%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL470+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:12:01 AM UTC 2026
% Result : Theorem 106.05s 71.09s
% Output : CNFRefutation 106.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 145 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 252 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 207 ( 100 ~; 94 |; 1 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 273 ( 273 !; 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_253,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
tff(f_261,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_262,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
tff(f_207,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_199,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_143,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_254,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn3) ).
tff(f_147,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(f_252,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn1) ).
tff(f_139,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn1) ).
tff(f_250,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_modus_ponens) ).
tff(f_61,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_263,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
tff(f_215,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_257,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',use_substitution_of_equivalents) ).
tff(f_68,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_156,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
tff(f_265,negated_conjecture,
~ or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
tff(f_105,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(c_132,plain,
cn2,
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_138,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_140,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_262]) ).
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_207]) ).
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_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_199]) ).
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_86,plain,
! [P_42,Q_43] :
( is_a_theorem(implies(P_42,implies(not(P_42),Q_43)))
| ~ cn2 ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_161,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_152,c_86]) ).
tff(c_134,plain,
cn3,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_90,plain,
! [P_44] :
( is_a_theorem(implies(implies(not(P_44),P_44),P_44))
| ~ cn3 ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_154,plain,
! [P_44] : is_a_theorem(implies(or(P_44,P_44),P_44)),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_152,c_90]) ).
tff(c_130,plain,
cn1,
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_82,plain,
! [P_39,Q_40,R_41] :
( is_a_theorem(implies(implies(P_39,Q_40),implies(implies(Q_40,R_41),implies(P_39,R_41))))
| ~ cn1 ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_364,plain,
! [P_98,Q_99,R_100] : is_a_theorem(implies(implies(P_98,Q_99),implies(implies(Q_99,R_100),implies(P_98,R_100)))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_82]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_250]) ).
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_61]) ).
tff(c_187,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_517,plain,
! [Q_111,R_112,P_113] :
( is_a_theorem(implies(implies(Q_111,R_112),implies(P_113,R_112)))
| ~ is_a_theorem(implies(P_113,Q_111)) ),
inference(resolution,[status(thm)],[c_364,c_187]) ).
tff(c_554,plain,
! [P_117,R_118,Q_119] :
( is_a_theorem(implies(P_117,R_118))
| ~ is_a_theorem(implies(Q_119,R_118))
| ~ is_a_theorem(implies(P_117,Q_119)) ),
inference(resolution,[status(thm)],[c_517,c_187]) ).
tff(c_620,plain,
! [P_123,P_124] :
( is_a_theorem(implies(P_123,P_124))
| ~ is_a_theorem(implies(P_123,or(P_124,P_124))) ),
inference(resolution,[status(thm)],[c_154,c_554]) ).
tff(c_654,plain,
! [Q_43] : is_a_theorem(implies(Q_43,Q_43)),
inference(resolution,[status(thm)],[c_161,c_620]) ).
tff(c_142,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_263]) ).
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_215]) ).
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_231,plain,
! [X_79,Y_80] : ( not(and(X_79,not(Y_80))) = implies(X_79,Y_80) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_116]) ).
tff(c_384,plain,
! [X_101,X_102,Y_103] : ( implies(X_101,and(X_102,not(Y_103))) = not(and(X_101,implies(X_102,Y_103))) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_231]) ).
tff(c_423,plain,
! [X_56,X_102,Y_103] : ( not(and(not(X_56),implies(X_102,Y_103))) = or(X_56,and(X_102,not(Y_103))) ),
inference(superposition,[status(thm),theory(equality)],[c_384,c_152]) ).
tff(c_246,plain,
! [X_79,X_60,Y_61] : ( implies(X_79,and(X_60,not(Y_61))) = not(and(X_79,implies(X_60,Y_61))) ),
inference(superposition,[status(thm),theory(equality)],[c_150,c_231]) ).
