TSTP Solution File: LCL457+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL457+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 10:48:10 EDT 2023
% Result : Theorem 131.31s 111.32s
% Output : CNFRefutation 131.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 123
% Syntax : Number of formulae : 224 ( 79 unt; 92 typ; 0 def)
% Number of atoms : 199 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 125 ( 58 ~; 48 |; 1 &)
% ( 12 <=>; 6 =>; 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 : 200 (; 200 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > or > implies > equiv > and > #nlpp > not > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_or > op_implies_or > op_implies_and > op_equiv > op_and > modus_tollens > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > and_3 > and_2 > and_1 > #skF_33 > #skF_41 > #skF_52 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_31 > #skF_15 > #skF_25 > #skF_55 > #skF_38 > #skF_36 > #skF_54 > #skF_43 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_10 > #skF_16 > #skF_47 > #skF_26 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_21 > #skF_9 > #skF_32 > #skF_50 > #skF_8 > #skF_30 > #skF_42 > #skF_4 > #skF_22 > #skF_29 > #skF_28 > #skF_35 > #skF_24 > #skF_27 > #skF_23 > #skF_44 > #skF_12 > #skF_34
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $o ).
tff(equiv,type,
equiv: ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_41',type,
'#skF_41': $i ).
tff(r3,type,
r3: $o ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(op_implies_or,type,
op_implies_or: $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(cn2,type,
cn2: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_54',type,
'#skF_54': $i ).
tff('#skF_43',type,
'#skF_43': $i ).
tff(op_and,type,
op_and: $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_40',type,
'#skF_40': $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_37',type,
'#skF_37': $i ).
tff(and_3,type,
and_3: $o ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(op_implies_and,type,
op_implies_and: $o ).
tff(equivalence_1,type,
equivalence_1: $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(kn2,type,
kn2: $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_53',type,
'#skF_53': $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff(or_1,type,
or_1: $o ).
tff(implies_3,type,
implies_3: $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_45',type,
'#skF_45': $i ).
tff('#skF_46',type,
'#skF_46': $i ).
tff('#skF_39',type,
'#skF_39': $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(modus_tollens,type,
modus_tollens: $o ).
tff(r2,type,
r2: $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(not,type,
not: $i > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(modus_ponens,type,
modus_ponens: $o ).
tff(op_or,type,
op_or: $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(or_3,type,
or_3: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(kn1,type,
kn1: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff(f_258,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
tff(f_104,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_2) ).
tff(f_253,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
tff(f_84,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
tff(f_248,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
tff(f_60,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_257,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
tff(f_100,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
tff(f_259,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
tff(f_108,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
tff(f_244,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
tff(f_245,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
tff(f_206,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_269,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
tff(f_210,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_270,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
tff(f_202,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_250,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
tff(f_72,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_159,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
tff(f_262,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
tff(f_120,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
tff(f_265,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
tff(f_67,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
tff(f_254,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
tff(f_88,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_255,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
tff(f_92,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_273,negated_conjecture,
~ r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
tff(c_146,plain,
or_2,
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_50,plain,
! [Y_23,X_22] :
( is_a_theorem(implies(Y_23,or(X_22,Y_23)))
| ~ or_2 ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_200,plain,
! [Y_23,X_22] : is_a_theorem(implies(Y_23,or(X_22,Y_23))),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_50]) ).
tff(c_136,plain,
implies_3,
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_30,plain,
! [X_11,Y_12,Z_13] :
( is_a_theorem(implies(implies(X_11,Y_12),implies(implies(Y_12,Z_13),implies(X_11,Z_13))))
| ~ implies_3 ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_29215,plain,
! [X_1583,Y_1584,Z_1585] : is_a_theorem(implies(implies(X_1583,Y_1584),implies(implies(Y_1584,Z_1585),implies(X_1583,Z_1585)))),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_30]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_248]) ).
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_255,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_37608,plain,
! [Y_1946,Z_1947,X_1948] :
( is_a_theorem(implies(implies(Y_1946,Z_1947),implies(X_1948,Z_1947)))
| ~ is_a_theorem(implies(X_1948,Y_1946)) ),
inference(resolution,[status(thm)],[c_29215,c_255]) ).
tff(c_59881,plain,
! [X_2449,Z_2450,Y_2451] :
( is_a_theorem(implies(X_2449,Z_2450))
| ~ is_a_theorem(implies(Y_2451,Z_2450))
| ~ is_a_theorem(implies(X_2449,Y_2451)) ),
inference(resolution,[status(thm)],[c_37608,c_255]) ).
