TSTP Solution File: LCL542+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL542+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 : n028.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 10:48:20 EDT 2023
% Result : Theorem 6.29s 2.41s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 171
% Syntax : Number of formulae : 186 ( 13 unt; 163 typ; 0 def)
% Number of atoms : 35 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 7 |; 0 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 19 (; 19 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > strict_implies > strict_equiv > or > implies > equiv > and > #nlpp > possibly > not > necessarily > substitution_strict_equiv > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_strict_implies > op_strict_equiv > op_possibly > op_or > op_necessarily > op_implies_or > op_implies_and > op_implies > op_equiv > op_and > necessitation > modus_tollens > modus_ponens_strict_implies > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > axiom_s4 > axiom_s3 > axiom_s2 > axiom_s1 > axiom_m9 > axiom_m8 > axiom_m7 > axiom_m6 > axiom_m5 > axiom_m4 > axiom_m3 > axiom_m2 > axiom_m10 > axiom_m1 > axiom_M > axiom_K > axiom_B > axiom_5 > axiom_4 > and_3 > and_2 > and_1 > adjunction > #skF_33 > #skF_41 > #skF_60 > #skF_57 > #skF_52 > #skF_76 > #skF_67 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_78 > #skF_94 > #skF_11 > #skF_86 > #skF_31 > #skF_15 > #skF_69 > #skF_25 > #skF_55 > #skF_87 > #skF_38 > #skF_36 > #skF_80 > #skF_56 > #skF_54 > #skF_43 > #skF_79 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_71 > #skF_10 > #skF_16 > #skF_85 > #skF_47 > #skF_92 > #skF_65 > #skF_26 > #skF_81 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_72 > #skF_6 > #skF_13 > #skF_61 > #skF_2 > #skF_68 > #skF_82 > #skF_84 > #skF_3 > #skF_1 > #skF_89 > #skF_21 > #skF_9 > #skF_32 > #skF_64 > #skF_50 > #skF_90 > #skF_8 > #skF_30 > #skF_42 > #skF_77 > #skF_4 > #skF_22 > #skF_93 > #skF_29 > #skF_28 > #skF_35 > #skF_70 > #skF_66 > #skF_24 > #skF_27 > #skF_23 > #skF_63 > #skF_88 > #skF_44 > #skF_83 > #skF_59 > #skF_73 > #skF_91 > #skF_58 > #skF_12 > #skF_62 > #skF_34 > #skF_75 > #skF_74
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $o ).
tff(axiom_s1,type,
axiom_s1: $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_60',type,
'#skF_60': $i ).
tff(op_possibly,type,
op_possibly: $o ).
tff('#skF_57',type,
'#skF_57': $i ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_76',type,
'#skF_76': $i ).
tff(axiom_m8,type,
axiom_m8: $o ).
tff('#skF_67',type,
'#skF_67': $i ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $o ).
tff(axiom_4,type,
axiom_4: $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('#skF_78',type,
'#skF_78': $i ).
tff(adjunction,type,
adjunction: $o ).
tff('#skF_94',type,
'#skF_94': $i ).
tff(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_86',type,
'#skF_86': $i ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_69',type,
'#skF_69': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(axiom_m3,type,
axiom_m3: $o ).
tff(cn2,type,
cn2: $o ).
tff(axiom_K,type,
axiom_K: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff('#skF_87',type,
'#skF_87': $i ).
tff(possibly,type,
possibly: $i > $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_80',type,
'#skF_80': $i ).
tff(axiom_B,type,
axiom_B: $o ).
tff('#skF_56',type,
'#skF_56': $i ).
tff(op_strict_equiv,type,
op_strict_equiv: $o ).
tff('#skF_54',type,
'#skF_54': $i ).
tff(axiom_5,type,
axiom_5: $o ).
tff('#skF_43',type,
'#skF_43': $i ).
tff('#skF_79',type,
'#skF_79': $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(op_strict_implies,type,
op_strict_implies: $o ).
tff('#skF_71',type,
'#skF_71': $i ).
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('#skF_85',type,
'#skF_85': $i ).
tff(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff('#skF_92',type,
'#skF_92': $i ).
tff('#skF_65',type,
'#skF_65': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_81',type,
'#skF_81': $i ).
tff(necessitation,type,
necessitation: $o ).
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(axiom_s4,type,
axiom_s4: $o ).
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('#skF_72',type,
'#skF_72': $i ).
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_61',type,
'#skF_61': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_68',type,
'#skF_68': $i ).
tff(axiom_m2,type,
axiom_m2: $o ).
tff(modus_ponens,type,
modus_ponens: $o ).
tff('#skF_82',type,
'#skF_82': $i ).
tff('#skF_84',type,
'#skF_84': $i ).
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(axiom_s3,type,
axiom_s3: $o ).
tff(substitution_strict_equiv,type,
substitution_strict_equiv: $o ).
tff(axiom_M,type,
axiom_M: $o ).
tff(strict_implies,type,
strict_implies: ( $i * $i ) > $i ).
tff('#skF_89',type,
'#skF_89': $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(necessarily,type,
necessarily: $i > $i ).
tff(axiom_m4,type,
axiom_m4: $o ).
tff('#skF_64',type,
'#skF_64': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_90',type,
'#skF_90': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(modus_ponens_strict_implies,type,
modus_ponens_strict_implies: $o ).
tff(axiom_m7,type,
axiom_m7: $o ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(axiom_s2,type,
axiom_s2: $o ).
tff('#skF_77',type,
'#skF_77': $i ).
tff(or_3,type,
or_3: $o ).
