TSTP Solution File: LCL503+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL503+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 : n014.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 10:48:15 EDT 2023
% Result : Theorem 93.23s 78.35s
% Output : CNFRefutation 93.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 116
% Syntax : Number of formulae : 382 ( 146 unt; 92 typ; 0 def)
% Number of atoms : 467 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 352 ( 175 ~; 159 |; 1 &)
% ( 12 <=>; 5 =>; 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 : 34 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 540 (; 540 !; 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/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_259,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_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',hilbert_op_equiv) ).
tff(f_214,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_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_146,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_100,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
tff(f_142,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn2) ).
tff(f_159,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
tff(f_104,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_2) ).
tff(f_254,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',substitution_of_equivalents) ).
tff(f_67,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_262,negated_conjecture,
~ implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
tff(f_76,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(c_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_62633,plain,
! [X_3533,Y_3534] : ( implies(not(X_3533),Y_3534) = or(X_3533,Y_3534) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_151,c_112]) ).
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_42522,plain,
! [X_2461,Y_2462] : ( not(and(X_2461,not(Y_2462))) = implies(X_2461,Y_2462) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_43143,plain,
! [X_2523,X_2524,Y_2525] : ( implies(X_2523,and(X_2524,not(Y_2525))) = not(and(X_2523,implies(X_2524,Y_2525))) ),
inference(superposition,[status(thm),theory(equality)],[c_42522,c_151]) ).
tff(c_43220,plain,
! [X_56,X_2524,Y_2525] : ( not(and(not(X_56),implies(X_2524,Y_2525))) = or(X_56,and(X_2524,not(Y_2525))) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_43143]) ).
tff(c_42525,plain,
! [X_60,X_2461,Y_2462] : ( implies(X_60,and(X_2461,not(Y_2462))) = not(and(X_60,implies(X_2461,Y_2462))) ),
inference(superposition,[status(thm),theory(equality)],[c_42522,c_151]) ).
tff(c_42534,plain,
! [X_2461,Y_2462,Y_57] : ( or(and(X_2461,not(Y_2462)),Y_57) = implies(implies(X_2461,Y_2462),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_42522,c_153]) ).
tff(c_229,plain,
! [X_76,Y_77] : ( not(and(X_76,not(Y_77))) = implies(X_76,Y_77) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_232,plain,
! [X_60,X_76,Y_77] : ( implies(X_60,and(X_76,not(Y_77))) = not(and(X_60,implies(X_76,Y_77))) ),
inference(superposition,[status(thm),theory(equality)],[c_229,c_151]) ).
tff(c_238,plain,
! [X_76,Y_77,Y_57] : ( or(and(X_76,not(Y_77)),Y_57) = implies(implies(X_76,Y_77),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_229,c_153]) ).
tff(c_203,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_210,plain,
! [X_71] : is_a_theorem(or(X_71,and(not(X_71),not(X_71)))),
inference(superposition,[status(thm),theory(equality)],[c_203,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_694,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_725,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_694]) ).
tff(c_734,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_725]) ).
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_771,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_734,c_184]) ).
tff(c_787,plain,
! [X_76,Y_77,Y_126] :
( is_a_theorem(implies(implies(X_76,Y_77),implies(not(Y_77),Y_126)))
| ~ is_a_theorem(or(Y_126,X_76)) ),
inference(superposition,[status(thm),theory(equality)],[c_238,c_771]) ).
tff(c_818,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_787]) ).
tff(c_840,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_818,c_184]) ).
tff(c_893,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_840]) ).
tff(c_916,plain,
! [X_141] : is_a_theorem(or(not(X_141),X_141)),
inference(resolution,[status(thm)],[c_210,c_893]) ).
tff(c_878,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_840]) ).
tff(c_927,plain,
! [P_34,Q_35] : is_a_theorem(or(P_34,not(and(P_34,Q_35)))),
inference(resolution,[status(thm)],[c_916,c_878]) ).
tff(c_879,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_840]) ).
tff(c_886,plain,
! [Y_77,Y_57] :
( is_a_theorem(implies(implies(not(Y_77),Y_77),Y_57))
| ~ is_a_theorem(or(Y_57,not(Y_77))) ),
inference(superposition,[status(thm),theory(equality)],[c_238,c_879]) ).
tff(c_1731,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_886]) ).
tff(c_1790,plain,
! [P_223,Q_224] : is_a_theorem(implies(or(and(P_223,Q_224),and(P_223,Q_224)),P_223)),
inference(resolution,[status(thm)],[c_927,c_1731]) ).
tff(c_1815,plain,
! [X_76,Y_77] : is_a_theorem(implies(implies(implies(X_76,Y_77),and(X_76,not(Y_77))),X_76)),
inference(superposition,[status(thm),theory(equality)],[c_238,c_1790]) ).
tff(c_1828,plain,
! [X_76,Y_77] : is_a_theorem(or(and(implies(X_76,Y_77),implies(X_76,Y_77)),X_76)),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_232,c_1815]) ).
tff(c_877,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_840]) ).
tff(c_6123,plain,
! [P_495,P_496,Q_497] :
( is_a_theorem(or(P_495,and(P_496,P_496)))
| ~ is_a_theorem(or(and(P_495,Q_497),P_496)) ),
inference(resolution,[status(thm)],[c_877,c_893]) ).
tff(c_6203,plain,
! [X_76,Y_77] : is_a_theorem(or(implies(X_76,Y_77),and(X_76,X_76))),
inference(resolution,[status(thm)],[c_1828,c_6123]) ).