tff(c_534320,plain,
! [X_4112,X_4113,Y_4114] :
( is_a_theorem(implies(X_4112,or(X_4113,Y_4114)))
| ~ is_a_theorem(implies(X_4112,Y_4114)) ),
inference(resolution,[status(thm)],[c_200,c_59881]) ).
tff(c_144,plain,
or_1,
inference(cnfTransformation,[status(thm)],[f_257]) ).
tff(c_46,plain,
! [X_20,Y_21] :
( is_a_theorem(implies(X_20,or(X_20,Y_21)))
| ~ or_1 ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_207,plain,
! [X_20,Y_21] : is_a_theorem(implies(X_20,or(X_20,Y_21))),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_46]) ).
tff(c_148,plain,
or_3,
inference(cnfTransformation,[status(thm)],[f_259]) ).
tff(c_54,plain,
! [X_24,Z_26,Y_25] :
( is_a_theorem(implies(implies(X_24,Z_26),implies(implies(Y_25,Z_26),implies(or(X_24,Y_25),Z_26))))
| ~ or_3 ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_29533,plain,
! [X_1608,Z_1609,Y_1610] : is_a_theorem(implies(implies(X_1608,Z_1609),implies(implies(Y_1610,Z_1609),implies(or(X_1608,Y_1610),Z_1609)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_39427,plain,
! [Y_2029,Z_2030,X_2031] :
( is_a_theorem(implies(implies(Y_2029,Z_2030),implies(or(X_2031,Y_2029),Z_2030)))
| ~ is_a_theorem(implies(X_2031,Z_2030)) ),
inference(resolution,[status(thm)],[c_29533,c_255]) ).
tff(c_39475,plain,
! [X_2031,Y_2029,Z_2030] :
( is_a_theorem(implies(or(X_2031,Y_2029),Z_2030))
| ~ is_a_theorem(implies(Y_2029,Z_2030))
| ~ is_a_theorem(implies(X_2031,Z_2030)) ),
inference(resolution,[status(thm)],[c_39427,c_255]) ).
tff(c_122,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_124,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_245]) ).
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_171,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_112,plain,
! [X_56,Y_57] :
( ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) )
| ~ op_or ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_175,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_171,c_112]) ).
tff(c_158,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_269]) ).
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_169,plain,
! [X_62,Y_63] : ( or(not(X_62),Y_63) = implies(X_62,Y_63) ),
inference(demodulation,[status(thm),theory(equality)],[c_158,c_118]) ).
tff(c_15617,plain,
! [X_928,Y_929] : ( not(and(X_928,not(Y_929))) = implies(X_928,Y_929) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_15635,plain,
! [X_928,Y_929,Y_57] : ( or(and(X_928,not(Y_929)),Y_57) = implies(implies(X_928,Y_929),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_15617,c_175]) ).
tff(c_15638,plain,
! [X_928,Y_929,Y_63] : ( implies(and(X_928,not(Y_929)),Y_63) = or(implies(X_928,Y_929),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_15617,c_169]) ).
tff(c_160,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_270]) ).
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_15527,plain,
! [X_917,Y_918] : ( not(implies(X_917,not(Y_918))) = and(X_917,Y_918) ),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_169,c_114]) ).
tff(c_15542,plain,
! [X_917,Y_918,Y_57] : ( or(implies(X_917,not(Y_918)),Y_57) = implies(and(X_917,Y_918),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_15527,c_175]) ).
tff(c_15545,plain,
! [X_917,Y_918,Y_63] : ( implies(implies(X_917,not(Y_918)),Y_63) = or(and(X_917,Y_918),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_15527,c_169]) ).
tff(c_130,plain,
modus_tollens,
inference(cnfTransformation,[status(thm)],[f_250]) ).
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_15735,plain,
! [Y_941,X_942] : is_a_theorem(implies(or(Y_941,not(X_942)),implies(X_942,Y_941))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_175,c_18]) ).
tff(c_15751,plain,
! [X_62,X_942] : is_a_theorem(implies(implies(X_62,not(X_942)),implies(X_942,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_169,c_15735]) ).
tff(c_17584,plain,
! [X_62,X_942] : is_a_theorem(or(and(X_62,X_942),implies(X_942,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_15545,c_15751]) ).
tff(c_15555,plain,
! [X_56,Y_918] : ( not(or(X_56,not(Y_918))) = and(not(X_56),Y_918) ),
inference(superposition,[status(thm),theory(equality)],[c_175,c_15527]) ).