tff(c_218,plain,
! [Y_75,X_76] :
( is_a_theorem(Y_75)
| ~ is_a_theorem(implies(X_76,Y_75))
| ~ is_a_theorem(X_76) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_228,plain,
! [P_42,Q_43] :
( is_a_theorem(or(P_42,Q_43))
| ~ is_a_theorem(P_42) ),
inference(resolution,[status(thm)],[c_161,c_218]) ).
tff(c_532,plain,
! [Q_111,Y_57,X_56] :
( is_a_theorem(implies(implies(Q_111,Y_57),or(X_56,Y_57)))
| ~ is_a_theorem(implies(not(X_56),Q_111)) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_517]) ).
tff(c_536,plain,
! [Q_111,Y_57,X_56] :
( is_a_theorem(implies(implies(Q_111,Y_57),or(X_56,Y_57)))
| ~ is_a_theorem(or(X_56,Q_111)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_532]) ).
tff(c_692,plain,
! [Q_127,Y_128] :
( is_a_theorem(implies(implies(Q_127,Y_128),Y_128))
| ~ is_a_theorem(or(Y_128,Q_127)) ),
inference(resolution,[status(thm)],[c_536,c_620]) ).
tff(c_1097,plain,
! [X_165,Y_166] :
( is_a_theorem(implies(or(X_165,Y_166),Y_166))
| ~ is_a_theorem(or(Y_166,not(X_165))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_692]) ).
tff(c_1117,plain,
! [X_167,P_168] :
( is_a_theorem(implies(or(X_167,P_168),P_168))
| ~ is_a_theorem(P_168) ),
inference(resolution,[status(thm)],[c_228,c_1097]) ).
tff(c_533,plain,
! [P_113,R_112,Q_111] :
( is_a_theorem(implies(P_113,R_112))
| ~ is_a_theorem(implies(Q_111,R_112))
| ~ is_a_theorem(implies(P_113,Q_111)) ),
inference(resolution,[status(thm)],[c_517,c_187]) ).
tff(c_1967,plain,
! [P_235,P_236,X_237] :
( is_a_theorem(implies(P_235,P_236))
| ~ is_a_theorem(implies(P_235,or(X_237,P_236)))
| ~ is_a_theorem(P_236) ),
inference(resolution,[status(thm)],[c_1117,c_533]) ).
tff(c_2042,plain,
! [P_238,Q_239] :
( is_a_theorem(implies(P_238,Q_239))
| ~ is_a_theorem(Q_239) ),
inference(resolution,[status(thm)],[c_161,c_1967]) ).
tff(c_2150,plain,
! [X_56,Y_57] :
( is_a_theorem(or(X_56,Y_57))
| ~ is_a_theorem(Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_2042]) ).
tff(c_2235,plain,
! [X_242,Y_243] :
( is_a_theorem(or(X_242,Y_243))
| ~ is_a_theorem(Y_243) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_2042]) ).
tff(c_714,plain,
! [X_56,Y_57] :
( is_a_theorem(implies(or(X_56,Y_57),Y_57))
| ~ is_a_theorem(or(Y_57,not(X_56))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_692]) ).
tff(c_2714,plain,
! [X_262,X_263] :
( is_a_theorem(implies(or(X_262,X_263),X_263))
| ~ is_a_theorem(not(X_262)) ),
inference(resolution,[status(thm)],[c_2235,c_714]) ).
tff(c_9261,plain,
! [P_721,X_722,X_723] :
( is_a_theorem(implies(P_721,X_722))
| ~ is_a_theorem(implies(P_721,or(X_723,X_722)))
| ~ is_a_theorem(not(X_723)) ),
inference(resolution,[status(thm)],[c_2714,c_533]) ).
tff(c_44292,plain,
! [Q_1692,Y_1693,X_1694] :
( is_a_theorem(implies(implies(Q_1692,Y_1693),Y_1693))
| ~ is_a_theorem(not(X_1694))
| ~ is_a_theorem(or(X_1694,Q_1692)) ),
inference(resolution,[status(thm)],[c_536,c_9261]) ).
