%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL485+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 : n006.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 11:12:02 AM UTC 2026
% Result : Theorem 68.05s 52.69s
% Output : CNFRefutation 68.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 34
% Syntax : Number of formulae : 245 ( 160 unt; 0 typ; 0 def)
% Number of atoms : 344 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 194 ( 95 ~; 75 |; 1 &)
% ( 16 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 34 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 353 ( 353 !; 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_246,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
tff(f_211,axiom,
( op_implies_or
=> ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
tff(f_257,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
tff(f_169,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
tff(f_264,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_265,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_247,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
tff(f_203,axiom,
( op_and
=> ! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
tff(f_266,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_253,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
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_256,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
tff(f_165,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
tff(f_250,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_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_252,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
tff(f_152,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_254,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
tff(f_160,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_73,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
tff(f_126,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_260,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.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_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_130,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
tff(f_89,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
tff(f_101,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_77,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(f_93,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_268,negated_conjecture,
~ implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
tff(f_81,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
tff(c_122,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_246]) ).
tff(c_118,plain,
! [X_62,Y_63] :
( ( or(not(X_62),Y_63) = implies(X_62,Y_63) )
| ~ op_implies_or ),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_153,plain,
! [X_62,Y_63] : ( or(not(X_62),Y_63) = implies(X_62,Y_63) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_138,plain,
r5,
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_110,plain,
! [Q_54,R_55,P_53] :
( is_a_theorem(implies(implies(Q_54,R_55),implies(or(P_53,Q_54),or(P_53,R_55))))
| ~ r5 ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_71680,plain,
! [Q_3562,R_3563,P_3564] : is_a_theorem(implies(implies(Q_3562,R_3563),implies(or(P_3564,Q_3562),or(P_3564,R_3563)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_71689,plain,
! [Q_3562,Y_63,X_62] : is_a_theorem(implies(implies(Q_3562,Y_63),implies(or(not(X_62),Q_3562),implies(X_62,Y_63)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_71680]) ).
tff(c_71695,plain,
! [Q_3562,Y_63,X_62] : is_a_theorem(implies(implies(Q_3562,Y_63),implies(implies(X_62,Q_3562),implies(X_62,Y_63)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_71689]) ).
tff(c_142,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_144,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_265]) ).
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_155,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,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_159,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_68860,plain,
! [X_3341,Y_3342] : ( or(not(X_3341),Y_3342) = implies(X_3341,Y_3342) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_64884,plain,
! [X_3075,Y_3076] : ( not(and(X_3075,not(Y_3076))) = implies(X_3075,Y_3076) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
tff(c_68602,plain,
! [X_3327,Y_3328,Y_3329] : ( implies(and(X_3327,not(Y_3328)),Y_3329) = or(implies(X_3327,Y_3328),Y_3329) ),
inference(superposition,[status(thm),theory(equality)],[c_64884,c_153]) ).
tff(c_124,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_114,plain,
! [X_58,Y_59] :
( ( not(or(not(X_58),not(Y_59))) = and(X_58,Y_59) )
| ~ op_and ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_54265,plain,
! [X_2326,Y_2327] : ( not(implies(X_2326,not(Y_2327))) = and(X_2326,Y_2327) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_57012,plain,
! [X_2506,Y_2507,Y_2508] : ( or(implies(X_2506,not(Y_2507)),Y_2508) = implies(and(X_2506,Y_2507),Y_2508) ),
inference(superposition,[status(thm),theory(equality)],[c_54265,c_159]) ).
tff(c_54166,plain,
! [X_2314,Y_2315] : ( implies(not(X_2314),Y_2315) = or(X_2314,Y_2315) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_146,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_266]) ).
