TSTP Solution File: LCL493+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL493+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n025.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 10:48:14 EDT 2023
% Result : Theorem 19.47s 9.32s
% Output : CNFRefutation 19.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 122
% Syntax : Number of formulae : 268 ( 115 unt; 92 typ; 0 def)
% Number of atoms : 248 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 135 ( 63 ~; 52 |; 1 &)
% ( 12 <=>; 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 : 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 : 253 (; 253 !; 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_263,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
tff(f_214,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_262,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_243,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
tff(f_210,axiom,
( op_implies_or
=> ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
tff(f_261,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_244,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
tff(f_202,axiom,
( op_and
=> ! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
tff(f_250,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
tff(f_155,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
tff(f_253,axiom,
r4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
tff(f_164,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r4) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
tff(f_60,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_249,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
tff(f_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_251,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
tff(f_159,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
tff(f_72,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
tff(f_125,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
tff(f_257,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',substitution_of_equivalents) ).
tff(f_67,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_92,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_254,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
tff(f_168,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r5) ).
tff(f_88,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
tff(f_265,negated_conjecture,
~ equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
tff(f_112,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_1) ).
tff(c_146,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_214]) ).
tff(c_44653,plain,
! [X_1990,Y_1991] : ( and(implies(X_1990,Y_1991),implies(Y_1991,X_1990)) = equiv(X_1990,Y_1991) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_120]) ).
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_144,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_206]) ).
tff(c_7907,plain,
! [X_603,Y_604] : ( not(and(X_603,not(Y_604))) = implies(X_603,Y_604) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_116]) ).
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_7910,plain,
! [X_60,X_603,Y_604] : ( implies(X_60,and(X_603,not(Y_604))) = not(and(X_60,implies(X_603,Y_604))) ),
inference(superposition,[status(thm),theory(equality)],[c_7907,c_155]) ).
tff(c_122,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_243]) ).
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_210]) ).
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_142,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_261]) ).
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_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_124,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_244]) ).
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_202]) ).
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_7855,plain,
! [X_597,Y_598] : ( not(implies(X_597,not(Y_598))) = and(X_597,Y_598) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_13641,plain,
! [X_895,X_896,Y_897] : ( and(X_895,implies(X_896,not(Y_897))) = not(implies(X_895,and(X_896,Y_897))) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_7855]) ).
tff(c_13770,plain,
! [Y_897,Y_65] : ( not(implies(implies(not(Y_897),Y_65),and(Y_65,Y_897))) = equiv(not(Y_897),Y_65) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_13641]) ).
tff(c_30953,plain,
! [Y_1580,Y_1581] : ( not(implies(or(Y_1580,Y_1581),and(Y_1581,Y_1580))) = equiv(not(Y_1580),Y_1581) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_13770]) ).
tff(c_31692,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_30953]) ).
tff(c_31830,plain,
! [X_1582,Y_1583] : ( equiv(not(not(X_1582)),Y_1583) = not(not(equiv(X_1582,Y_1583))) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_7910,c_31692]) ).
tff(c_7806,plain,
! [X_591,Y_592] : ( implies(not(X_591),Y_592) = or(X_591,Y_592) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_132,plain,
r2,
inference(cnfTransformation,[status(thm)],[f_250]) ).
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_155]) ).
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_7817,plain,
! [X_591,P_46] : is_a_theorem(or(X_591,or(P_46,not(X_591)))),
inference(superposition,[status(thm),theory(equality)],[c_7806,c_173]) ).
tff(c_136,plain,
r4,
inference(cnfTransformation,[status(thm)],[f_253]) ).
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_164]) ).
tff(c_9700,plain,
! [P_722,Q_723,R_724] : is_a_theorem(implies(or(P_722,or(Q_723,R_724)),or(Q_723,or(P_722,R_724)))),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_106]) ).