tff(c_44570,plain,
! [Y_57,Y_1693,X_56] :
( is_a_theorem(implies(implies(Y_57,Y_1693),Y_1693))
| ~ is_a_theorem(not(X_56))
| ~ is_a_theorem(Y_57) ),
inference(resolution,[status(thm)],[c_2150,c_44292]) ).
tff(c_44579,plain,
! [X_56] : ~ is_a_theorem(not(X_56)),
inference(splitLeft,[status(thm)],[c_44570]) ).
tff(c_276,plain,
! [X_84,Y_85] : ( and(implies(X_84,Y_85),implies(Y_85,X_84)) = equiv(X_84,Y_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_120]) ).
tff(c_285,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_152,c_276]) ).
tff(c_1066,plain,
! [P_162,X_163,Y_164] : is_a_theorem(implies(implies(P_162,not(X_163)),implies(or(X_163,Y_164),implies(P_162,Y_164)))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_364]) ).
tff(c_1577,plain,
! [X_206,Y_207,P_208] :
( is_a_theorem(implies(or(X_206,Y_207),implies(P_208,Y_207)))
| ~ is_a_theorem(implies(P_208,not(X_206))) ),
inference(resolution,[status(thm)],[c_1066,c_187]) ).
tff(c_12534,plain,
! [P_811,P_812,Y_813,X_814] :
( is_a_theorem(implies(P_811,implies(P_812,Y_813)))
| ~ is_a_theorem(implies(P_811,or(X_814,Y_813)))
| ~ is_a_theorem(implies(P_812,not(X_814))) ),
inference(resolution,[status(thm)],[c_1577,c_533]) ).
tff(c_12672,plain,
! [P_821,P_822,Q_823] :
( is_a_theorem(implies(P_821,implies(P_822,Q_823)))
| ~ is_a_theorem(implies(P_822,not(P_821))) ),
inference(resolution,[status(thm)],[c_161,c_12534]) ).
tff(c_13206,plain,
! [P_841,Q_842] : is_a_theorem(implies(P_841,implies(or(not(P_841),not(P_841)),Q_842))),
inference(resolution,[status(thm)],[c_154,c_12672]) ).
tff(c_36950,plain,
! [P_1516,X_1517,Y_1518] : is_a_theorem(implies(P_1516,not(and(or(not(P_1516),not(P_1516)),implies(X_1517,Y_1518))))),
inference(superposition,[status(thm),theory(equality)],[c_246,c_13206]) ).
tff(c_37095,plain,
! [P_1519] : is_a_theorem(implies(P_1519,not(equiv(not(not(P_1519)),not(P_1519))))),
inference(superposition,[status(thm),theory(equality)],[c_285,c_36950]) ).
tff(c_304,plain,
! [X_89,Y_90,Y_91] : ( or(and(X_89,not(Y_90)),Y_91) = implies(implies(X_89,Y_90),Y_91) ),
inference(superposition,[status(thm),theory(equality)],[c_231,c_152]) ).
tff(c_328,plain,
! [X_89,Y_90] : is_a_theorem(implies(implies(implies(X_89,Y_90),and(X_89,not(Y_90))),and(X_89,not(Y_90)))),
inference(superposition,[status(thm),theory(equality)],[c_304,c_154]) ).
tff(c_2323,plain,
! [X_244,Y_245] : is_a_theorem(or(and(implies(X_244,Y_245),implies(X_244,Y_245)),and(X_244,not(Y_245)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_246,c_328]) ).
tff(c_2346,plain,
! [Y_65] : is_a_theorem(or(equiv(Y_65,Y_65),and(Y_65,not(Y_65)))),
inference(superposition,[status(thm),theory(equality)],[c_148,c_2323]) ).
tff(c_9391,plain,
! [P_724,Q_725] :
( is_a_theorem(implies(P_724,Q_725))
| ~ is_a_theorem(not(P_724)) ),
inference(resolution,[status(thm)],[c_161,c_9261]) ).