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_6393,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_877,c_6123]) ).
tff(c_8253,plain,
! [P_587,Y_588] :
( is_a_theorem(or(P_587,equiv(Y_588,Y_588)))
| ~ is_a_theorem(or(implies(Y_588,Y_588),P_587)) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_6393]) ).
tff(c_8360,plain,
! [Y_589] : is_a_theorem(or(and(Y_589,Y_589),equiv(Y_589,Y_589))),
inference(resolution,[status(thm)],[c_6203,c_8253]) ).
tff(c_914,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_877,c_893]) ).
tff(c_8392,plain,
! [Y_589] : is_a_theorem(or(Y_589,and(equiv(Y_589,Y_589),equiv(Y_589,Y_589)))),
inference(resolution,[status(thm)],[c_8360,c_914]) ).
tff(c_760,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_734,c_184]) ).
tff(c_3869,plain,
! [Y_352,Y_353] :
( is_a_theorem(or(equiv(Y_352,Y_352),Y_353))
| ~ is_a_theorem(or(Y_353,implies(Y_352,Y_352))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_879]) ).
tff(c_11643,plain,
! [Y_733,Q_734] :
( is_a_theorem(or(equiv(Y_733,Y_733),and(Q_734,Y_733)))
| ~ is_a_theorem(or(Y_733,Q_734)) ),
inference(resolution,[status(thm)],[c_760,c_3869]) ).
tff(c_11683,plain,
! [Q_735,Y_736] :
( is_a_theorem(or(Q_735,equiv(Y_736,Y_736)))
| ~ is_a_theorem(or(Y_736,Q_735)) ),
inference(resolution,[status(thm)],[c_11643,c_878]) ).
tff(c_1831,plain,
! [P_225,Q_226] :
( is_a_theorem(P_225)
| ~ is_a_theorem(or(and(P_225,Q_226),and(P_225,Q_226))) ),
inference(resolution,[status(thm)],[c_1790,c_184]) ).
tff(c_1858,plain,
! [P_33] :
( is_a_theorem(P_33)
| ~ is_a_theorem(or(and(P_33,P_33),P_33)) ),
inference(resolution,[status(thm)],[c_877,c_1831]) ).
tff(c_11737,plain,
! [Y_736] :
( is_a_theorem(equiv(Y_736,Y_736))
| ~ is_a_theorem(or(Y_736,and(equiv(Y_736,Y_736),equiv(Y_736,Y_736)))) ),
inference(resolution,[status(thm)],[c_11683,c_1858]) ).
tff(c_11790,plain,
! [Y_736] : is_a_theorem(equiv(Y_736,Y_736)),
inference(demodulation,[status(thm),theory(equality)],[c_8392,c_11737]) ).
tff(c_915,plain,
! [X_71] : is_a_theorem(or(not(X_71),X_71)),
inference(resolution,[status(thm)],[c_210,c_893]) ).
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_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_262,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_262,c_56]) ).
tff(c_318,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_294,c_266]) ).
tff(c_321,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_328,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_321,c_184]) ).
tff(c_5079,plain,
! [Y_424,Y_425,X_426] :
( is_a_theorem(or(Y_424,Y_425))
| ~ is_a_theorem(or(Y_425,X_426))
| ~ is_a_theorem(equiv(X_426,Y_424)) ),
inference(resolution,[status(thm)],[c_328,c_840]) ).
tff(c_5217,plain,
! [Y_430,X_431] :
( is_a_theorem(or(Y_430,not(X_431)))
| ~ is_a_theorem(equiv(X_431,Y_430)) ),
inference(resolution,[status(thm)],[c_915,c_5079]) ).
tff(c_892,plain,
! [Y_77,Y_57] :
( is_a_theorem(implies(or(Y_77,Y_77),Y_57))
| ~ is_a_theorem(or(Y_57,not(Y_77))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_886]) ).
tff(c_5327,plain,
! [X_435,Y_436] :
( is_a_theorem(implies(or(X_435,X_435),Y_436))
| ~ is_a_theorem(equiv(X_435,Y_436)) ),
inference(resolution,[status(thm)],[c_5217,c_892]) ).
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_188,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_189,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_188,c_155]) ).
tff(c_5365,plain,
~ is_a_theorem(equiv('#skF_44','#skF_44')),
inference(resolution,[status(thm)],[c_5327,c_189]) ).
tff(c_11854,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11790,c_5365]) ).
tff(c_11855,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_43202,plain,
! [X_2524,Y_2525] : is_a_theorem(not(and(or(and(X_2524,not(Y_2525)),and(X_2524,not(Y_2525))),implies(X_2524,Y_2525)))),
inference(superposition,[status(thm),theory(equality)],[c_43143,c_11855]) ).
tff(c_43227,plain,
! [X_2524,Y_2525] : is_a_theorem(not(and(not(and(implies(X_2524,Y_2525),implies(X_2524,Y_2525))),implies(X_2524,Y_2525)))),
inference(demodulation,[status(thm),theory(equality)],[c_42525,c_42534,c_43202]) ).
tff(c_44471,plain,
! [X_2620,Y_2621] : is_a_theorem(or(and(implies(X_2620,Y_2621),implies(X_2620,Y_2621)),and(X_2620,not(Y_2621)))),
inference(demodulation,[status(thm),theory(equality)],[c_43220,c_43227]) ).
tff(c_43108,plain,
! [P_2520,Q_2521,R_2522] : is_a_theorem(implies(implies(P_2520,Q_2521),or(and(Q_2521,R_2522),not(and(R_2522,P_2520))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_43136,plain,
! [Y_61,Q_2521,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_2521),or(and(Q_2521,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_43108]) ).
tff(c_43259,plain,
! [Y_2527,Q_2528,X_2529] : is_a_theorem(implies(or(Y_2527,Q_2528),or(and(Q_2528,X_2529),implies(X_2529,Y_2527)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_43136]) ).
tff(c_43284,plain,
! [Y_57,Q_2528,X_56] : is_a_theorem(implies(or(Y_57,Q_2528),or(and(Q_2528,not(X_56)),or(X_56,Y_57)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_43259]) ).
tff(c_43352,plain,
! [Y_2536,Q_2537,X_2538] : is_a_theorem(implies(or(Y_2536,Q_2537),implies(implies(Q_2537,X_2538),or(X_2538,Y_2536)))),
inference(demodulation,[status(thm),theory(equality)],[c_42534,c_43284]) ).
tff(c_43424,plain,
! [Q_2541,X_2542,Y_2543] :
( is_a_theorem(implies(implies(Q_2541,X_2542),or(X_2542,Y_2543)))
| ~ is_a_theorem(or(Y_2543,Q_2541)) ),
inference(resolution,[status(thm)],[c_43352,c_184]) ).
tff(c_43489,plain,
! [X_2549,Y_2550,Q_2551] :
( is_a_theorem(or(X_2549,Y_2550))
| ~ is_a_theorem(implies(Q_2551,X_2549))
| ~ is_a_theorem(or(Y_2550,Q_2551)) ),
inference(resolution,[status(thm)],[c_43424,c_184]) ).
tff(c_43545,plain,
! [P_34,Y_2550,Q_35] :
( is_a_theorem(or(P_34,Y_2550))
| ~ is_a_theorem(or(Y_2550,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_43489]) ).