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_151,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_146,c_120]) ).
tff(c_8446,plain,
! [X_604,Y_605] : ( not(and(X_604,not(Y_605))) = implies(X_604,Y_605) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
tff(c_8449,plain,
! [X_60,X_604,Y_605] : ( implies(X_60,and(X_604,not(Y_605))) = not(and(X_60,implies(X_604,Y_605))) ),
inference(superposition,[status(thm),theory(equality)],[c_8446,c_155]) ).
tff(c_157,plain,
! [X_58,Y_59] : ( not(implies(X_58,not(Y_59))) = and(X_58,Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_8338,plain,
! [X_592,Y_593] : ( not(implies(X_592,not(Y_593))) = and(X_592,Y_593) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_13728,plain,
! [X_880,X_881,Y_882] : ( and(X_880,implies(X_881,not(Y_882))) = not(implies(X_880,and(X_881,Y_882))) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_8338]) ).
tff(c_13854,plain,
! [Y_882,Y_65] : ( not(implies(implies(not(Y_882),Y_65),and(Y_65,Y_882))) = equiv(not(Y_882),Y_65) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_13728]) ).
tff(c_25141,plain,
! [Y_1340,Y_1341] : ( not(implies(or(Y_1340,Y_1341),and(Y_1341,Y_1340))) = equiv(not(Y_1340),Y_1341) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_13854]) ).
tff(c_25790,plain,
! [X_62,Y_63] : ( not(implies(implies(X_62,Y_63),and(Y_63,not(X_62)))) = equiv(not(not(X_62)),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_25141]) ).
tff(c_42386,plain,
! [X_1844,Y_1845] : ( equiv(not(not(X_1844)),Y_1845) = not(not(equiv(X_1844,Y_1845))) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_8449,c_25790]) ).
tff(c_8238,plain,
! [X_578,Y_579] : ( implies(not(X_578),Y_579) = or(X_578,Y_579) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_132,plain,
r2,
inference(cnfTransformation,[status(thm)],[f_253]) ).
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_173,plain,
! [Q_47,P_46] : is_a_theorem(implies(Q_47,or(P_46,Q_47))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_98]) ).
tff(c_8249,plain,
! [X_578,P_46] : is_a_theorem(or(X_578,or(P_46,not(X_578)))),
inference(superposition,[status(thm),theory(equality)],[c_8238,c_173]) ).
tff(c_136,plain,
r4,
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_106,plain,
! [P_50,Q_51,R_52] :
( is_a_theorem(implies(or(P_50,or(Q_51,R_52)),or(Q_51,or(P_50,R_52))))
| ~ r4 ),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_10051,plain,
! [P_711,Q_712,R_713] : is_a_theorem(implies(or(P_711,or(Q_712,R_713)),or(Q_712,or(P_711,R_713)))),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_106]) ).
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_201,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_15281,plain,
! [Q_937,P_938,R_939] :
( is_a_theorem(or(Q_937,or(P_938,R_939)))
| ~ is_a_theorem(or(P_938,or(Q_937,R_939))) ),
inference(resolution,[status(thm)],[c_10051,c_201]) ).
tff(c_15329,plain,
! [P_940,X_941] : is_a_theorem(or(P_940,or(X_941,not(X_941)))),
inference(resolution,[status(thm)],[c_8249,c_15281]) ).
tff(c_130,plain,
r1,
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_177,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_94]) ).
tff(c_8369,plain,
! [Y_594,X_595] :
( is_a_theorem(Y_594)
| ~ is_a_theorem(implies(X_595,Y_594))
| ~ is_a_theorem(X_595) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_8396,plain,
! [P_45] :
( is_a_theorem(P_45)
| ~ is_a_theorem(or(P_45,P_45)) ),
inference(resolution,[status(thm)],[c_177,c_8369]) ).
tff(c_15394,plain,
! [X_942] : is_a_theorem(or(X_942,not(X_942))),
inference(resolution,[status(thm)],[c_15329,c_8396]) ).
tff(c_134,plain,
r3,
inference(cnfTransformation,[status(thm)],[f_254]) ).