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_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_12298,plain,
! [Q_846,P_847,R_848] :
( is_a_theorem(or(Q_846,or(P_847,R_848)))
| ~ is_a_theorem(or(P_847,or(Q_846,R_848))) ),
inference(resolution,[status(thm)],[c_9700,c_201]) ).
tff(c_12342,plain,
! [P_849,X_850] : is_a_theorem(or(P_849,or(X_850,not(X_850)))),
inference(resolution,[status(thm)],[c_7817,c_12298]) ).
tff(c_130,plain,
r1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_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_7947,plain,
! [Y_607,X_608] :
( is_a_theorem(Y_607)
| ~ is_a_theorem(implies(X_608,Y_607))
| ~ is_a_theorem(X_608) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_7974,plain,
! [P_45] :
( is_a_theorem(P_45)
| ~ is_a_theorem(or(P_45,P_45)) ),
inference(resolution,[status(thm)],[c_177,c_7947]) ).
tff(c_12407,plain,
! [X_851] : is_a_theorem(or(X_851,not(X_851))),
inference(resolution,[status(thm)],[c_12342,c_7974]) ).
tff(c_134,plain,
r3,
inference(cnfTransformation,[status(thm)],[f_251]) ).
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_7940,plain,
! [P_605,Q_606] : is_a_theorem(implies(or(P_605,Q_606),or(Q_606,P_605))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_7946,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_7940]) ).
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_72]) ).
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_8479,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(splitLeft,[status(thm)],[c_192]) ).
tff(c_9317,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7946,c_8479]) ).
tff(c_9318,plain,
modus_tollens,
inference(splitRight,[status(thm)],[c_192]) ).
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_72]) ).
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_9432,plain,
! [Y_700,X_701] : is_a_theorem(implies(or(Y_700,not(X_701)),implies(X_701,Y_700))),
inference(demodulation,[status(thm),theory(equality)],[c_9318,c_191]) ).
tff(c_9449,plain,
! [X_701,Y_700] :
( is_a_theorem(implies(X_701,Y_700))
| ~ is_a_theorem(or(Y_700,not(X_701))) ),
inference(resolution,[status(thm)],[c_9432,c_201]) ).
tff(c_12437,plain,
! [X_851] : is_a_theorem(implies(X_851,X_851)),
inference(resolution,[status(thm)],[c_12407,c_9449]) ).
tff(c_8431,plain,
! [X_645,Y_646] : ( and(implies(X_645,Y_646),implies(Y_646,X_645)) = equiv(X_645,Y_646) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_120]) ).
tff(c_5584,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_5599,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_5584,c_153]) ).
tff(c_5128,plain,
! [X_399,Y_400] : ( or(not(X_399),Y_400) = implies(X_399,Y_400) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_5138,plain,
! [X_399] : is_a_theorem(implies(implies(X_399,not(X_399)),not(X_399))),
inference(superposition,[status(thm),theory(equality)],[c_5128,c_177]) ).
tff(c_7763,plain,
! [X_587] : is_a_theorem(or(and(X_587,X_587),not(X_587))),
inference(demodulation,[status(thm),theory(equality)],[c_5599,c_5138]) ).
tff(c_5625,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_5634,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_5625]) ).
tff(c_5832,plain,
~ modus_tollens,
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_5849,plain,
~ is_a_theorem(implies(or('#skF_6',not('#skF_5')),implies('#skF_5','#skF_6'))),
inference(negUnitSimplification,[status(thm)],[c_5832,c_192]) ).
tff(c_6245,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5634,c_5849]) ).
tff(c_6265,plain,
! [Y_486,X_487] : is_a_theorem(implies(or(Y_486,not(X_487)),implies(X_487,Y_486))),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_6282,plain,
! [X_487,Y_486] :
( is_a_theorem(implies(X_487,Y_486))
| ~ is_a_theorem(or(Y_486,not(X_487))) ),
inference(resolution,[status(thm)],[c_6265,c_201]) ).
tff(c_7790,plain,
! [X_587] : is_a_theorem(implies(X_587,and(X_587,X_587))),
inference(resolution,[status(thm)],[c_7763,c_6282]) ).
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_5085,plain,
~ kn1,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_68,plain,
( kn1
| ~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_5105,plain,
~ is_a_theorem(implies('#skF_33',and('#skF_33','#skF_33'))),
inference(negUnitSimplification,[status(thm)],[c_5085,c_68]) ).
tff(c_7795,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7790,c_5105]) ).
tff(c_7796,plain,
! [P_33] : is_a_theorem(implies(P_33,and(P_33,P_33))),
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_7972,plain,
! [P_33] :
( is_a_theorem(and(P_33,P_33))
| ~ is_a_theorem(P_33) ),
inference(resolution,[status(thm)],[c_7796,c_7947]) ).