tff(c_44672,plain,
! [X_2641,Y_2642] : is_a_theorem(or(X_2641,and(implies(X_2641,Y_2642),implies(X_2641,Y_2642)))),
inference(resolution,[status(thm)],[c_44471,c_43545]) ).
tff(c_44699,plain,
! [X_2641,Y_2642] : is_a_theorem(or(implies(X_2641,Y_2642),X_2641)),
inference(resolution,[status(thm)],[c_44672,c_43545]) ).
tff(c_43458,plain,
! [Q_2546,R_2547,P_2548] :
( is_a_theorem(or(and(Q_2546,R_2547),not(and(R_2547,P_2548))))
| ~ is_a_theorem(implies(P_2548,Q_2546)) ),
inference(resolution,[status(thm)],[c_43108,c_184]) ).
tff(c_45243,plain,
! [X_2703,Y_2704,P_2705] :
( is_a_theorem(implies(implies(X_2703,Y_2704),not(and(not(Y_2704),P_2705))))
| ~ is_a_theorem(implies(P_2705,X_2703)) ),
inference(superposition,[status(thm),theory(equality)],[c_42534,c_43458]) ).
tff(c_61622,plain,
! [Y_3507,P_3508,X_3509] :
( is_a_theorem(not(and(not(Y_3507),P_3508)))
| ~ is_a_theorem(implies(X_3509,Y_3507))
| ~ is_a_theorem(implies(P_3508,X_3509)) ),
inference(resolution,[status(thm)],[c_45243,c_184]) ).
tff(c_61903,plain,
! [P_3513,P_3514,Q_3515] :
( is_a_theorem(not(and(not(P_3513),P_3514)))
| ~ is_a_theorem(implies(P_3514,and(P_3513,Q_3515))) ),
inference(resolution,[status(thm)],[c_163,c_61622]) ).
tff(c_61997,plain,
! [P_3516] : is_a_theorem(not(and(not(P_3516),P_3516))),
inference(resolution,[status(thm)],[c_167,c_61903]) ).
tff(c_43325,plain,
! [Q_2533,X_2534,Y_2535] :
( is_a_theorem(or(and(Q_2533,X_2534),implies(X_2534,Y_2535)))
| ~ is_a_theorem(or(Y_2535,Q_2533)) ),
inference(resolution,[status(thm)],[c_43259,c_184]) ).
tff(c_42544,plain,
! [Y_2463,X_2464] :
( is_a_theorem(Y_2463)
| ~ is_a_theorem(implies(X_2464,Y_2463))
| ~ is_a_theorem(X_2464) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_42547,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_42544]) ).
tff(c_43348,plain,
! [X_2534,Y_2535,Q_2533] :
( is_a_theorem(implies(X_2534,Y_2535))
| ~ is_a_theorem(not(and(Q_2533,X_2534)))
| ~ is_a_theorem(or(Y_2535,Q_2533)) ),
inference(resolution,[status(thm)],[c_43325,c_42547]) ).
tff(c_62064,plain,
! [P_3519,Y_3520] :
( is_a_theorem(implies(P_3519,Y_3520))
| ~ is_a_theorem(or(Y_3520,not(P_3519))) ),
inference(resolution,[status(thm)],[c_61997,c_43348]) ).
tff(c_62256,plain,
! [P_3519,Y_2642] : is_a_theorem(implies(P_3519,implies(not(P_3519),Y_2642))),
inference(resolution,[status(thm)],[c_44699,c_62064]) ).
tff(c_62366,plain,
! [P_3519,Y_2642] : is_a_theorem(implies(P_3519,or(P_3519,Y_2642))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_62256]) ).
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_42497,plain,
~ or_1,
inference(splitLeft,[status(thm)],[c_46]) ).
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_42499,plain,
~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))),
inference(negUnitSimplification,[status(thm)],[c_42497,c_44]) ).
tff(c_62603,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_62366,c_42499]) ).
tff(c_62604,plain,
! [X_20,Y_21] : is_a_theorem(implies(X_20,or(X_20,Y_21))),
inference(splitRight,[status(thm)],[c_46]) ).
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_42496,plain,
~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))),
inference(splitLeft,[status(thm)],[c_157]) ).
tff(c_62608,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_62604,c_42496]) ).
tff(c_62609,plain,
cn2,
inference(splitRight,[status(thm)],[c_157]) ).
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_62627,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(demodulation,[status(thm),theory(equality)],[c_62609,c_156]) ).
tff(c_62640,plain,
! [X_3533,Q_43] : is_a_theorem(or(X_3533,or(not(X_3533),Q_43))),
inference(superposition,[status(thm),theory(equality)],[c_62633,c_62627]) ).
tff(c_62657,plain,
! [X_3539,Y_3540] : ( not(and(X_3539,not(Y_3540))) = implies(X_3539,Y_3540) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_62672,plain,
! [X_3539,Y_3540,Y_57] : ( or(and(X_3539,not(Y_3540)),Y_57) = implies(implies(X_3539,Y_3540),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_62657,c_153]) ).
tff(c_63555,plain,
! [P_3619,Q_3620,R_3621] : is_a_theorem(implies(implies(P_3619,Q_3620),or(and(Q_3620,R_3621),not(and(R_3621,P_3619))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_63586,plain,
! [Y_61,Q_3620,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_3620),or(and(Q_3620,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_63555]) ).
tff(c_63620,plain,
! [Y_3624,Q_3625,X_3626] : is_a_theorem(implies(or(Y_3624,Q_3625),or(and(Q_3625,X_3626),implies(X_3626,Y_3624)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_63586]) ).
tff(c_63704,plain,
! [Q_3633,X_3634,Y_3635] :
( is_a_theorem(or(and(Q_3633,X_3634),implies(X_3634,Y_3635)))
| ~ is_a_theorem(or(Y_3635,Q_3633)) ),
inference(resolution,[status(thm)],[c_63620,c_184]) ).
tff(c_63720,plain,
! [X_3539,Y_3540,Y_3635] :
( is_a_theorem(implies(implies(X_3539,Y_3540),implies(not(Y_3540),Y_3635)))
| ~ is_a_theorem(or(Y_3635,X_3539)) ),
inference(superposition,[status(thm),theory(equality)],[c_62672,c_63704]) ).
tff(c_63790,plain,
! [X_3642,Y_3643,Y_3644] :
( is_a_theorem(implies(implies(X_3642,Y_3643),or(Y_3643,Y_3644)))
| ~ is_a_theorem(or(Y_3644,X_3642)) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_63720]) ).