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_160]) ).
tff(c_8331,plain,
! [P_590,Q_591] : is_a_theorem(implies(or(P_590,Q_591),or(Q_591,P_590))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_8337,plain,
! [Y_63,X_62] : is_a_theorem(implies(or(Y_63,not(X_62)),implies(X_62,Y_63))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_8331]) ).
tff(c_18,plain,
! [Y_6,X_5] :
( is_a_theorem(implies(implies(not(Y_6),not(X_5)),implies(X_5,Y_6)))
| ~ modus_tollens ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_191,plain,
! [Y_6,X_5] :
( is_a_theorem(implies(or(Y_6,not(X_5)),implies(X_5,Y_6)))
| ~ modus_tollens ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_18]) ).
tff(c_8981,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_16,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not('#skF_6'),not('#skF_5')),implies('#skF_5','#skF_6'))) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_192,plain,
( modus_tollens
| ~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_16]) ).
tff(c_9137,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_8981,c_192]) ).
tff(c_9746,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8337,c_9137]) ).
tff(c_9750,plain,
! [Y_687,X_688] : is_a_theorem(implies(or(Y_687,not(X_688)),implies(X_688,Y_687))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_9767,plain,
! [X_688,Y_687] :
( is_a_theorem(implies(X_688,Y_687))
| ~ is_a_theorem(or(Y_687,not(X_688))) ),
inference(resolution,[status(thm)],[c_9750,c_201]) ).
tff(c_15430,plain,
! [X_942] : is_a_theorem(implies(X_942,X_942)),
inference(resolution,[status(thm)],[c_15394,c_9767]) ).
tff(c_9940,plain,
! [X_704,Y_705] : ( and(implies(X_704,Y_705),implies(Y_705,X_704)) = equiv(X_704,Y_705) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_120]) ).
tff(c_6225,plain,
! [X_438,Y_439] : ( not(implies(X_438,not(Y_439))) = and(X_438,Y_439) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_6240,plain,
! [X_438,Y_439,Y_63] : ( implies(implies(X_438,not(Y_439)),Y_63) = or(and(X_438,Y_439),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_6225,c_153]) ).
tff(c_5824,plain,
! [X_402,Y_403] : ( or(not(X_402),Y_403) = implies(X_402,Y_403) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_5834,plain,
! [X_402] : is_a_theorem(implies(implies(X_402,not(X_402)),not(X_402))),
inference(superposition,[status(thm),theory(equality)],[c_5824,c_177]) ).
tff(c_8197,plain,
! [X_576] : is_a_theorem(or(and(X_576,X_576),not(X_576))),
inference(demodulation,[status(thm),theory(equality)],[c_6240,c_5834]) ).
tff(c_6257,plain,
! [P_440,Q_441] : is_a_theorem(implies(or(P_440,Q_441),or(Q_441,P_440))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_6263,plain,
! [Y_63,X_62] : is_a_theorem(implies(or(Y_63,not(X_62)),implies(X_62,Y_63))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_6257]) ).
tff(c_6525,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_6593,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_6525,c_192]) ).
tff(c_6984,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6263,c_6593]) ).
tff(c_7055,plain,
! [Y_497,X_498] : is_a_theorem(implies(or(Y_497,not(X_498)),implies(X_498,Y_497))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_7072,plain,
! [X_498,Y_497] :
( is_a_theorem(implies(X_498,Y_497))
| ~ is_a_theorem(or(Y_497,not(X_498))) ),
inference(resolution,[status(thm)],[c_7055,c_201]) ).
tff(c_8224,plain,
! [X_576] : is_a_theorem(implies(X_576,and(X_576,X_576))),
inference(resolution,[status(thm)],[c_8197,c_7072]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_5805,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(splitLeft,[status(thm)],[c_68]) ).
tff(c_8229,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8224,c_5805]) ).
tff(c_8230,plain,
kn1,
inference(splitRight,[status(thm)],[c_68]) ).
tff(c_70,plain,
! [P_33] :
( is_a_theorem(implies(P_33,and(P_33,P_33)))
| ~ kn1 ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_8233,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(demodulation,[status(thm),theory(equality)],[c_8230,c_70]) ).
tff(c_8393,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_8233,c_8369]) ).
