TSTP Solution File: LCL456+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL456+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 : n026.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 16.52s 6.81s
% Output : CNFRefutation 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 106
% Syntax : Number of formulae : 148 ( 36 unt; 92 typ; 0 def)
% Number of atoms : 83 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 21 ~; 18 |; 1 &)
% ( 3 <=>; 5 =>; 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 : 82 (; 82 !; 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_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_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_273,negated_conjecture,
~ r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
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(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_15857,plain,
! [X_959,Y_960] : ( not(and(X_959,not(Y_960))) = implies(X_959,Y_960) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
tff(c_15881,plain,
! [X_959,Y_960,Y_57] : ( or(and(X_959,not(Y_960)),Y_57) = implies(implies(X_959,Y_960),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_15857,c_175]) ).
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_15878,plain,
! [X_959,Y_960,Y_63] : ( implies(and(X_959,not(Y_960)),Y_63) = or(implies(X_959,Y_960),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_15857,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_15760,plain,
! [X_947,Y_948] : ( not(implies(X_947,not(Y_948))) = and(X_947,Y_948) ),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_169,c_114]) ).
tff(c_15775,plain,
! [X_947,Y_948,Y_57] : ( or(implies(X_947,not(Y_948)),Y_57) = implies(and(X_947,Y_948),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_15760,c_175]) ).
tff(c_15772,plain,
! [X_947,Y_948,Y_63] : ( implies(implies(X_947,not(Y_948)),Y_63) = or(and(X_947,Y_948),Y_63) ),
inference(superposition,[status(thm),theory(equality)],[c_15760,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_15939,plain,
! [Y_969,X_970] : is_a_theorem(implies(or(Y_969,not(X_970)),implies(X_970,Y_969))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_175,c_18]) ).
tff(c_15952,plain,
! [X_62,X_970] : is_a_theorem(implies(implies(X_62,not(X_970)),implies(X_970,not(X_62)))),
inference(superposition,[status(thm),theory(equality)],[c_169,c_15939]) ).
tff(c_18606,plain,
! [X_62,X_970] : is_a_theorem(or(and(X_62,X_970),implies(X_970,not(X_62)))),
inference(demodulation,[status(thm),theory(equality)],[c_15772,c_15952]) ).
tff(c_15785,plain,
! [X_56,Y_948] : ( not(or(X_56,not(Y_948))) = and(not(X_56),Y_948) ),
inference(superposition,[status(thm),theory(equality)],[c_175,c_15760]) ).
tff(c_15955,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_15939]) ).
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_15693,plain,
! [Y_936,X_937] :
( is_a_theorem(Y_936)
| ~ is_a_theorem(implies(X_937,Y_936))
| ~ is_a_theorem(X_937) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_16688,plain,
! [Y_1024,X_1025] :
( is_a_theorem(Y_1024)
| ~ is_a_theorem(or(X_1025,Y_1024))
| ~ is_a_theorem(not(X_1025)) ),
inference(superposition,[status(thm),theory(equality)],[c_175,c_15693]) ).
tff(c_27737,plain,
! [Y_1515,X_1516] :
( is_a_theorem(Y_1515)
| ~ is_a_theorem(implies(X_1516,Y_1515))
| ~ is_a_theorem(not(not(X_1516))) ),
inference(superposition,[status(thm),theory(equality)],[c_169,c_16688]) ).
tff(c_27795,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_15955,c_27737]) ).
tff(c_27970,plain,
! [X_1518,Y_1519] :
( is_a_theorem(or(X_1518,Y_1519))
| ~ is_a_theorem(or(Y_1519,X_1518)) ),
inference(demodulation,[status(thm),theory(equality)],[c_175,c_171,c_15785,c_27795]) ).
tff(c_28036,plain,
! [X_970,X_62] : is_a_theorem(or(implies(X_970,not(X_62)),and(X_62,X_970))),
inference(resolution,[status(thm)],[c_18606,c_27970]) ).