tff(c_63935,plain,
! [Y_3659,Y_3660,X_3661] :
( is_a_theorem(or(Y_3659,Y_3660))
| ~ is_a_theorem(implies(X_3661,Y_3659))
| ~ is_a_theorem(or(Y_3660,X_3661)) ),
inference(resolution,[status(thm)],[c_63790,c_184]) ).
tff(c_64046,plain,
! [P_3668,Y_3669] :
( is_a_theorem(or(P_3668,Y_3669))
| ~ is_a_theorem(or(Y_3669,or(P_3668,P_3668))) ),
inference(resolution,[status(thm)],[c_11855,c_63935]) ).
tff(c_64084,plain,
! [X_3533] : is_a_theorem(or(not(X_3533),X_3533)),
inference(resolution,[status(thm)],[c_62640,c_64046]) ).
tff(c_63758,plain,
! [Q_3639,R_3640,P_3641] :
( is_a_theorem(or(and(Q_3639,R_3640),not(and(R_3640,P_3641))))
| ~ is_a_theorem(implies(P_3641,Q_3639)) ),
inference(resolution,[status(thm)],[c_63555,c_184]) ).
tff(c_64793,plain,
! [X_3719,Y_3720,P_3721] :
( is_a_theorem(implies(implies(X_3719,Y_3720),not(and(not(Y_3720),P_3721))))
| ~ is_a_theorem(implies(P_3721,X_3719)) ),
inference(superposition,[status(thm),theory(equality)],[c_62672,c_63758]) ).
tff(c_81683,plain,
! [Y_4639,P_4640,X_4641] :
( is_a_theorem(not(and(not(Y_4639),P_4640)))
| ~ is_a_theorem(implies(X_4641,Y_4639))
| ~ is_a_theorem(implies(P_4640,X_4641)) ),
inference(resolution,[status(thm)],[c_64793,c_184]) ).
tff(c_95640,plain,
! [P_5048,P_5049,Q_5050] :
( is_a_theorem(not(and(not(P_5048),P_5049)))
| ~ is_a_theorem(implies(P_5049,and(P_5048,Q_5050))) ),
inference(resolution,[status(thm)],[c_163,c_81683]) ).
tff(c_95729,plain,
! [P_5051] : is_a_theorem(not(and(not(P_5051),P_5051))),
inference(resolution,[status(thm)],[c_167,c_95640]) ).
tff(c_62681,plain,
! [Y_3541,X_3542] :
( is_a_theorem(Y_3541)
| ~ is_a_theorem(implies(X_3542,Y_3541))
| ~ is_a_theorem(X_3542) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_62684,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_62681]) ).
tff(c_63727,plain,
! [X_3634,Y_3635,Q_3633] :
( is_a_theorem(implies(X_3634,Y_3635))
| ~ is_a_theorem(not(and(Q_3633,X_3634)))
| ~ is_a_theorem(or(Y_3635,Q_3633)) ),
inference(resolution,[status(thm)],[c_63704,c_62684]) ).
tff(c_95805,plain,
! [P_5053,Y_5054] :
( is_a_theorem(implies(P_5053,Y_5054))
| ~ is_a_theorem(or(Y_5054,not(P_5053))) ),
inference(resolution,[status(thm)],[c_95729,c_63727]) ).
tff(c_96296,plain,
! [P_5053] : is_a_theorem(implies(P_5053,not(not(P_5053)))),
inference(resolution,[status(thm)],[c_64084,c_95805]) ).
tff(c_62915,plain,
! [X_3572,Y_3573] : ( and(implies(X_3572,Y_3573),implies(Y_3573,X_3572)) = equiv(X_3572,Y_3573) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_62938,plain,
! [X_56,Y_57] : ( and(or(X_56,Y_57),implies(Y_57,not(X_56))) = equiv(not(X_56),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_62915]) ).
tff(c_96501,plain,
! [P_5061] : is_a_theorem(implies(P_5061,not(not(P_5061)))),
inference(resolution,[status(thm)],[c_64084,c_95805]) ).
tff(c_96908,plain,
! [X_5070] : is_a_theorem(or(X_5070,not(not(not(X_5070))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_96501]) ).
tff(c_64005,plain,
! [P_42,Q_43,Y_3660] :
( is_a_theorem(or(or(P_42,Q_43),Y_3660))
| ~ is_a_theorem(or(Y_3660,P_42)) ),
inference(resolution,[status(thm)],[c_62627,c_63935]) ).
tff(c_11874,plain,
! [X_739,Y_740] : ( implies(not(X_739),Y_740) = or(X_739,Y_740) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_151,c_112]) ).
tff(c_11881,plain,
! [X_739] : is_a_theorem(or(X_739,and(not(X_739),not(X_739)))),
inference(superposition,[status(thm),theory(equality)],[c_11874,c_167]) ).
tff(c_11887,plain,
! [X_741,Y_742] : ( not(and(X_741,not(Y_742))) = implies(X_741,Y_742) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_11896,plain,
! [X_741,Y_742,Y_57] : ( or(and(X_741,not(Y_742)),Y_57) = implies(implies(X_741,Y_742),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_11887,c_153]) ).
tff(c_12375,plain,
! [P_787,Q_788,R_789] : is_a_theorem(implies(implies(P_787,Q_788),or(and(Q_788,R_789),not(and(R_789,P_787))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_12406,plain,
! [Y_61,Q_788,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_788),or(and(Q_788,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_12375]) ).
tff(c_12414,plain,
! [Y_790,Q_791,X_792] : is_a_theorem(implies(or(Y_790,Q_791),or(and(Q_791,X_792),implies(X_792,Y_790)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_12406]) ).
tff(c_12439,plain,
! [Y_57,Q_791,X_56] : is_a_theorem(implies(or(Y_57,Q_791),or(and(Q_791,not(X_56)),or(X_56,Y_57)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_12414]) ).
tff(c_12478,plain,
! [Y_796,Q_797,X_798] : is_a_theorem(implies(or(Y_796,Q_797),implies(implies(Q_797,X_798),or(X_798,Y_796)))),
inference(demodulation,[status(thm),theory(equality)],[c_11896,c_12439]) ).