tff(c_538,plain,
! [Q_114,Y_115,X_116] :
( is_a_theorem(implies(implies(Q_114,Y_115),or(X_116,Y_115)))
| ~ is_a_theorem(or(X_116,Q_114)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_532]) ).
tff(c_551,plain,
! [X_116,Y_115,Q_114] :
( is_a_theorem(or(X_116,Y_115))
| ~ is_a_theorem(implies(Q_114,Y_115))
| ~ is_a_theorem(or(X_116,Q_114)) ),
inference(resolution,[status(thm)],[c_538,c_187]) ).
tff(c_10687,plain,
! [X_772,Q_773,P_774] :
( is_a_theorem(or(X_772,Q_773))
| ~ is_a_theorem(or(X_772,P_774))
| ~ is_a_theorem(not(P_774)) ),
inference(resolution,[status(thm)],[c_9391,c_551]) ).
tff(c_10727,plain,
! [Y_65,Q_773] :
( is_a_theorem(or(equiv(Y_65,Y_65),Q_773))
| ~ is_a_theorem(not(and(Y_65,not(Y_65)))) ),
inference(resolution,[status(thm)],[c_2346,c_10687]) ).
tff(c_10779,plain,
! [Y_775,Q_776] : is_a_theorem(or(equiv(Y_775,Y_775),Q_776)),
inference(demodulation,[status(thm),theory(equality)],[c_654,c_150,c_10727]) ).
tff(c_640,plain,
! [X_56,P_124] :
( is_a_theorem(implies(not(X_56),P_124))
| ~ is_a_theorem(or(X_56,or(P_124,P_124))) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_620]) ).
tff(c_653,plain,
! [X_56,P_124] :
( is_a_theorem(or(X_56,P_124))
| ~ is_a_theorem(or(X_56,or(P_124,P_124))) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_640]) ).
tff(c_2318,plain,
! [X_242,P_124] :
( is_a_theorem(or(X_242,P_124))
| ~ is_a_theorem(or(P_124,P_124)) ),
inference(resolution,[status(thm)],[c_2235,c_653]) ).
tff(c_10993,plain,
! [X_779,Y_780] : is_a_theorem(or(X_779,equiv(Y_780,Y_780))),
inference(resolution,[status(thm)],[c_10779,c_2318]) ).
tff(c_718,plain,
! [Y_128,Q_127] :
( is_a_theorem(Y_128)
| ~ is_a_theorem(implies(Q_127,Y_128))
| ~ is_a_theorem(or(Y_128,Q_127)) ),
inference(resolution,[status(thm)],[c_692,c_187]) ).
tff(c_11091,plain,
! [X_779,Y_780] :
( is_a_theorem(X_779)
| ~ is_a_theorem(implies(equiv(Y_780,Y_780),X_779)) ),
inference(resolution,[status(thm)],[c_10993,c_718]) ).
tff(c_37203,plain,
! [Y_780] : is_a_theorem(not(equiv(not(not(equiv(Y_780,Y_780))),not(equiv(Y_780,Y_780))))),
inference(resolution,[status(thm)],[c_37095,c_11091]) ).
tff(c_44614,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44579,c_37203]) ).
tff(c_44616,plain,
! [Y_1695,Y_1696] :
( is_a_theorem(implies(implies(Y_1695,Y_1696),Y_1696))
| ~ is_a_theorem(Y_1695) ),
inference(splitRight,[status(thm)],[c_44570]) ).
tff(c_44684,plain,
! [X_79,X_60,Y_61] :
( is_a_theorem(implies(not(and(X_79,implies(X_60,Y_61))),and(X_60,not(Y_61))))
| ~ is_a_theorem(X_79) ),
inference(superposition,[status(thm),theory(equality)],[c_246,c_44616]) ).
tff(c_96494,plain,
! [X_2508,X_2509,Y_2510] :
( is_a_theorem(or(and(X_2508,implies(X_2509,Y_2510)),and(X_2509,not(Y_2510))))
| ~ is_a_theorem(X_2508) ),
inference(demodulation,[status(thm),theory(equality)],[c_423,c_246,c_44684]) ).