tff(c_9950,plain,
! [Y_705] :
( is_a_theorem(equiv(Y_705,Y_705))
| ~ is_a_theorem(implies(Y_705,Y_705)) ),
inference(superposition,[status(thm),theory(equality)],[c_9940,c_8393]) ).
tff(c_15441,plain,
! [Y_705] : is_a_theorem(equiv(Y_705,Y_705)),
inference(demodulation,[status(thm),theory(equality)],[c_15430,c_9950]) ).
tff(c_42766,plain,
! [X_1848] : is_a_theorem(not(not(equiv(X_1848,not(not(X_1848)))))),
inference(superposition,[status(thm),theory(equality)],[c_42386,c_15441]) ).
tff(c_8280,plain,
! [X_582,Y_583] : ( or(not(X_582),Y_583) = implies(X_582,Y_583) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_8298,plain,
! [Y_584,X_585] : is_a_theorem(implies(Y_584,implies(X_585,Y_584))),
inference(superposition,[status(thm),theory(equality)],[c_8280,c_173]) ).
tff(c_8320,plain,
! [X_588,X_589] : is_a_theorem(or(X_588,implies(X_589,not(X_588)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_8298]) ).
tff(c_9848,plain,
! [X_694,X_695] : is_a_theorem(implies(X_694,implies(X_695,not(not(X_694))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_8320]) ).
tff(c_10711,plain,
! [X_740,X_741] : is_a_theorem(or(X_740,implies(X_741,not(not(not(X_740)))))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_9848]) ).
tff(c_169,plain,
! [P_48,Q_49] : is_a_theorem(implies(or(P_48,Q_49),or(Q_49,P_48))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_8391,plain,
! [Q_49,P_48] :
( is_a_theorem(or(Q_49,P_48))
| ~ is_a_theorem(or(P_48,Q_49)) ),
inference(resolution,[status(thm)],[c_169,c_8369]) ).
tff(c_10799,plain,
! [X_746,X_747] : is_a_theorem(or(implies(X_746,not(not(not(X_747)))),X_747)),
inference(resolution,[status(thm)],[c_10711,c_8391]) ).
tff(c_8378,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_159,c_8369]) ).
tff(c_10806,plain,
! [X_747,X_746] :
( is_a_theorem(X_747)
| ~ is_a_theorem(not(implies(X_746,not(not(not(X_747)))))) ),
inference(resolution,[status(thm)],[c_10799,c_8378]) ).
tff(c_10828,plain,
! [X_748,X_749] :
( is_a_theorem(X_748)
| ~ is_a_theorem(and(X_749,not(not(X_748)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_157,c_10806]) ).
tff(c_10850,plain,
! [X_748] :
( is_a_theorem(X_748)
| ~ is_a_theorem(not(not(X_748))) ),
inference(resolution,[status(thm)],[c_8393,c_10828]) ).
tff(c_42812,plain,
! [X_1849] : is_a_theorem(equiv(X_1849,not(not(X_1849)))),
inference(resolution,[status(thm)],[c_42766,c_10850]) ).
tff(c_140,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_260]) ).
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_196,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_10]) ).
tff(c_42874,plain,
! [X_1849] : ( not(not(X_1849)) = X_1849 ),
inference(resolution,[status(thm)],[c_42812,c_196]) ).
tff(c_43033,plain,
! [X_1850] : ( not(not(X_1850)) = X_1850 ),
inference(resolution,[status(thm)],[c_42812,c_196]) ).
tff(c_8366,plain,
! [X_56,Y_593] : ( not(or(X_56,not(Y_593))) = and(not(X_56),Y_593) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_8338]) ).
tff(c_43491,plain,
! [X_56,X_1850] : ( and(not(X_56),not(X_1850)) = not(or(X_56,X_1850)) ),
inference(superposition,[status(thm),theory(equality)],[c_43033,c_8366]) ).
tff(c_43545,plain,
! [X_58,Y_59] : ( implies(X_58,not(Y_59)) = not(and(X_58,Y_59)) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_43033]) ).