tff(c_28393,plain,
! [X_1531,X_1532] : is_a_theorem(implies(and(X_1531,X_1532),and(X_1532,X_1531))),
inference(demodulation,[status(thm),theory(equality)],[c_15775,c_28036]) ).
tff(c_28786,plain,
! [X_1549,Y_1550] : is_a_theorem(or(implies(X_1549,Y_1550),and(not(Y_1550),X_1549))),
inference(superposition,[status(thm),theory(equality)],[c_15878,c_28393]) ).
tff(c_27893,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_15785,c_27795]) ).
tff(c_29204,plain,
! [Y_1567,X_1568] : is_a_theorem(or(and(not(Y_1567),X_1568),implies(X_1568,Y_1567))),
inference(resolution,[status(thm)],[c_28786,c_27893]) ).
tff(c_29233,plain,
! [Y_1567,Y_960] : is_a_theorem(implies(implies(not(Y_1567),Y_960),implies(not(Y_960),Y_1567))),
inference(superposition,[status(thm),theory(equality)],[c_15881,c_29204]) ).
tff(c_29258,plain,
! [Y_1567,Y_960] : is_a_theorem(implies(or(Y_1567,Y_960),or(Y_960,Y_1567))),
inference(demodulation,[status(thm),theory(equality)],[c_175,c_175,c_29233]) ).
tff(c_164,plain,
~ r3,
inference(cnfTransformation,[status(thm)],[f_273]) ).
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_176,plain,
~ is_a_theorem(implies(or('#skF_48','#skF_49'),or('#skF_49','#skF_48'))),
inference(negUnitSimplification,[status(thm)],[c_164,c_100]) ).
tff(c_29267,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29258,c_176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL456+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
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 14:11:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.52/6.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.52/6.81
% 16.52/6.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.52/6.85
% 16.52/6.85 Inference rules
% 16.52/6.85 ----------------------
% 16.52/6.85 #Ref : 0
% 16.52/6.85 #Sup : 7139
% 16.52/6.85 #Fact : 0
% 16.52/6.85 #Define : 0
% 16.52/6.85 #Split : 37
% 16.52/6.85 #Chain : 0
% 16.52/6.85 #Close : 0
% 16.52/6.85
% 16.52/6.85 Ordering : KBO
% 16.52/6.85
% 16.52/6.85 Simplification rules
% 16.52/6.85 ----------------------
% 16.52/6.85 #Subsume : 1524
% 16.52/6.85 #Demod : 4783
% 16.52/6.85 #Tautology : 1410
% 16.52/6.85 #SimpNegUnit : 81
% 16.52/6.85 #BackRed : 65
% 16.52/6.85
% 16.52/6.85 #Partial instantiations: 0
% 16.52/6.85 #Strategies tried : 1
% 16.52/6.85
% 16.52/6.85 Timing (in seconds)
% 16.52/6.85 ----------------------
% 16.52/6.85 Preprocessing : 0.64
% 16.52/6.85 Parsing : 0.33
% 16.52/6.85 CNF conversion : 0.05
% 16.52/6.85 Main loop : 5.03
% 16.52/6.85 Inferencing : 1.19
% 16.52/6.85 Reduction : 2.31
% 16.52/6.85 Demodulation : 1.76
% 16.52/6.85 BG Simplification : 0.08
% 16.52/6.85 Subsumption : 1.13
% 16.52/6.85 Abstraction : 0.09
% 16.52/6.85 MUC search : 0.00
% 16.52/6.85 Cooper : 0.00
% 16.52/6.85 Total : 5.73
% 16.52/6.85 Index Insertion : 0.00
% 16.52/6.85 Index Deletion : 0.00
% 16.52/6.85 Index Matching : 0.00
% 16.52/6.85 BG Taut test : 0.00
%------------------------------------------------------------------------------