tff(c_585,plain,
! [P_120,P_121,Q_122] :
( is_a_theorem(implies(P_120,or(P_121,Q_122)))
| ~ is_a_theorem(implies(P_120,P_121)) ),
inference(resolution,[status(thm)],[c_161,c_554]) ).
tff(c_606,plain,
! [X_56,P_121,Q_122] :
( is_a_theorem(or(X_56,or(P_121,Q_122)))
| ~ is_a_theorem(implies(not(X_56),P_121)) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_585]) ).
tff(c_613,plain,
! [X_56,P_121,Q_122] :
( is_a_theorem(or(X_56,or(P_121,Q_122)))
| ~ is_a_theorem(or(X_56,P_121)) ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_606]) ).
tff(c_895,plain,
! [Y_145,Q_146] :
( is_a_theorem(Y_145)
| ~ is_a_theorem(implies(Q_146,Y_145))
| ~ is_a_theorem(or(Y_145,Q_146)) ),
inference(resolution,[status(thm)],[c_692,c_187]) ).
tff(c_915,plain,
! [X_56,P_121,Q_122] :
( is_a_theorem(X_56)
| ~ is_a_theorem(implies(or(P_121,Q_122),X_56))
| ~ is_a_theorem(or(X_56,P_121)) ),
inference(resolution,[status(thm)],[c_613,c_895]) ).
tff(c_2750,plain,
! [X_263,X_262] :
( is_a_theorem(X_263)
| ~ is_a_theorem(or(X_263,X_262))
| ~ is_a_theorem(not(X_262)) ),
inference(resolution,[status(thm)],[c_2714,c_915]) ).
tff(c_96539,plain,
! [X_2508,X_2509,Y_2510] :
( is_a_theorem(and(X_2508,implies(X_2509,Y_2510)))
| ~ is_a_theorem(not(and(X_2509,not(Y_2510))))
| ~ is_a_theorem(X_2508) ),
inference(resolution,[status(thm)],[c_96494,c_2750]) ).
tff(c_112344,plain,
! [X_2763,X_2764,Y_2765] :
( is_a_theorem(and(X_2763,implies(X_2764,Y_2765)))
| ~ is_a_theorem(implies(X_2764,Y_2765))
| ~ is_a_theorem(X_2763) ),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_96539]) ).
tff(c_112982,plain,
! [X_2771,Y_2772] :
( is_a_theorem(equiv(X_2771,Y_2772))
| ~ is_a_theorem(implies(Y_2772,X_2771))
| ~ is_a_theorem(implies(X_2771,Y_2772)) ),
inference(superposition,[status(thm),theory(equality)],[c_148,c_112344]) ).
tff(c_113390,plain,
! [P_44] :
( is_a_theorem(equiv(P_44,or(P_44,P_44)))
| ~ is_a_theorem(implies(P_44,or(P_44,P_44))) ),
inference(resolution,[status(thm)],[c_154,c_112982]) ).
tff(c_114018,plain,
! [P_2775] : is_a_theorem(equiv(P_2775,or(P_2775,P_2775))),
inference(demodulation,[status(thm),theory(equality)],[c_161,c_113390]) ).
tff(c_136,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_257]) ).
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_68]) ).
tff(c_182,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_114059,plain,
! [P_2775] : ( or(P_2775,P_2775) = P_2775 ),
inference(resolution,[status(thm)],[c_114018,c_182]) ).
tff(c_2040,plain,
! [P_42,Q_43] :
( is_a_theorem(implies(P_42,Q_43))
| ~ is_a_theorem(Q_43) ),
inference(resolution,[status(thm)],[c_161,c_1967]) ).
tff(c_113629,plain,
! [P_2773,Q_2774] :
( is_a_theorem(equiv(or(P_2773,Q_2774),P_2773))
| ~ is_a_theorem(implies(or(P_2773,Q_2774),P_2773)) ),
inference(resolution,[status(thm)],[c_161,c_112982]) ).