tff(c_8353,plain,
! [X_592,Y_593,Y_63] : ( implies(implies(X_592,not(Y_593)),Y_63) = or(and(X_592,Y_593),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_8338,c_153]) ).
tff(c_9763,plain,
! [X_62,X_688] : is_a_theorem(implies(implies(X_62,not(X_688)),implies(X_688,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_9750]) ).
tff(c_11967,plain,
! [X_62,X_688] : is_a_theorem(or(and(X_62,X_688),implies(X_688,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_8353,c_9763]) ).
tff(c_43722,plain,
! [X_62,X_688] : is_a_theorem(or(and(X_62,X_688),not(and(X_688,X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_43545,c_11967]) ).
tff(c_8305,plain,
! [X_56,X_585] : is_a_theorem(or(X_56,implies(X_585,not(X_56)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_8298]) ).
tff(c_10293,plain,
! [Q_719,R_720,P_721] : is_a_theorem(implies(implies(Q_719,R_720),implies(or(P_721,Q_719),or(P_721,R_720)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_13529,plain,
! [P_866,Q_867,R_868] :
( is_a_theorem(implies(or(P_866,Q_867),or(P_866,R_868)))
| ~ is_a_theorem(implies(Q_867,R_868)) ),
inference(resolution,[status(thm)],[c_10293,c_201]) ).
tff(c_37631,plain,
! [P_1718,R_1719,Q_1720] :
( is_a_theorem(or(P_1718,R_1719))
| ~ is_a_theorem(or(P_1718,Q_1720))
| ~ is_a_theorem(implies(Q_1720,R_1719)) ),
inference(resolution,[status(thm)],[c_13529,c_201]) ).
tff(c_37825,plain,
! [X_56,R_1719,X_585] :
( is_a_theorem(or(X_56,R_1719))
| ~ is_a_theorem(implies(implies(X_585,not(X_56)),R_1719)) ),
inference(resolution,[status(thm)],[c_8305,c_37631]) ).
tff(c_50193,plain,
! [X_2044,R_2045,X_2046] :
( is_a_theorem(or(X_2044,R_2045))
| ~ is_a_theorem(or(and(X_2046,X_2044),R_2045)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8353,c_37825]) ).
tff(c_50469,plain,
! [X_2047,X_2048] : is_a_theorem(or(X_2047,not(and(X_2047,X_2048)))),
inference(resolution,[status(thm)],[c_43722,c_50193]) ).
tff(c_50499,plain,
! [X_56,X_1850] : is_a_theorem(or(not(X_56),not(not(or(X_56,X_1850))))),
inference(superposition,[status(thm),theory(equality)],[c_43491,c_50469]) ).
tff(c_50532,plain,
! [X_56,X_1850] : is_a_theorem(implies(X_56,or(X_56,X_1850))),
inference(demodulation,[status(thm),theory(equality)],[c_42874,c_153,c_50499]) ).
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_183,plain,
! [P_42,Q_43] :
( is_a_theorem(implies(P_42,or(P_42,Q_43)))
| ~ cn2 ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_86]) ).
tff(c_5803,plain,
~ cn2,
inference(splitLeft,[status(thm)],[c_183]) ).
tff(c_84,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',implies(not('#skF_42'),'#skF_43'))) ),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_184,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_84]) ).
tff(c_8296,plain,
~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))),
inference(negUnitSimplification,[status(thm)],[c_5803,c_184]) ).
tff(c_50611,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50532,c_8296]) ).
tff(c_50612,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_54180,plain,
! [X_2314,Q_43] : is_a_theorem(or(X_2314,or(not(X_2314),Q_43))),
inference(superposition,[status(thm),theory(equality)],[c_54166,c_50612]) ).
tff(c_54194,plain,
! [X_2314,Q_43] : is_a_theorem(or(X_2314,implies(X_2314,Q_43))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_54180]) ).