tff(c_8438,plain,
! [Y_646] :
( is_a_theorem(equiv(Y_646,Y_646))
| ~ is_a_theorem(implies(Y_646,Y_646)) ),
inference(superposition,[status(thm),theory(equality)],[c_8431,c_7972]) ).
tff(c_12446,plain,
! [Y_646] : is_a_theorem(equiv(Y_646,Y_646)),
inference(demodulation,[status(thm),theory(equality)],[c_12437,c_8438]) ).
tff(c_32110,plain,
! [X_1587] : is_a_theorem(not(not(equiv(X_1587,not(not(X_1587)))))),
inference(superposition,[status(thm),theory(equality)],[c_31830,c_12446]) ).
tff(c_7823,plain,
! [X_593,Y_594] : ( or(not(X_593),Y_594) = implies(X_593,Y_594) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_7839,plain,
! [Y_595,X_596] : is_a_theorem(implies(Y_595,implies(X_596,Y_595))),
inference(superposition,[status(thm),theory(equality)],[c_7823,c_173]) ).
tff(c_7892,plain,
! [X_601,X_602] : is_a_theorem(or(X_601,implies(X_602,not(X_601)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_7839]) ).
tff(c_9607,plain,
! [X_714,X_715] : is_a_theorem(implies(X_714,implies(X_715,not(not(X_714))))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_7892]) ).
tff(c_10445,plain,
! [X_754,X_755] : is_a_theorem(or(X_754,implies(X_755,not(not(not(X_754)))))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_9607]) ).
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_7969,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_7947]) ).
tff(c_10472,plain,
! [X_756,X_757] : is_a_theorem(or(implies(X_756,not(not(not(X_757)))),X_757)),
inference(resolution,[status(thm)],[c_10445,c_7969]) ).
tff(c_7956,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_7947]) ).
tff(c_10479,plain,
! [X_757,X_756] :
( is_a_theorem(X_757)
| ~ is_a_theorem(not(implies(X_756,not(not(not(X_757)))))) ),
inference(resolution,[status(thm)],[c_10472,c_7956]) ).
tff(c_10501,plain,
! [X_758,X_759] :
( is_a_theorem(X_758)
| ~ is_a_theorem(and(X_759,not(not(X_758)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_157,c_10479]) ).
tff(c_10523,plain,
! [X_758] :
( is_a_theorem(X_758)
| ~ is_a_theorem(not(not(X_758))) ),
inference(resolution,[status(thm)],[c_7972,c_10501]) ).
tff(c_32159,plain,
! [X_1588] : is_a_theorem(equiv(X_1588,not(not(X_1588)))),
inference(resolution,[status(thm)],[c_32110,c_10523]) ).
tff(c_140,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_67]) ).
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_32359,plain,
! [X_1589] : ( not(not(X_1589)) = X_1589 ),
inference(resolution,[status(thm)],[c_32159,c_196]) ).
tff(c_32802,plain,
! [X_60,X_1589] : ( implies(X_60,not(X_1589)) = not(and(X_60,X_1589)) ),
inference(superposition,[status(thm),theory(equality)],[c_32359,c_155]) ).
tff(c_7864,plain,
! [X_597,Y_598,Y_63] : ( implies(implies(X_597,not(Y_598)),Y_63) = or(and(X_597,Y_598),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_7855,c_153]) ).
tff(c_9445,plain,
! [X_62,X_701] : is_a_theorem(implies(implies(X_62,not(X_701)),implies(X_701,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_9432]) ).
tff(c_11422,plain,
! [X_62,X_701] : is_a_theorem(or(and(X_62,X_701),implies(X_701,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_7864,c_9445]) ).
tff(c_32977,plain,
! [X_62,X_701] : is_a_theorem(or(and(X_62,X_701),not(and(X_701,X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_32802,c_11422]) ).
tff(c_7867,plain,
! [X_597,Y_598,Y_57] : ( or(implies(X_597,not(Y_598)),Y_57) = implies(and(X_597,Y_598),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_7855,c_159]) ).
tff(c_11832,plain,
! [X_818,Y_819,Y_820] : ( implies(and(X_818,not(Y_819)),Y_820) = or(implies(X_818,Y_819),Y_820) ),
inference(superposition,[status(thm),theory(equality)],[c_7907,c_153]) ).