tff(c_117692,plain,
! [Q_2808,Q_2809] :
( is_a_theorem(equiv(or(Q_2808,Q_2809),Q_2808))
| ~ is_a_theorem(Q_2808) ),
inference(resolution,[status(thm)],[c_2040,c_113629]) ).
tff(c_117739,plain,
! [Q_2810,Q_2811] :
( ( or(Q_2810,Q_2811) = Q_2810 )
| ~ is_a_theorem(Q_2810) ),
inference(resolution,[status(thm)],[c_117692,c_182]) ).
tff(c_118716,plain,
! [Q_43,Q_2811] : ( or(implies(Q_43,Q_43),Q_2811) = implies(Q_43,Q_43) ),
inference(resolution,[status(thm)],[c_654,c_117739]) ).
tff(c_124188,plain,
! [Q_2863,Q_2864] : ( or(implies(Q_2863,Q_2863),Q_2864) = implies(Q_2863,Q_2863) ),
inference(resolution,[status(thm)],[c_654,c_117739]) ).
tff(c_2507,plain,
! [X_253,P_254] :
( is_a_theorem(or(X_253,P_254))
| ~ is_a_theorem(or(P_254,P_254)) ),
inference(resolution,[status(thm)],[c_2235,c_653]) ).
tff(c_2529,plain,
! [X_253,P_121,Q_122] :
( is_a_theorem(or(X_253,or(P_121,Q_122)))
| ~ is_a_theorem(or(or(P_121,Q_122),P_121)) ),
inference(resolution,[status(thm)],[c_613,c_2507]) ).
tff(c_125221,plain,
! [X_253,Q_2863,Q_2864] :
( is_a_theorem(or(X_253,or(implies(Q_2863,Q_2863),Q_2864)))
| ~ is_a_theorem(or(implies(Q_2863,Q_2863),implies(Q_2863,Q_2863))) ),
inference(superposition,[status(thm),theory(equality)],[c_124188,c_2529]) ).
tff(c_125738,plain,
! [X_253,Q_2863] : is_a_theorem(or(X_253,implies(Q_2863,Q_2863))),
inference(demodulation,[status(thm),theory(equality)],[c_654,c_114059,c_118716,c_125221]) ).
tff(c_114217,plain,
! [P_2776] : ( or(P_2776,P_2776) = P_2776 ),
inference(resolution,[status(thm)],[c_114018,c_182]) ).
tff(c_370,plain,
! [X_56,Y_57,R_100] : is_a_theorem(implies(or(X_56,Y_57),implies(implies(Y_57,R_100),implies(not(X_56),R_100)))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_364]) ).
tff(c_378,plain,
! [X_56,Y_57,R_100] : is_a_theorem(implies(or(X_56,Y_57),implies(implies(Y_57,R_100),or(X_56,R_100)))),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_370]) ).
tff(c_97321,plain,
! [P_2519,P_2520,Q_2521,P_2522] :
( is_a_theorem(implies(P_2519,or(P_2520,Q_2521)))
| ~ is_a_theorem(implies(P_2519,P_2522))
| ~ is_a_theorem(implies(P_2522,P_2520)) ),
inference(resolution,[status(thm)],[c_585,c_533]) ).
tff(c_100968,plain,
! [P_2565,P_2566,Q_2567,Q_2568] :
( is_a_theorem(implies(P_2565,or(P_2566,Q_2567)))
| ~ is_a_theorem(implies(or(P_2565,Q_2568),P_2566)) ),
inference(resolution,[status(thm)],[c_161,c_97321]) ).
tff(c_105543,plain,
! [X_2647,Y_2648,R_2649,Q_2650] : is_a_theorem(implies(X_2647,or(implies(implies(Y_2648,R_2649),or(X_2647,R_2649)),Q_2650))),
inference(resolution,[status(thm)],[c_378,c_100968]) ).