tff(c_54302,plain,
! [Y_2328,X_2329] :
( is_a_theorem(Y_2328)
| ~ is_a_theorem(implies(X_2329,Y_2328))
| ~ is_a_theorem(X_2329) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_54861,plain,
! [Q_2379,P_2380] :
( is_a_theorem(or(Q_2379,P_2380))
| ~ is_a_theorem(or(P_2380,Q_2379)) ),
inference(resolution,[status(thm)],[c_169,c_54302]) ).
tff(c_54878,plain,
! [X_2314,Q_43] : is_a_theorem(or(implies(X_2314,Q_43),X_2314)),
inference(resolution,[status(thm)],[c_54194,c_54861]) ).
tff(c_57126,plain,
! [Y_2508,Y_2507] : is_a_theorem(implies(and(Y_2508,Y_2507),Y_2508)),
inference(superposition,[status(thm),theory(equality)],[c_57012,c_54878]) ).
tff(c_72,plain,
( kn2
| ~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')) ),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_54132,plain,
~ is_a_theorem(implies(and('#skF_34','#skF_35'),'#skF_34')),
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_57219,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57126,c_54132]) ).
tff(c_57220,plain,
kn2,
inference(splitRight,[status(thm)],[c_72]) ).
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_130]) ).
tff(c_57272,plain,
! [P_34,Q_35] : is_a_theorem(implies(and(P_34,Q_35),P_34)),
inference(demodulation,[status(thm),theory(equality)],[c_57220,c_74]) ).
tff(c_32,plain,
( and_1
| ~ is_a_theorem(implies(and('#skF_14','#skF_15'),'#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_5802,plain,
~ is_a_theorem(implies(and('#skF_14','#skF_15'),'#skF_14')),
inference(splitLeft,[status(thm)],[c_32]) ).
tff(c_57276,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57272,c_5802]) ).
tff(c_57277,plain,
and_1,
inference(splitRight,[status(thm)],[c_32]) ).
tff(c_34,plain,
! [X_14,Y_15] :
( is_a_theorem(implies(and(X_14,Y_15),X_14))
| ~ and_1 ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_64848,plain,
! [X_14,Y_15] : is_a_theorem(implies(and(X_14,Y_15),X_14)),
inference(demodulation,[status(thm),theory(equality)],[c_57277,c_34]) ).
tff(c_68769,plain,
! [Y_3330,Y_3331] : is_a_theorem(or(implies(Y_3330,Y_3331),Y_3330)),
inference(superposition,[status(thm),theory(equality)],[c_68602,c_64848]) ).
tff(c_64877,plain,
! [P_3073,Q_3074] : is_a_theorem(implies(or(P_3073,Q_3074),or(Q_3074,P_3073))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_64883,plain,
! [Y_63,X_62] : is_a_theorem(implies(or(Y_63,not(X_62)),implies(X_62,Y_63))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_64877]) ).
tff(c_66224,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_66274,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_66224,c_192]) ).
tff(c_67222,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_64883,c_66274]) ).
tff(c_67298,plain,
! [Y_3248,X_3249] : is_a_theorem(implies(or(Y_3248,not(X_3249)),implies(X_3249,Y_3248))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_67315,plain,
! [X_3249,Y_3248] :
( is_a_theorem(implies(X_3249,Y_3248))
| ~ is_a_theorem(or(Y_3248,not(X_3249))) ),
inference(resolution,[status(thm)],[c_67298,c_201]) ).
tff(c_68773,plain,
! [X_3249,Y_3331] : is_a_theorem(implies(X_3249,implies(not(X_3249),Y_3331))),
inference(resolution,[status(thm)],[c_68769,c_67315]) ).
tff(c_68786,plain,
! [X_3249,Y_3331] : is_a_theorem(implies(X_3249,or(X_3249,Y_3331))),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_68773]) ).
tff(c_64846,plain,
~ cn2,
inference(splitLeft,[status(thm)],[c_183]) ).
tff(c_64852,plain,
~ is_a_theorem(implies('#skF_42',or('#skF_42','#skF_43'))),
inference(negUnitSimplification,[status(thm)],[c_64846,c_184]) ).
tff(c_68793,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_68786,c_64852]) ).
tff(c_68794,plain,
! [P_42,Q_43] : is_a_theorem(implies(P_42,or(P_42,Q_43))),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_44,plain,
( or_1
| ~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_64771,plain,
~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))),
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_68803,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_68794,c_64771]) ).
tff(c_68804,plain,
or_1,
inference(splitRight,[status(thm)],[c_44]) ).