tff(c_15747,plain,
! [Y_57,X_56] : is_a_theorem(implies(or(Y_57,not(not(X_56))),or(X_56,Y_57))),
inference(superposition,[status(thm),theory(equality)],[c_175,c_15735]) ).
tff(c_15567,plain,
! [Y_923,X_924] :
( is_a_theorem(Y_923)
| ~ is_a_theorem(implies(X_924,Y_923))
| ~ is_a_theorem(X_924) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_16176,plain,
! [Y_986,X_987] :
( is_a_theorem(Y_986)
| ~ is_a_theorem(or(X_987,Y_986))
| ~ is_a_theorem(not(X_987)) ),
inference(superposition,[status(thm),theory(equality)],[c_175,c_15567]) ).
tff(c_26800,plain,
! [Y_1460,X_1461] :
( is_a_theorem(Y_1460)
| ~ is_a_theorem(implies(X_1461,Y_1460))
| ~ is_a_theorem(not(not(X_1461))) ),
inference(superposition,[status(thm),theory(equality)],[c_169,c_16176]) ).
tff(c_26858,plain,
! [X_56,Y_57] :
( is_a_theorem(or(X_56,Y_57))
| ~ is_a_theorem(not(not(or(Y_57,not(not(X_56)))))) ),
inference(resolution,[status(thm)],[c_15747,c_26800]) ).
tff(c_27029,plain,
! [X_1463,Y_1464] :
( is_a_theorem(or(X_1463,Y_1464))
| ~ is_a_theorem(or(Y_1464,X_1463)) ),
inference(demodulation,[status(thm),theory(equality)],[c_175,c_171,c_15555,c_26858]) ).
tff(c_27097,plain,
! [X_942,X_62] : is_a_theorem(or(implies(X_942,not(X_62)),and(X_62,X_942))),
inference(resolution,[status(thm)],[c_17584,c_27029]) ).
tff(c_27513,plain,
! [X_1481,X_1482] : is_a_theorem(implies(and(X_1481,X_1482),and(X_1482,X_1481))),
inference(demodulation,[status(thm),theory(equality)],[c_15542,c_27097]) ).
tff(c_28548,plain,
! [X_1521,Y_1522] : is_a_theorem(or(implies(X_1521,Y_1522),and(not(Y_1522),X_1521))),
inference(superposition,[status(thm),theory(equality)],[c_15638,c_27513]) ).
tff(c_26953,plain,
! [X_56,Y_57] :
( is_a_theorem(or(X_56,Y_57))
| ~ is_a_theorem(or(Y_57,X_56)) ),
inference(demodulation,[status(thm),theory(equality)],[c_175,c_171,c_15555,c_26858]) ).
tff(c_28725,plain,
! [Y_1529,X_1530] : is_a_theorem(or(and(not(Y_1529),X_1530),implies(X_1530,Y_1529))),
inference(resolution,[status(thm)],[c_28548,c_26953]) ).
tff(c_28751,plain,
! [Y_1529,Y_929] : is_a_theorem(implies(implies(not(Y_1529),Y_929),implies(not(Y_929),Y_1529))),
inference(superposition,[status(thm),theory(equality)],[c_15635,c_28725]) ).
tff(c_28778,plain,
! [Y_1529,Y_929] : is_a_theorem(implies(or(Y_1529,Y_929),or(Y_929,Y_1529))),
inference(demodulation,[status(thm),theory(equality)],[c_175,c_175,c_28751]) ).
tff(c_100,plain,
( r3
| ~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_15558,plain,
~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))),
inference(splitLeft,[status(thm)],[c_100]) ).
tff(c_28788,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28778,c_15558]) ).
tff(c_28789,plain,
r3,
inference(splitRight,[status(thm)],[c_100]) ).
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_28833,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_28789,c_102]) ).
tff(c_154,plain,
equivalence_3,
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_66,plain,
! [X_31,Y_32] :
( is_a_theorem(implies(implies(X_31,Y_32),implies(implies(Y_32,X_31),equiv(X_31,Y_32))))
| ~ equivalence_3 ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_29374,plain,
! [X_1598,Y_1599] : is_a_theorem(implies(implies(X_1598,Y_1599),implies(implies(Y_1599,X_1598),equiv(X_1598,Y_1599)))),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_66]) ).
tff(c_35506,plain,
! [Y_1865,X_1866] :
( is_a_theorem(implies(implies(Y_1865,X_1866),equiv(X_1866,Y_1865)))
| ~ is_a_theorem(implies(X_1866,Y_1865)) ),
inference(resolution,[status(thm)],[c_29374,c_255]) ).
