
! [X_1762,Y_1763,Q_1761] :
( is_a_theorem(implies(X_1762,Y_1763))
| ~ is_a_theorem(not(and(Q_1761,X_1762)))
| ~ is_a_theorem(or(Y_1763,Q_1761)) ),
inference(resolution,[status(thm)],[c_30471,c_29602]) ).
tff(c_52355,plain,
! [P_2834,Y_2835] :
( is_a_theorem(implies(P_2834,Y_2835))
| ~ is_a_theorem(or(Y_2835,not(P_2834))) ),
inference(resolution,[status(thm)],[c_52288,c_30494]) ).
tff(c_52720,plain,
! [Y_2836] : is_a_theorem(implies(Y_2836,Y_2836)),
inference(resolution,[status(thm)],[c_31397,c_52355]) ).
tff(c_30540,plain,
! [X_1768,Y_1769,Q_1767] :
( is_a_theorem(or(X_1768,Y_1769))
| ~ is_a_theorem(implies(Q_1767,X_1768))
| ~ is_a_theorem(or(Y_1769,Q_1767)) ),
inference(resolution,[status(thm)],[c_30527,c_184]) ).
tff(c_54835,plain,
! [Y_2908,Y_2909] :
( is_a_theorem(or(Y_2908,Y_2909))
| ~ is_a_theorem(or(Y_2909,Y_2908)) ),
inference(resolution,[status(thm)],[c_52720,c_30540]) ).
tff(c_61470,plain,
! [X_3032,Y_3033] : is_a_theorem(or(not(equiv(X_3032,Y_3033)),equiv(Y_3033,X_3032))),
inference(resolution,[status(thm)],[c_34822,c_54835]) ).
tff(c_29705,plain,
! [X_1680,Y_1681] : ( and(implies(X_1680,Y_1681),implies(Y_1681,X_1680)) = equiv(X_1680,Y_1681) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_29722,plain,
! [X_1680,Y_1681] : is_a_theorem(implies(equiv(X_1680,Y_1681),implies(X_1680,Y_1681))),
inference(superposition,[status(thm),theory(equality)],[c_29705,c_163]) ).
tff(c_29666,plain,
~ is_a_theorem(implies(equiv('#skF_27','#skF_28'),implies('#skF_27','#skF_28'))),
inference(splitLeft,[status(thm)],[c_56]) ).
tff(c_29745,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29722,c_29666]) ).
tff(c_29746,plain,
equivalence_1,
inference(splitRight,[status(thm)],[c_56]) ).
tff(c_29749,plain,
! [X_27,Y_28] : is_a_theorem(implies(equiv(X_27,Y_28),implies(X_27,Y_28))),
inference(demodulation,[status(thm),theory(equality)],[c_29746,c_58]) ).
tff(c_30596,plain,
! [X_27,Y_28,Y_1771] :
( is_a_theorem(or(implies(X_27,Y_28),Y_1771))
| ~ is_a_theorem(or(Y_1771,equiv(X_27,Y_28))) ),
inference(resolution,[status(thm)],[c_29749,c_30544]) ).
tff(c_63120,plain,
! [Y_3071,X_3072] : is_a_theorem(or(implies(Y_3071,X_3072),not(equiv(X_3072,Y_3071)))),
inference(resolution,[status(thm)],[c_61470,c_30596]) ).
tff(c_52314,plain,
! [P_2831,Y_1763] :
( is_a_theorem(implies(P_2831,Y_1763))
| ~ is_a_theorem(or(Y_1763,not(P_2831))) ),
inference(resolution,[status(thm)],[c_52288,c_30494]) ).
tff(c_63158,plain,
! [X_3072,Y_3071] : is_a_theorem(implies(equiv(X_3072,Y_3071),implies(Y_3071,X_3072))),
inference(resolution,[status(thm)],[c_63120,c_52314]) ).
tff(c_144,plain,
~ equivalence_2,
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_60,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv('#skF_29','#skF_30'),implies('#skF_30','#skF_29'))) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_170,plain,
~ is_a_theorem(implies(equiv('#skF_29','#skF_30'),implies('#skF_30','#skF_29'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_60]) ).
tff(c_63169,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_63158,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : LCL513+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % 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
% 0.14/0.37 % Computer : n011.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 13:55:05 EDT 2023
% 0.14/0.37 % CPUTime :
% 23.96/13.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.07/13.69
% 24.07/13.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.23/13.74
% 24.23/13.74 Inference rules
% 24.23/13.74 ----------------------
% 24.23/13.74 #Ref : 0
% 24.23/13.74 #Sup : 15467
% 24.23/13.74 #Fact : 0
% 24.23/13.74 #Define : 0
% 24.23/13.74 #Split : 108
% 24.23/13.74 #Chain : 0
% 24.23/13.74 #Close : 0
% 24.23/13.74
% 24.23/13.74 Ordering : KBO
% 24.23/13.74
% 24.23/13.74 Simplification rules
% 24.23/13.74 ----------------------
% 24.23/13.74 #Subsume : 4407
% 24.23/13.74 #Demod : 7339
% 24.23/13.74 #Tautology : 2103
% 24.23/13.74 #SimpNegUnit : 32
% 24.23/13.74 #BackRed : 34
% 24.23/13.74
% 24.23/13.74 #Partial instantiations: 0
% 24.23/13.74 #Strategies tried : 1
% 24.23/13.74
% 24.23/13.74 Timing (in seconds)
% 24.23/13.74 ----------------------
% 24.23/13.74 Preprocessing : 0.61
% 24.23/13.74 Parsing : 0.31
% 24.23/13.74 CNF conversion : 0.05
% 24.23/13.74 Main loop : 11.92
% 24.23/13.74 Inferencing : 2.41
% 24.23/13.74 Reduction : 4.94
% 24.23/13.74 Demodulation : 3.60
% 24.23/13.74 BG Simplification : 0.12
% 24.23/13.74 Subsumption : 3.84
% 24.23/13.74 Abstraction : 0.14
% 24.23/13.74 MUC search : 0.00
% 24.23/13.74 Cooper : 0.00
% 24.23/13.74 Total : 12.61
% 24.23/13.74 Index Insertion : 0.00
% 24.23/13.74 Index Deletion : 0.00
% 24.23/13.74 Index Matching : 0.00
% 24.23/13.74 BG Taut test : 0.00
%------------------------------------------------------------------------------