tff(c_584,plain,
! [P_117,P_44] :
( is_a_theorem(implies(P_117,P_44))
| ~ is_a_theorem(implies(P_117,or(P_44,P_44))) ),
inference(resolution,[status(thm)],[c_154,c_554]) ).
tff(c_105841,plain,
! [X_2647,Y_2648,R_2649] : is_a_theorem(implies(X_2647,implies(implies(Y_2648,R_2649),or(X_2647,R_2649)))),
inference(resolution,[status(thm)],[c_105543,c_584]) ).
tff(c_119468,plain,
! [P_2823,Y_2824] : is_a_theorem(implies(P_2823,implies(implies(Y_2824,P_2823),P_2823))),
inference(superposition,[status(thm),theory(equality)],[c_114217,c_105841]) ).
tff(c_119641,plain,
! [Y_57,X_56] : is_a_theorem(implies(Y_57,implies(or(X_56,Y_57),Y_57))),
inference(superposition,[status(thm),theory(equality)],[c_152,c_119468]) ).
tff(c_127492,plain,
! [Q_2883,Q_2884] : is_a_theorem(implies(Q_2883,implies(implies(Q_2884,Q_2884),Q_2883))),
inference(superposition,[status(thm),theory(equality)],[c_124188,c_119641]) ).
tff(c_575,plain,
! [P_117,X_56,Y_57,Q_111] :
( is_a_theorem(implies(P_117,or(X_56,Y_57)))
| ~ is_a_theorem(implies(P_117,implies(Q_111,Y_57)))
| ~ is_a_theorem(or(X_56,Q_111)) ),
inference(resolution,[status(thm)],[c_536,c_554]) ).
tff(c_127603,plain,
! [Q_2883,X_56,Q_2884] :
( is_a_theorem(implies(Q_2883,or(X_56,Q_2883)))
| ~ is_a_theorem(or(X_56,implies(Q_2884,Q_2884))) ),
inference(resolution,[status(thm)],[c_127492,c_575]) ).
tff(c_127699,plain,
! [Q_2883,X_56] : is_a_theorem(implies(Q_2883,or(X_56,Q_2883))),
inference(demodulation,[status(thm),theory(equality)],[c_125738,c_127603]) ).
tff(c_98,plain,
! [Q_47,P_46] :
( is_a_theorem(implies(Q_47,or(P_46,Q_47)))
| ~ r2 ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_198,plain,
~ r2,
inference(splitLeft,[status(thm)],[c_98]) ).
tff(c_96,plain,
( r2
| ~ is_a_theorem(implies('#skF_47',or('#skF_46','#skF_47'))) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_200,plain,
~ is_a_theorem(implies('#skF_47',or('#skF_46','#skF_47'))),
inference(negUnitSimplification,[status(thm)],[c_198,c_96]) ).
tff(c_127718,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_127699,c_200]) ).
tff(c_127719,plain,
! [Q_47,P_46] : is_a_theorem(implies(Q_47,or(P_46,Q_47))),
inference(splitRight,[status(thm)],[c_98]) ).
tff(c_144,plain,
~ or_2,
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_48,plain,
( or_2
| ~ is_a_theorem(implies('#skF_23',or('#skF_22','#skF_23'))) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_170,plain,
~ is_a_theorem(implies('#skF_23',or('#skF_22','#skF_23'))),
inference(negUnitSimplification,[status(thm)],[c_144,c_48]) ).
tff(c_127724,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_127719,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL470+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % 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
% 0.18/0.41 % Computer : n003.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8046.5625MB
% 0.18/0.41 % OS : Linux 6.8.0-71-generic
% 0.18/0.41 % CPULimit : 300
% 0.18/0.41 % WCLimit : 300
% 0.18/0.41 % DateTime : Sat Sep 5 00:25:35 UTC 2026
% 0.18/0.42 % CPUTime :
% 106.05/71.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 106.05/71.12
% 106.05/71.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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