tff(c_63075,plain,
! [X_2463,Y_2464] :
( is_a_theorem(equiv(X_2463,Y_2464))
| ~ is_a_theorem(implies(Y_2464,X_2463))
| ~ is_a_theorem(implies(X_2463,Y_2464)) ),
inference(resolution,[status(thm)],[c_35506,c_255]) ).
tff(c_63223,plain,
! [Q_49,P_48] :
( is_a_theorem(equiv(or(Q_49,P_48),or(P_48,Q_49)))
| ~ is_a_theorem(implies(or(Q_49,P_48),or(P_48,Q_49))) ),
inference(resolution,[status(thm)],[c_28833,c_63075]) ).
tff(c_69506,plain,
! [Q_2532,P_2533] : is_a_theorem(equiv(or(Q_2532,P_2533),or(P_2533,Q_2532))),
inference(demodulation,[status(thm),theory(equality)],[c_28833,c_63223]) ).
tff(c_156,plain,
substitution_of_equivalents,
inference(cnfTransformation,[status(thm)],[f_265]) ).
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_250,plain,
! [Y_4,X_3] :
( ( Y_4 = X_3 )
| ~ is_a_theorem(equiv(X_3,Y_4)) ),
inference(demodulation,[status(thm),theory(equality)],[c_156,c_10]) ).
tff(c_69558,plain,
! [Q_2532,P_2533] : ( or(Q_2532,P_2533) = or(P_2533,Q_2532) ),
inference(resolution,[status(thm)],[c_69506,c_250]) ).
tff(c_69576,plain,
! [Q_2534,P_2535] : ( or(Q_2534,P_2535) = or(P_2535,Q_2534) ),
inference(resolution,[status(thm)],[c_69506,c_250]) ).
tff(c_70152,plain,
! [Q_2534,X_62] : ( or(Q_2534,not(X_62)) = implies(X_62,Q_2534) ),
inference(superposition,[status(thm),theory(equality)],[c_69576,c_169]) ).
tff(c_70317,plain,
! [X_56,Y_918] : ( and(not(X_56),Y_918) = not(implies(Y_918,X_56)) ),
inference(demodulation,[status(thm),theory(equality)],[c_70152,c_15555]) ).
tff(c_138,plain,
and_1,
inference(cnfTransformation,[status(thm)],[f_254]) ).
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_222,plain,
! [X_14,Y_15] : is_a_theorem(implies(and(X_14,Y_15),X_14)),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_34]) ).
tff(c_140,plain,
and_2,
inference(cnfTransformation,[status(thm)],[f_255]) ).
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_218,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_38]) ).
tff(c_278184,plain,
! [X_3429,Y_3430,X_3431] :
( is_a_theorem(implies(X_3429,Y_3430))
| ~ is_a_theorem(implies(X_3429,and(X_3431,Y_3430))) ),
inference(resolution,[status(thm)],[c_218,c_59881]) ).
tff(c_279206,plain,
! [X_3438,Y_3439,Y_3440] : is_a_theorem(implies(and(and(X_3438,Y_3439),Y_3440),Y_3439)),
inference(resolution,[status(thm)],[c_222,c_278184]) ).
tff(c_279470,plain,
! [Y_918,X_56,Y_3440] : is_a_theorem(implies(and(not(implies(Y_918,X_56)),Y_3440),Y_918)),
inference(superposition,[status(thm),theory(equality)],[c_70317,c_279206]) ).
tff(c_282524,plain,
! [Y_3468,Y_3469,X_3470] : is_a_theorem(or(Y_3468,implies(Y_3469,implies(Y_3468,X_3470)))),
inference(demodulation,[status(thm),theory(equality)],[c_69558,c_175,c_70317,c_279470]) ).
tff(c_283039,plain,
! [X_62,Y_3469,X_3470] : is_a_theorem(implies(X_62,implies(Y_3469,implies(not(X_62),X_3470)))),
inference(superposition,[status(thm),theory(equality)],[c_169,c_282524]) ).
tff(c_283730,plain,
! [X_3474,Y_3475,X_3476] : is_a_theorem(implies(X_3474,implies(Y_3475,or(X_3474,X_3476)))),
inference(demodulation,[status(thm),theory(equality)],[c_175,c_283039]) ).
tff(c_284242,plain,
! [X_3474,X_56,X_3476] : is_a_theorem(implies(X_3474,or(X_56,or(X_3474,X_3476)))),
inference(superposition,[status(thm),theory(equality)],[c_175,c_283730]) ).