tff(c_2174,plain,
! [X_224,Y_225] : ( not(implies(X_224,not(Y_225))) = and(X_224,Y_225) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_2192,plain,
! [X_224,Y_225,Y_57] : ( or(implies(X_224,not(Y_225)),Y_57) = implies(and(X_224,Y_225),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_2174,c_159]) ).
tff(c_2103,plain,
! [X_214,Y_215] : ( implies(not(X_214),Y_215) = or(X_214,Y_215) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_2114,plain,
! [X_214,P_46] : is_a_theorem(or(X_214,or(P_46,not(X_214)))),
inference(superposition,[status(thm),theory(equality)],[c_2103,c_173]) ).
tff(c_2245,plain,
! [Y_230,X_231] :
( is_a_theorem(Y_230)
| ~ is_a_theorem(implies(X_231,Y_230))
| ~ is_a_theorem(X_231) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_2348,plain,
! [Q_238,P_239] :
( is_a_theorem(or(Q_238,P_239))
| ~ is_a_theorem(or(P_239,Q_238)) ),
inference(resolution,[status(thm)],[c_169,c_2245]) ).
tff(c_3172,plain,
! [P_293,X_294] : is_a_theorem(or(or(P_293,not(X_294)),X_294)),
inference(resolution,[status(thm)],[c_2114,c_2348]) ).
tff(c_3184,plain,
! [X_62,X_294] : is_a_theorem(or(implies(X_62,not(X_294)),X_294)),
inference(superposition,[status(thm),theory(equality)],[c_153,c_3172]) ).
tff(c_4902,plain,
! [X_62,X_294] : is_a_theorem(implies(and(X_62,X_294),X_294)),
inference(demodulation,[status(thm),theory(equality)],[c_2192,c_3184]) ).
tff(c_36,plain,
( and_2
| ~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_207,plain,
~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')),
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_5081,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4902,c_207]) ).
tff(c_5082,plain,
and_2,
inference(splitRight,[status(thm)],[c_36]) ).
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_92]) ).
tff(c_7803,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_5082,c_38]) ).
tff(c_12001,plain,
! [X_821,Y_822] : is_a_theorem(or(implies(X_821,Y_822),not(Y_822))),
inference(superposition,[status(thm),theory(equality)],[c_11832,c_7803]) ).
tff(c_12019,plain,
! [X_597,Y_598] : is_a_theorem(implies(and(X_597,Y_598),not(not(Y_598)))),
inference(superposition,[status(thm),theory(equality)],[c_7867,c_12001]) ).
tff(c_10381,plain,
! [X_750,X_751] : is_a_theorem(implies(implies(X_750,not(X_751)),implies(X_751,not(X_750)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_9432]) ).
tff(c_20017,plain,
! [X_1164,X_1165] :
( is_a_theorem(implies(X_1164,not(X_1165)))
| ~ is_a_theorem(implies(X_1165,not(X_1164))) ),
inference(resolution,[status(thm)],[c_10381,c_201]) ).
tff(c_20043,plain,
! [Y_598,X_597] : is_a_theorem(implies(not(Y_598),not(and(X_597,Y_598)))),
inference(resolution,[status(thm)],[c_12019,c_20017]) ).
tff(c_20092,plain,
! [Y_598,X_597] : is_a_theorem(or(Y_598,not(and(X_597,Y_598)))),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_20043]) ).
tff(c_138,plain,
r5,
inference(cnfTransformation,[status(thm)],[f_254]) ).
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_168]) ).
tff(c_9591,plain,
! [Q_711,R_712,P_713] : is_a_theorem(implies(implies(Q_711,R_712),implies(or(P_713,Q_711),or(P_713,R_712)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_16234,plain,
! [P_1002,Q_1003,R_1004] :
( is_a_theorem(implies(or(P_1002,Q_1003),or(P_1002,R_1004)))
| ~ is_a_theorem(implies(Q_1003,R_1004)) ),
inference(resolution,[status(thm)],[c_9591,c_201]) ).
tff(c_38929,plain,
! [P_1761,R_1762,Q_1763] :
( is_a_theorem(or(P_1761,R_1762))
| ~ is_a_theorem(or(P_1761,Q_1763))
| ~ is_a_theorem(implies(Q_1763,R_1762)) ),
inference(resolution,[status(thm)],[c_16234,c_201]) ).