tff(c_12499,plain,
! [Q_799,X_800,Y_801] :
( is_a_theorem(implies(implies(Q_799,X_800),or(X_800,Y_801)))
| ~ is_a_theorem(or(Y_801,Q_799)) ),
inference(resolution,[status(thm)],[c_12478,c_184]) ).
tff(c_12520,plain,
! [X_802,Y_803,Q_804] :
( is_a_theorem(or(X_802,Y_803))
| ~ is_a_theorem(implies(Q_804,X_802))
| ~ is_a_theorem(or(Y_803,Q_804)) ),
inference(resolution,[status(thm)],[c_12499,c_184]) ).
tff(c_12597,plain,
! [P_809,Y_810,Q_811] :
( is_a_theorem(or(P_809,Y_810))
| ~ is_a_theorem(or(Y_810,and(P_809,Q_811))) ),
inference(resolution,[status(thm)],[c_163,c_12520]) ).
tff(c_12620,plain,
! [X_812] : is_a_theorem(or(not(X_812),X_812)),
inference(resolution,[status(thm)],[c_11881,c_12597]) ).
tff(c_12561,plain,
! [P_34,Y_803,Q_35] :
( is_a_theorem(or(P_34,Y_803))
| ~ is_a_theorem(or(Y_803,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_12520]) ).
tff(c_12643,plain,
! [P_814,Q_815] : is_a_theorem(or(P_814,not(and(P_814,Q_815)))),
inference(resolution,[status(thm)],[c_12620,c_12561]) ).
tff(c_12664,plain,
! [X_816,Y_817] : is_a_theorem(or(X_816,implies(X_816,Y_817))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_12643]) ).
tff(c_12852,plain,
! [X_827,Y_828] : is_a_theorem(or(not(X_827),or(X_827,Y_828))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_12664]) ).
tff(c_12559,plain,
! [P_44,Y_803] :
( is_a_theorem(or(P_44,Y_803))
| ~ is_a_theorem(or(Y_803,or(P_44,P_44))) ),
inference(resolution,[status(thm)],[c_11855,c_12520]) ).
tff(c_12866,plain,
! [Y_828] : is_a_theorem(or(Y_828,not(Y_828))),
inference(resolution,[status(thm)],[c_12852,c_12559]) ).
tff(c_19730,plain,
! [Y_1263,X_1264,Y_1265] : is_a_theorem(implies(or(Y_1263,not(X_1264)),implies(or(X_1264,Y_1265),or(Y_1265,Y_1263)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_12478]) ).
tff(c_23372,plain,
! [X_1446,Y_1447,Y_1448] :
( is_a_theorem(implies(or(X_1446,Y_1447),or(Y_1447,Y_1448)))
| ~ is_a_theorem(or(Y_1448,not(X_1446))) ),
inference(resolution,[status(thm)],[c_19730,c_184]) ).
tff(c_102,plain,
! [P_48,Q_49] :
( is_a_theorem(implies(or(P_48,Q_49),or(Q_49,P_48)))
| ~ r3 ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_11929,plain,
~ r3,
inference(splitLeft,[status(thm)],[c_102]) ).
tff(c_100,plain,
( r3
| ~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_12005,plain,
~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))),
inference(negUnitSimplification,[status(thm)],[c_11929,c_100]) ).
tff(c_23381,plain,
~ is_a_theorem(or('#skF_48',not('#skF_48'))),
inference(resolution,[status(thm)],[c_23372,c_12005]) ).
tff(c_23398,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12866,c_23381]) ).
tff(c_23399,plain,
! [P_48,Q_49] : is_a_theorem(implies(or(P_48,Q_49),or(Q_49,P_48))),
inference(splitRight,[status(thm)],[c_102]) ).
tff(c_23661,plain,
! [X_1477,Y_1478,Y_1479] : ( or(and(X_1477,not(Y_1478)),Y_1479) = implies(implies(X_1477,Y_1478),Y_1479) ),
inference(superposition,[status(thm),theory(equality)],[c_11887,c_153]) ).
tff(c_23401,plain,
! [P_1449,Q_1450] : is_a_theorem(implies(or(P_1449,Q_1450),or(Q_1450,P_1449))),
inference(splitRight,[status(thm)],[c_102]) ).
tff(c_23405,plain,
! [Q_1450,P_1449] :
( is_a_theorem(or(Q_1450,P_1449))
| ~ is_a_theorem(or(P_1449,Q_1450)) ),
inference(resolution,[status(thm)],[c_23401,c_184]) ).
tff(c_25450,plain,
! [Y_1619,X_1620,Y_1621] :
( is_a_theorem(or(Y_1619,and(X_1620,not(Y_1621))))
| ~ is_a_theorem(implies(implies(X_1620,Y_1621),Y_1619)) ),
inference(superposition,[status(thm),theory(equality)],[c_23661,c_23405]) ).
tff(c_23911,plain,
! [P_1493,Q_1494,R_1495] : is_a_theorem(implies(implies(P_1493,Q_1494),or(and(Q_1494,R_1495),not(and(R_1495,P_1493))))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_153,c_78]) ).
tff(c_23942,plain,
! [Y_61,Q_1494,X_60] : is_a_theorem(implies(implies(not(Y_61),Q_1494),or(and(Q_1494,X_60),implies(X_60,Y_61)))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_23911]) ).
tff(c_23950,plain,
! [Y_1496,Q_1497,X_1498] : is_a_theorem(implies(or(Y_1496,Q_1497),or(and(Q_1497,X_1498),implies(X_1498,Y_1496)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_23942]) ).
tff(c_23975,plain,
! [Y_57,Q_1497,X_56] : is_a_theorem(implies(or(Y_57,Q_1497),or(and(Q_1497,not(X_56)),or(X_56,Y_57)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_23950]) ).
tff(c_23987,plain,
! [Y_1499,Q_1500,X_1501] : is_a_theorem(implies(or(Y_1499,Q_1500),implies(implies(Q_1500,X_1501),or(X_1501,Y_1499)))),
inference(demodulation,[status(thm),theory(equality)],[c_11896,c_23975]) ).
tff(c_24042,plain,
! [Q_1505,X_1506,Y_1507] :
( is_a_theorem(implies(implies(Q_1505,X_1506),or(X_1506,Y_1507)))
| ~ is_a_theorem(or(Y_1507,Q_1505)) ),
inference(resolution,[status(thm)],[c_23987,c_184]) ).