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_101]) ).
tff(c_68825,plain,
! [X_20,Y_21] : is_a_theorem(implies(X_20,or(X_20,Y_21))),
inference(demodulation,[status(thm),theory(equality)],[c_68804,c_46]) ).
tff(c_68866,plain,
! [X_3341,Y_3342] : is_a_theorem(implies(not(X_3341),implies(X_3341,Y_3342))),
inference(superposition,[status(thm),theory(equality)],[c_68860,c_68825]) ).
tff(c_68878,plain,
! [X_3341,Y_3342] : is_a_theorem(or(X_3341,implies(X_3341,Y_3342))),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_68866]) ).
tff(c_78233,plain,
! [P_3850,Q_3851,R_3852] :
( is_a_theorem(implies(or(P_3850,Q_3851),or(P_3850,R_3852)))
| ~ is_a_theorem(implies(Q_3851,R_3852)) ),
inference(resolution,[status(thm)],[c_71680,c_201]) ).
tff(c_92169,plain,
! [P_4447,R_4448,Q_4449] :
( is_a_theorem(or(P_4447,R_4448))
| ~ is_a_theorem(or(P_4447,Q_4449))
| ~ is_a_theorem(implies(Q_4449,R_4448)) ),
inference(resolution,[status(thm)],[c_78233,c_201]) ).
tff(c_96158,plain,
! [X_4541,R_4542,Y_4543] :
( is_a_theorem(or(X_4541,R_4542))
| ~ is_a_theorem(implies(implies(X_4541,Y_4543),R_4542)) ),
inference(resolution,[status(thm)],[c_68878,c_92169]) ).
tff(c_141537,plain,
! [Q_5819,X_5820,Y_5821] : is_a_theorem(or(Q_5819,implies(implies(X_5820,Q_5819),implies(X_5820,Y_5821)))),
inference(resolution,[status(thm)],[c_71695,c_96158]) ).
tff(c_69027,plain,
! [X_3365,Y_3366] : ( not(and(X_3365,not(Y_3366))) = implies(X_3365,Y_3366) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
tff(c_73543,plain,
! [X_3649,Y_3650,Y_3651] : ( implies(and(X_3649,not(Y_3650)),Y_3651) = or(implies(X_3649,Y_3650),Y_3651) ),
inference(superposition,[status(thm),theory(equality)],[c_69027,c_153]) ).
tff(c_2314,plain,
! [X_221,Y_222] : ( not(implies(X_221,not(Y_222))) = and(X_221,Y_222) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_2332,plain,
! [X_221,Y_222,Y_57] : ( or(implies(X_221,not(Y_222)),Y_57) = implies(and(X_221,Y_222),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_2314,c_159]) ).
tff(c_2192,plain,
! [X_207,Y_208] : ( or(not(X_207),Y_208) = implies(X_207,Y_208) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_2198,plain,
! [Y_208,X_207] : is_a_theorem(implies(Y_208,implies(X_207,Y_208))),
inference(superposition,[status(thm),theory(equality)],[c_2192,c_173]) ).
tff(c_20,plain,
( implies_1
| ~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_2208,plain,
~ is_a_theorem(implies('#skF_7',implies('#skF_8','#skF_7'))),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_2211,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2198,c_2208]) ).
tff(c_2212,plain,
implies_1,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_22,plain,
! [X_7,Y_8] :
( is_a_theorem(implies(X_7,implies(Y_8,X_7)))
| ~ implies_1 ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_2216,plain,
! [X_209,Y_210] : is_a_theorem(implies(X_209,implies(Y_210,X_209))),
inference(demodulation,[status(thm),theory(equality)],[c_2212,c_22]) ).