tff(c_39003,plain,
! [Y_598,R_1762,X_597] :
( is_a_theorem(or(Y_598,R_1762))
| ~ is_a_theorem(implies(not(and(X_597,Y_598)),R_1762)) ),
inference(resolution,[status(thm)],[c_20092,c_38929]) ).
tff(c_43817,plain,
! [Y_1943,R_1944,X_1945] :
( is_a_theorem(or(Y_1943,R_1944))
| ~ is_a_theorem(or(and(X_1945,Y_1943),R_1944)) ),
inference(demodulation,[status(thm),theory(equality)],[c_159,c_39003]) ).
tff(c_44175,plain,
! [X_1949,X_1950] : is_a_theorem(or(X_1949,not(and(X_1949,X_1950)))),
inference(resolution,[status(thm)],[c_32977,c_43817]) ).
tff(c_44235,plain,
! [X_1949,X_1950] : is_a_theorem(implies(and(X_1949,X_1950),X_1949)),
inference(resolution,[status(thm)],[c_44175,c_9449]) ).
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_88]) ).
tff(c_205,plain,
~ and_1,
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_32,plain,
( and_1
| ~ is_a_theorem(implies(and('#skF_14','#skF_15'),'#skF_14')) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_7854,plain,
~ is_a_theorem(implies(and('#skF_14','#skF_15'),'#skF_14')),
inference(negUnitSimplification,[status(thm)],[c_205,c_32]) ).
tff(c_44249,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44235,c_7854]) ).
tff(c_44250,plain,
! [X_14,Y_15] : is_a_theorem(implies(and(X_14,Y_15),X_14)),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_44662,plain,
! [X_1990,Y_1991] : is_a_theorem(implies(equiv(X_1990,Y_1991),implies(X_1990,Y_1991))),
inference(superposition,[status(thm),theory(equality)],[c_44653,c_44250]) ).
tff(c_148,plain,
~ equivalence_1,
inference(cnfTransformation,[status(thm)],[f_265]) ).
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_187,plain,
~ is_a_theorem(implies(equiv('#skF_27','#skF_28'),implies('#skF_27','#skF_28'))),
inference(negUnitSimplification,[status(thm)],[c_148,c_56]) ).
tff(c_44711,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44662,c_187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL493+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 13:41:19 EDT 2023
% 0.13/0.36 % CPUTime :
% 19.47/9.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.47/9.34
% 19.47/9.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.88/9.39
% 19.88/9.39 Inference rules
% 19.88/9.39 ----------------------
% 19.88/9.39 #Ref : 0
% 19.88/9.39 #Sup : 10537
% 19.88/9.39 #Fact : 0
% 19.88/9.39 #Define : 0
% 19.88/9.39 #Split : 142
% 19.88/9.39 #Chain : 0
% 19.88/9.39 #Close : 0
% 19.88/9.39
% 19.88/9.39 Ordering : KBO
% 19.88/9.39
% 19.88/9.39 Simplification rules
% 19.88/9.39 ----------------------
% 19.88/9.39 #Subsume : 2398
% 19.88/9.39 #Demod : 7384
% 19.88/9.39 #Tautology : 2615
% 19.88/9.39 #SimpNegUnit : 43
% 19.88/9.40 #BackRed : 231
% 19.88/9.40
% 19.88/9.40 #Partial instantiations: 0
% 19.88/9.40 #Strategies tried : 1
% 19.88/9.40
% 19.88/9.40 Timing (in seconds)
% 19.88/9.40 ----------------------
% 19.88/9.40 Preprocessing : 0.63
% 19.88/9.40 Parsing : 0.32
% 19.88/9.40 CNF conversion : 0.05
% 19.88/9.40 Main loop : 7.65
% 19.88/9.40 Inferencing : 1.57
% 19.88/9.40 Reduction : 3.61
% 19.88/9.40 Demodulation : 2.61
% 19.88/9.40 BG Simplification : 0.09
% 19.88/9.40 Subsumption : 1.88
% 19.88/9.40 Abstraction : 0.10
% 19.88/9.40 MUC search : 0.00
% 19.88/9.40 Cooper : 0.00
% 19.88/9.40 Total : 8.37
% 19.88/9.40 Index Insertion : 0.00
% 19.88/9.40 Index Deletion : 0.00
% 19.88/9.40 Index Matching : 0.00
% 19.88/9.40 BG Taut test : 0.00
%------------------------------------------------------------------------------