tff(c_24084,plain,
! [X_1511,Y_1512,Q_1513] :
( is_a_theorem(or(X_1511,Y_1512))
| ~ is_a_theorem(implies(Q_1513,X_1511))
| ~ is_a_theorem(or(Y_1512,Q_1513)) ),
inference(resolution,[status(thm)],[c_24042,c_184]) ).
tff(c_24128,plain,
! [P_34,Y_1512,Q_35] :
( is_a_theorem(or(P_34,Y_1512))
| ~ is_a_theorem(or(Y_1512,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_24084]) ).
tff(c_25515,plain,
! [X_1628,Y_1629,Y_1630] :
( is_a_theorem(or(X_1628,Y_1629))
| ~ is_a_theorem(implies(implies(X_1628,Y_1630),Y_1629)) ),
inference(resolution,[status(thm)],[c_25450,c_24128]) ).
tff(c_28263,plain,
! [X_1833,Y_1834,Y_1835] :
( is_a_theorem(or(not(X_1833),Y_1834))
| ~ is_a_theorem(implies(or(X_1833,Y_1835),Y_1834)) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_25515]) ).
tff(c_28318,plain,
! [P_1836,Q_1837] : is_a_theorem(or(not(P_1836),or(Q_1837,P_1836))),
inference(resolution,[status(thm)],[c_23399,c_28263]) ).
tff(c_28340,plain,
! [Q_1837,P_1836] : is_a_theorem(or(or(Q_1837,P_1836),not(P_1836))),
inference(resolution,[status(thm)],[c_28318,c_23405]) ).
tff(c_24515,plain,
! [Q_1539,R_1540,P_1541] :
( is_a_theorem(or(and(Q_1539,R_1540),not(and(R_1540,P_1541))))
| ~ is_a_theorem(implies(P_1541,Q_1539)) ),
inference(resolution,[status(thm)],[c_23911,c_184]) ).
tff(c_11906,plain,
! [Y_743,X_744] :
( is_a_theorem(Y_743)
| ~ is_a_theorem(implies(X_744,Y_743))
| ~ is_a_theorem(X_744) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_11909,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_11906]) ).
tff(c_28005,plain,
! [R_1815,P_1816,Q_1817] :
( is_a_theorem(not(and(R_1815,P_1816)))
| ~ is_a_theorem(not(and(Q_1817,R_1815)))
| ~ is_a_theorem(implies(P_1816,Q_1817)) ),
inference(resolution,[status(thm)],[c_24515,c_11909]) ).
tff(c_40187,plain,
! [Y_2396,P_2397,X_2398] :
( is_a_theorem(not(and(not(Y_2396),P_2397)))
| ~ is_a_theorem(implies(X_2398,Y_2396))
| ~ is_a_theorem(implies(P_2397,X_2398)) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_28005]) ).
tff(c_41038,plain,
! [P_2427,P_2428,Q_2429] :
( is_a_theorem(not(and(not(P_2427),P_2428)))
| ~ is_a_theorem(implies(P_2428,and(P_2427,Q_2429))) ),
inference(resolution,[status(thm)],[c_163,c_40187]) ).
tff(c_41124,plain,
! [P_2430] : is_a_theorem(not(and(not(P_2430),P_2430))),
inference(resolution,[status(thm)],[c_167,c_41038]) ).
tff(c_24011,plain,
! [Q_1502,X_1503,Y_1504] :
( is_a_theorem(or(and(Q_1502,X_1503),implies(X_1503,Y_1504)))
| ~ is_a_theorem(or(Y_1504,Q_1502)) ),
inference(resolution,[status(thm)],[c_23950,c_184]) ).
tff(c_24036,plain,
! [X_1503,Y_1504,Q_1502] :
( is_a_theorem(implies(X_1503,Y_1504))
| ~ is_a_theorem(not(and(Q_1502,X_1503)))
| ~ is_a_theorem(or(Y_1504,Q_1502)) ),
inference(resolution,[status(thm)],[c_24011,c_11909]) ).
tff(c_41306,plain,
! [P_2439,Y_2440] :
( is_a_theorem(implies(P_2439,Y_2440))
| ~ is_a_theorem(or(Y_2440,not(P_2439))) ),
inference(resolution,[status(thm)],[c_41124,c_24036]) ).
tff(c_41643,plain,
! [P_1836,Q_1837] : is_a_theorem(implies(P_1836,or(Q_1837,P_1836))),
inference(resolution,[status(thm)],[c_28340,c_41306]) ).
tff(c_50,plain,
! [Y_23,X_22] :
( is_a_theorem(implies(Y_23,or(X_22,Y_23)))
| ~ or_2 ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_11857,plain,
~ or_2,
inference(splitLeft,[status(thm)],[c_50]) ).
tff(c_48,plain,
( or_2
| ~ is_a_theorem(implies('#skF_23',or('#skF_22','#skF_23'))) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_11865,plain,
~ is_a_theorem(implies('#skF_23',or('#skF_22','#skF_23'))),
inference(negUnitSimplification,[status(thm)],[c_11857,c_48]) ).
tff(c_42482,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_41643,c_11865]) ).
tff(c_42483,plain,
! [Y_23,X_22] : is_a_theorem(implies(Y_23,or(X_22,Y_23))),
inference(splitRight,[status(thm)],[c_50]) ).
tff(c_64028,plain,
! [X_3665,Y_3666,Y_3667] :
( is_a_theorem(or(or(X_3665,Y_3666),Y_3667))
| ~ is_a_theorem(or(Y_3667,Y_3666)) ),
inference(resolution,[status(thm)],[c_42483,c_63935]) ).
tff(c_62702,plain,
! [P_44] :
( is_a_theorem(P_44)
| ~ is_a_theorem(or(P_44,P_44)) ),
inference(resolution,[status(thm)],[c_11855,c_62681]) ).
tff(c_64985,plain,
! [X_3731,Y_3732] :
( is_a_theorem(or(X_3731,Y_3732))
| ~ is_a_theorem(or(or(X_3731,Y_3732),Y_3732)) ),
inference(resolution,[status(thm)],[c_64028,c_62702]) ).
tff(c_65006,plain,
! [P_42,Y_3660] :
( is_a_theorem(or(P_42,Y_3660))
| ~ is_a_theorem(or(Y_3660,P_42)) ),
inference(resolution,[status(thm)],[c_64005,c_64985]) ).
tff(c_96969,plain,
! [X_5071] : is_a_theorem(or(not(not(not(X_5071))),X_5071)),
inference(resolution,[status(thm)],[c_96908,c_65006]) ).