tff(op_necessarily,type,
op_necessarily: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(strict_equiv,type,
strict_equiv: ( $i * $i ) > $i ).
tff('#skF_93',type,
'#skF_93': $i ).
tff(kn1,type,
kn1: $o ).
tff(axiom_m6,type,
axiom_m6: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $i ).
tff('#skF_70',type,
'#skF_70': $i ).
tff('#skF_66',type,
'#skF_66': $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('#skF_63',type,
'#skF_63': $i ).
tff(axiom_m1,type,
axiom_m1: $o ).
tff('#skF_88',type,
'#skF_88': $i ).
tff(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff('#skF_83',type,
'#skF_83': $i ).
tff(axiom_m10,type,
axiom_m10: $o ).
tff(op_implies,type,
op_implies: $o ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff('#skF_59',type,
'#skF_59': $i ).
tff(axiom_m9,type,
axiom_m9: $o ).
tff('#skF_73',type,
'#skF_73': $i ).
tff('#skF_91',type,
'#skF_91': $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_58',type,
'#skF_58': $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(axiom_m5,type,
axiom_m5: $o ).
tff('#skF_62',type,
'#skF_62': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff('#skF_75',type,
'#skF_75': $i ).
tff('#skF_74',type,
'#skF_74': $i ).
tff(f_253,axiom,
and_1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
tff(f_484,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
tff(f_437,axiom,
( op_strict_implies
=> ! [X,Y] : ( strict_implies(X,Y) = necessarily(implies(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
tff(f_472,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
tff(f_297,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
tff(f_489,negated_conjecture,
~ axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
tff(f_366,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
tff(c_138,plain,
and_1,
inference(cnfTransformation,[status(thm)],[f_253]) ).
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_378,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_288,plain,
op_strict_implies,
inference(cnfTransformation,[status(thm)],[f_484]) ).
tff(c_266,plain,
! [X_107,Y_108] :
( ( necessarily(implies(X_107,Y_108)) = strict_implies(X_107,Y_108) )
| ~ op_strict_implies ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_449,plain,
! [X_129,Y_130] : ( necessarily(implies(X_129,Y_130)) = strict_implies(X_129,Y_130) ),
inference(demodulation,[status(thm),theory(equality)],[c_288,c_266]) ).
tff(c_272,plain,
necessitation,
inference(cnfTransformation,[status(thm)],[f_472]) ).
tff(c_158,plain,
! [X_66] :
( is_a_theorem(necessarily(X_66))
| ~ is_a_theorem(X_66)
| ~ necessitation ),
inference(cnfTransformation,[status(thm)],[f_297]) ).
tff(c_324,plain,
! [X_66] :
( is_a_theorem(necessarily(X_66))
| ~ is_a_theorem(X_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_272,c_158]) ).
tff(c_1005,plain,
! [X_197,Y_198] :
( is_a_theorem(strict_implies(X_197,Y_198))
| ~ is_a_theorem(implies(X_197,Y_198)) ),
inference(superposition,[status(thm),theory(equality)],[c_449,c_324]) ).
tff(c_294,plain,
~ axiom_m2,
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_226,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')) ),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_302,plain,
~ is_a_theorem(strict_implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(negUnitSimplification,[status(thm)],[c_294,c_226]) ).
tff(c_1026,plain,
~ is_a_theorem(implies(and('#skF_79','#skF_80'),'#skF_79')),
inference(resolution,[status(thm)],[c_1005,c_302]) ).
tff(c_1036,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_378,c_1026]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % 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
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 13:45:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.29/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.29/2.41
% 6.29/2.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.29/2.44
% 6.29/2.44 Inference rules
% 6.29/2.44 ----------------------
% 6.29/2.44 #Ref : 0
% 6.29/2.44 #Sup : 141
% 6.29/2.44 #Fact : 0
% 6.29/2.45 #Define : 0
% 6.29/2.45 #Split : 29
% 6.29/2.45 #Chain : 0
% 6.29/2.45 #Close : 0
% 6.29/2.45
% 6.29/2.45 Ordering : KBO
% 6.29/2.45
% 6.29/2.45 Simplification rules
% 6.29/2.45 ----------------------
% 6.29/2.45 #Subsume : 7
% 6.29/2.45 #Demod : 114
% 6.29/2.45 #Tautology : 54
% 6.29/2.45 #SimpNegUnit : 11
% 6.29/2.45 #BackRed : 0
% 6.29/2.45
% 6.29/2.45 #Partial instantiations: 0
% 6.29/2.45 #Strategies tried : 1
% 6.29/2.45
% 6.29/2.45 Timing (in seconds)
% 6.29/2.45 ----------------------
% 6.29/2.45 Preprocessing : 0.73
% 6.29/2.45 Parsing : 0.36
% 6.29/2.45 CNF conversion : 0.07
% 6.29/2.45 Main loop : 0.63
% 6.29/2.45 Inferencing : 0.21
% 6.29/2.45 Reduction : 0.22
% 6.29/2.45 Demodulation : 0.16
% 6.29/2.45 BG Simplification : 0.05
% 6.29/2.45 Subsumption : 0.11
% 6.29/2.45 Abstraction : 0.03
% 6.29/2.45 MUC search : 0.00
% 6.29/2.45 Cooper : 0.00
% 6.29/2.45 Total : 1.41
% 6.29/2.45 Index Insertion : 0.00
% 6.29/2.45 Index Deletion : 0.00
% 6.29/2.45 Index Matching : 0.00
% 6.29/2.45 BG Taut test : 0.00
%------------------------------------------------------------------------------