tff(c_2223,plain,
! [X_56,Y_210] : is_a_theorem(or(X_56,implies(Y_210,not(X_56)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_2216]) ).
tff(c_2258,plain,
! [Y_217,X_218] :
( is_a_theorem(Y_217)
| ~ is_a_theorem(implies(X_218,Y_217))
| ~ is_a_theorem(X_218) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_2452,plain,
! [Q_231,P_232] :
( is_a_theorem(or(Q_231,P_232))
| ~ is_a_theorem(or(P_232,Q_231)) ),
inference(resolution,[status(thm)],[c_169,c_2258]) ).
tff(c_2465,plain,
! [Y_210,X_56] : is_a_theorem(or(implies(Y_210,not(X_56)),X_56)),
inference(resolution,[status(thm)],[c_2223,c_2452]) ).
tff(c_5594,plain,
! [Y_210,X_56] : is_a_theorem(implies(and(Y_210,X_56),X_56)),
inference(demodulation,[status(thm),theory(equality)],[c_2332,c_2465]) ).
tff(c_38,plain,
! [X_16,Y_17] :
( is_a_theorem(implies(and(X_16,Y_17),Y_17))
| ~ and_2 ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_205,plain,
~ and_2,
inference(splitLeft,[status(thm)],[c_38]) ).
tff(c_36,plain,
( and_2
| ~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_2191,plain,
~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')),
inference(negUnitSimplification,[status(thm)],[c_205,c_36]) ).
tff(c_5798,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5594,c_2191]) ).
tff(c_5799,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(splitRight,[status(thm)],[c_38]) ).
tff(c_73704,plain,
! [X_3649,Y_3650] : is_a_theorem(or(implies(X_3649,Y_3650),not(Y_3650))),
inference(superposition,[status(thm),theory(equality)],[c_73543,c_5799]) ).
tff(c_92327,plain,
! [X_3649,Y_3650,R_4448] :
( is_a_theorem(or(implies(X_3649,Y_3650),R_4448))
| ~ is_a_theorem(implies(not(Y_3650),R_4448)) ),
inference(resolution,[status(thm)],[c_73704,c_92169]) ).
tff(c_125512,plain,
! [X_5352,Y_5353,R_5354] :
( is_a_theorem(or(implies(X_5352,Y_5353),R_5354))
| ~ is_a_theorem(or(Y_5353,R_5354)) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_92327]) ).
tff(c_68974,plain,
! [Y_3357,X_3358] :
( is_a_theorem(Y_3357)
| ~ is_a_theorem(implies(X_3358,Y_3357))
| ~ is_a_theorem(X_3358) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_69009,plain,
! [P_45] :
( is_a_theorem(P_45)
| ~ is_a_theorem(or(P_45,P_45)) ),
inference(resolution,[status(thm)],[c_177,c_68974]) ).
tff(c_125565,plain,
! [X_5352,Y_5353] :
( is_a_theorem(implies(X_5352,Y_5353))
| ~ is_a_theorem(or(Y_5353,implies(X_5352,Y_5353))) ),
inference(resolution,[status(thm)],[c_125512,c_69009]) ).
tff(c_141592,plain,
! [X_5820,Y_5821] : is_a_theorem(implies(implies(X_5820,implies(X_5820,Y_5821)),implies(X_5820,Y_5821))),
inference(resolution,[status(thm)],[c_141537,c_125565]) ).
tff(c_148,plain,
~ implies_2,
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_24,plain,
( implies_2
| ~ is_a_theorem(implies(implies('#skF_9',implies('#skF_9','#skF_10')),implies('#skF_9','#skF_10'))) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_190,plain,
~ is_a_theorem(implies(implies('#skF_9',implies('#skF_9','#skF_10')),implies('#skF_9','#skF_10'))),
inference(negUnitSimplification,[status(thm)],[c_148,c_24]) ).
tff(c_141891,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_141592,c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL485+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % 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
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 19:24:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 68.05/52.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.15/52.73
% 68.15/52.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------