tff(c_64009,plain,
! [P_34,Y_3660,Q_35] :
( is_a_theorem(or(P_34,Y_3660))
| ~ is_a_theorem(or(Y_3660,and(P_34,Q_35))) ),
inference(resolution,[status(thm)],[c_163,c_63935]) ).
tff(c_99115,plain,
! [P_5150,Q_5151] : is_a_theorem(or(P_5150,not(not(not(and(P_5150,Q_5151)))))),
inference(resolution,[status(thm)],[c_96969,c_64009]) ).
tff(c_99189,plain,
! [X_5152,Y_5153] : is_a_theorem(or(X_5152,not(not(implies(X_5152,Y_5153))))),
inference(superposition,[status(thm),theory(equality)],[c_151,c_99115]) ).
tff(c_99243,plain,
! [X_5154,Y_5155] : is_a_theorem(or(not(not(implies(X_5154,Y_5155))),X_5154)),
inference(resolution,[status(thm)],[c_99189,c_65006]) ).
tff(c_95766,plain,
! [P_5051,Y_3635] :
( is_a_theorem(implies(P_5051,Y_3635))
| ~ is_a_theorem(or(Y_3635,not(P_5051))) ),
inference(resolution,[status(thm)],[c_95729,c_63727]) ).
tff(c_99247,plain,
! [P_5051,Y_5155] : is_a_theorem(implies(P_5051,not(not(implies(not(P_5051),Y_5155))))),
inference(resolution,[status(thm)],[c_99243,c_95766]) ).
tff(c_99323,plain,
! [P_5156,Y_5157] : is_a_theorem(implies(P_5156,not(not(or(P_5156,Y_5157))))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_99247]) ).
tff(c_101002,plain,
! [X_5198,Y_5199] : is_a_theorem(or(X_5198,not(not(or(not(X_5198),Y_5199))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_99323]) ).
tff(c_101060,plain,
! [X_5198,Y_5199] : is_a_theorem(or(not(not(or(not(X_5198),Y_5199))),X_5198)),
inference(resolution,[status(thm)],[c_101002,c_65006]) ).
tff(c_64006,plain,
! [X_22,Y_23,Y_3660] :
( is_a_theorem(or(or(X_22,Y_23),Y_3660))
| ~ is_a_theorem(or(Y_3660,Y_23)) ),
inference(resolution,[status(thm)],[c_42483,c_63935]) ).
tff(c_130539,plain,
! [P_5852,X_5853,Y_5854] :
( is_a_theorem(implies(P_5852,or(X_5853,Y_5854)))
| ~ is_a_theorem(or(not(P_5852),Y_5854)) ),
inference(resolution,[status(thm)],[c_64006,c_95805]) ).
tff(c_130653,plain,
! [X_5198,Y_5199,X_5853] : is_a_theorem(implies(not(or(not(X_5198),Y_5199)),or(X_5853,X_5198))),
inference(resolution,[status(thm)],[c_101060,c_130539]) ).
tff(c_143402,plain,
! [X_6109,Y_6110,X_6111] : is_a_theorem(or(or(not(X_6109),Y_6110),or(X_6111,X_6109))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_130653]) ).
tff(c_62648,plain,
! [X_3533] : is_a_theorem(or(X_3533,and(not(X_3533),not(X_3533)))),
inference(superposition,[status(thm),theory(equality)],[c_62633,c_167]) ).
tff(c_64200,plain,
! [P_3681,Y_3682,Q_3683] :
( is_a_theorem(or(P_3681,Y_3682))
| ~ is_a_theorem(or(Y_3682,and(P_3681,Q_3683))) ),
inference(resolution,[status(thm)],[c_163,c_63935]) ).
tff(c_64264,plain,
! [P_3686,Q_3687] : is_a_theorem(or(P_3686,not(and(P_3686,Q_3687)))),
inference(resolution,[status(thm)],[c_64084,c_64200]) ).
tff(c_64284,plain,
! [P_3686,Q_3687] :
( is_a_theorem(not(and(P_3686,Q_3687)))
| ~ is_a_theorem(not(P_3686)) ),
inference(resolution,[status(thm)],[c_64264,c_62684]) ).
tff(c_78434,plain,
! [X_4522,Y_4523,Q_4524] :
( is_a_theorem(implies(X_4522,Y_4523))
| ~ is_a_theorem(not(and(Q_4524,X_4522)))
| ~ is_a_theorem(or(Y_4523,Q_4524)) ),
inference(resolution,[status(thm)],[c_63704,c_62684]) ).
tff(c_78891,plain,
! [Q_4561,Y_4562,P_4563] :
( is_a_theorem(implies(Q_4561,Y_4562))
| ~ is_a_theorem(or(Y_4562,P_4563))
| ~ is_a_theorem(not(P_4563)) ),
inference(resolution,[status(thm)],[c_64284,c_78434]) ).
tff(c_79175,plain,
! [Q_4561,X_3533] :
( is_a_theorem(implies(Q_4561,X_3533))
| ~ is_a_theorem(not(and(not(X_3533),not(X_3533)))) ),
inference(resolution,[status(thm)],[c_62648,c_78891]) ).
tff(c_79333,plain,
! [Q_4561,X_3533] :
( is_a_theorem(implies(Q_4561,X_3533))
| ~ is_a_theorem(or(X_3533,X_3533)) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_151,c_79175]) ).
tff(c_143532,plain,
! [Q_4561,X_6109] : is_a_theorem(implies(Q_4561,or(not(X_6109),X_6109))),
inference(resolution,[status(thm)],[c_143402,c_79333]) ).
tff(c_63590,plain,
! [Q_3620,R_3621,P_3619] :
( is_a_theorem(or(and(Q_3620,R_3621),not(and(R_3621,P_3619))))
| ~ is_a_theorem(implies(P_3619,Q_3620)) ),
inference(resolution,[status(thm)],[c_63555,c_184]) ).
tff(c_62701,plain,
! [X_22,Y_23] :
( is_a_theorem(or(X_22,Y_23))
| ~ is_a_theorem(Y_23) ),
inference(resolution,[status(thm)],[c_42483,c_62681]) ).
tff(c_64008,plain,
! [P_33,Y_3660] :
( is_a_theorem(or(and(P_33,P_33),Y_3660))
| ~ is_a_theorem(or(Y_3660,P_33)) ),
inference(resolution,[status(thm)],[c_167,c_63935]) ).