tff(c_170500,plain,
! [X_3089,Y_3090,Z_3091] :
( is_a_theorem(implies(or(X_3089,Y_3090),Z_3091))
| ~ is_a_theorem(implies(Y_3090,Z_3091))
| ~ is_a_theorem(implies(X_3089,Z_3091)) ),
inference(resolution,[status(thm)],[c_39427,c_255]) ).
tff(c_164,plain,
~ r4,
inference(cnfTransformation,[status(thm)],[f_273]) ).
tff(c_104,plain,
( r4
| ~ is_a_theorem(implies(or('#skF_50',or('#skF_51','#skF_52')),or('#skF_51',or('#skF_50','#skF_52')))) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_176,plain,
~ is_a_theorem(implies(or('#skF_50',or('#skF_51','#skF_52')),or('#skF_51',or('#skF_50','#skF_52')))),
inference(negUnitSimplification,[status(thm)],[c_164,c_104]) ).
tff(c_170769,plain,
( ~ is_a_theorem(implies(or('#skF_51','#skF_52'),or('#skF_51',or('#skF_50','#skF_52'))))
| ~ is_a_theorem(implies('#skF_50',or('#skF_51',or('#skF_50','#skF_52')))) ),
inference(resolution,[status(thm)],[c_170500,c_176]) ).
tff(c_170861,plain,
~ is_a_theorem(implies('#skF_50',or('#skF_51',or('#skF_50','#skF_52')))),
inference(splitLeft,[status(thm)],[c_170769]) ).
tff(c_285605,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_284242,c_170861]) ).
tff(c_285606,plain,
~ is_a_theorem(implies(or('#skF_51','#skF_52'),or('#skF_51',or('#skF_50','#skF_52')))),
inference(splitRight,[status(thm)],[c_170769]) ).
tff(c_286002,plain,
( ~ is_a_theorem(implies('#skF_52',or('#skF_51',or('#skF_50','#skF_52'))))
| ~ is_a_theorem(implies('#skF_51',or('#skF_51',or('#skF_50','#skF_52')))) ),
inference(resolution,[status(thm)],[c_39475,c_285606]) ).
tff(c_286029,plain,
~ is_a_theorem(implies('#skF_52',or('#skF_51',or('#skF_50','#skF_52')))),
inference(demodulation,[status(thm),theory(equality)],[c_207,c_286002]) ).
tff(c_534367,plain,
~ is_a_theorem(implies('#skF_52',or('#skF_50','#skF_52'))),
inference(resolution,[status(thm)],[c_534320,c_286029]) ).
tff(c_534965,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_200,c_534367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL457+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 13:47:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 131.31/111.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 131.31/111.34
% 131.31/111.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 131.47/111.38
% 131.47/111.38 Inference rules
% 131.47/111.38 ----------------------
% 131.47/111.38 #Ref : 0
% 131.47/111.38 #Sup : 140246
% 131.47/111.38 #Fact : 0
% 131.47/111.38 #Define : 0
% 131.47/111.38 #Split : 52
% 131.47/111.38 #Chain : 0
% 131.47/111.38 #Close : 0
% 131.47/111.38
% 131.47/111.38 Ordering : KBO
% 131.47/111.38
% 131.47/111.38 Simplification rules
% 131.47/111.38 ----------------------
% 131.47/111.38 #Subsume : 31474
% 131.47/111.38 #Demod : 141736
% 131.47/111.38 #Tautology : 45957
% 131.47/111.38 #SimpNegUnit : 1328
% 131.47/111.38 #BackRed : 835
% 131.47/111.38
% 131.47/111.38 #Partial instantiations: 0
% 131.47/111.38 #Strategies tried : 1
% 131.47/111.38
% 131.47/111.38 Timing (in seconds)
% 131.47/111.38 ----------------------
% 131.47/111.39 Preprocessing : 0.68
% 131.47/111.39 Parsing : 0.32
% 131.47/111.39 CNF conversion : 0.06
% 131.47/111.39 Main loop : 109.59
% 131.47/111.39 Inferencing : 6.36
% 131.47/111.39 Reduction : 68.17
% 131.47/111.39 Demodulation : 60.70
% 131.47/111.39 BG Simplification : 0.55
% 131.47/111.39 Subsumption : 21.41
% 131.47/111.39 Abstraction : 0.99
% 131.47/111.39 MUC search : 0.00
% 131.47/111.39 Cooper : 0.00
% 131.47/111.39 Total : 110.34
% 131.47/111.39 Index Insertion : 0.00
% 131.47/111.39 Index Deletion : 0.00
% 131.47/111.39 Index Matching : 0.00
% 131.47/111.39 BG Taut test : 0.00
%------------------------------------------------------------------------------