tff(c_116307,plain,
! [P_5654,P_5655] :
( is_a_theorem(implies(P_5654,and(P_5655,P_5655)))
| ~ is_a_theorem(or(not(P_5654),P_5655)) ),
inference(resolution,[status(thm)],[c_64008,c_95805]) ).
tff(c_117048,plain,
! [P_5661,Y_5662] :
( is_a_theorem(implies(P_5661,and(Y_5662,Y_5662)))
| ~ is_a_theorem(Y_5662) ),
inference(resolution,[status(thm)],[c_62701,c_116307]) ).
tff(c_117319,plain,
! [X_5669,Y_5670] :
( is_a_theorem(or(X_5669,and(Y_5670,Y_5670)))
| ~ is_a_theorem(Y_5670) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_117048]) ).
tff(c_64825,plain,
! [P_3722,Y_3723] :
( is_a_theorem(or(and(P_3722,P_3722),Y_3723))
| ~ is_a_theorem(or(Y_3723,P_3722)) ),
inference(resolution,[status(thm)],[c_167,c_63935]) ).
tff(c_69107,plain,
! [Y_4093,P_4094] :
( is_a_theorem(Y_4093)
| ~ is_a_theorem(not(and(P_4094,P_4094)))
| ~ is_a_theorem(or(Y_4093,P_4094)) ),
inference(resolution,[status(thm)],[c_64825,c_62684]) ).
tff(c_69125,plain,
! [Y_4093,Y_61] :
( is_a_theorem(Y_4093)
| ~ is_a_theorem(implies(not(Y_61),Y_61))
| ~ is_a_theorem(or(Y_4093,not(Y_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_69107]) ).
tff(c_69129,plain,
! [Y_4093,Y_61] :
( is_a_theorem(Y_4093)
| ~ is_a_theorem(or(Y_61,Y_61))
| ~ is_a_theorem(or(Y_4093,not(Y_61))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_69125]) ).
tff(c_202555,plain,
! [Y_7489,Y_7490] :
( is_a_theorem(Y_7489)
| ~ is_a_theorem(or(Y_7489,not(and(Y_7490,Y_7490))))
| ~ is_a_theorem(Y_7490) ),
inference(resolution,[status(thm)],[c_117319,c_69129]) ).
tff(c_203583,plain,
! [Q_7493,P_7494] :
( is_a_theorem(and(Q_7493,P_7494))
| ~ is_a_theorem(P_7494)
| ~ is_a_theorem(implies(P_7494,Q_7493)) ),
inference(resolution,[status(thm)],[c_63590,c_202555]) ).
tff(c_211438,plain,
! [X_7551,Q_7552] :
( is_a_theorem(and(or(not(X_7551),X_7551),Q_7552))
| ~ is_a_theorem(Q_7552) ),
inference(resolution,[status(thm)],[c_143532,c_203583]) ).
tff(c_211602,plain,
! [Y_57] :
( is_a_theorem(equiv(not(not(Y_57)),Y_57))
| ~ is_a_theorem(implies(Y_57,not(not(Y_57)))) ),
inference(superposition,[status(thm),theory(equality)],[c_62938,c_211438]) ).
tff(c_211669,plain,
! [Y_7553] : is_a_theorem(equiv(not(not(Y_7553)),Y_7553)),
inference(demodulation,[status(thm),theory(equality)],[c_96296,c_211602]) ).
tff(c_136,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_10,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4))
| ~ substitution_of_equivalents ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_179,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_10]) ).
tff(c_212347,plain,
! [Y_7554] : ( not(not(Y_7554)) = Y_7554 ),
inference(resolution,[status(thm)],[c_211669,c_179]) ).
tff(c_214625,plain,
! [Y_7555,Y_7556] : ( or(not(Y_7555),Y_7556) = implies(Y_7555,Y_7556) ),
inference(superposition,[status(thm),theory(equality)],[c_212347,c_153]) ).
tff(c_217181,plain,
! [Y_7556,Y_7555] : is_a_theorem(implies(Y_7556,implies(Y_7555,Y_7556))),
inference(superposition,[status(thm),theory(equality)],[c_214625,c_42483]) ).
tff(c_144,plain,
~ implies_1,
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_20,plain,
( implies_1
| ~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_173,plain,
~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_20]) ).
tff(c_217650,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_217181,c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL503+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 13:21:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 93.23/78.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 93.23/78.39
% 93.23/78.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 93.57/78.45
% 93.57/78.45 Inference rules
% 93.57/78.45 ----------------------
% 93.57/78.45 #Ref : 0
% 93.57/78.45 #Sup : 53245
% 93.57/78.45 #Fact : 0
% 93.57/78.45 #Define : 0
% 93.57/78.45 #Split : 184
% 93.57/78.45 #Chain : 0
% 93.57/78.45 #Close : 0
% 93.57/78.45
% 93.57/78.45 Ordering : KBO
% 93.57/78.45
% 93.57/78.45 Simplification rules
% 93.57/78.45 ----------------------
% 93.57/78.45 #Subsume : 13044
% 93.57/78.45 #Demod : 26559
% 93.57/78.45 #Tautology : 9321
% 93.57/78.45 #SimpNegUnit : 61
% 93.57/78.45 #BackRed : 602
% 93.57/78.45
% 93.57/78.45 #Partial instantiations: 0
% 93.57/78.45 #Strategies tried : 1
% 93.57/78.45
% 93.57/78.45 Timing (in seconds)
% 93.57/78.45 ----------------------
% 93.57/78.46 Preprocessing : 0.61
% 93.57/78.46 Parsing : 0.31
% 93.57/78.46 CNF conversion : 0.05
% 93.57/78.46 Main loop : 76.71
% 93.57/78.46 Inferencing : 8.10
% 93.57/78.46 Reduction : 38.68
% 93.57/78.46 Demodulation : 30.10
% 93.57/78.46 BG Simplification : 0.25
% 93.57/78.46 Subsumption : 25.39
% 93.57/78.46 Abstraction : 0.38
% 93.57/78.46 MUC search : 0.00
% 93.57/78.46 Cooper : 0.00
% 93.57/78.46 Total : 77.44
% 93.57/78.46 Index Insertion : 0.00
% 93.57/78.46 Index Deletion : 0.00
% 93.57/78.46 Index Matching : 0.00
% 93.57/78.46 BG Taut test : 0.00
%------------------------------------------------------------------------------