TSTP Solution File: KLE021+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE021+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n032.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 10:44:41 EDT 2023
% Result : Theorem 3.51s 1.88s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 53 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 12 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 (; 33 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > complement > test > multiplication > addition > #nlpp > c > zero > one > #skF_1 > #skF_2 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(c,type,
c: $i > $i ).
tff(multiplication,type,
multiplication: ( $i * $i ) > $i ).
tff(addition,type,
addition: ( $i * $i ) > $i ).
tff(complement,type,
complement: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(test,type,
test: $i > $o ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_59,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
tff(f_81,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
tff(f_142,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(f_66,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_53,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_128,axiom,
! [X0,X1] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(f_122,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
tff(f_71,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_26,plain,
! [A_21,B_22] :
( leq(A_21,B_22)
| ( addition(A_21,B_22) != B_22 ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_48,plain,
test('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_42,plain,
! [X0_29] :
( complement(X0_29,c(X0_29))
| ~ test(X0_29) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_502,plain,
! [X0_67,X1_68] :
( ( addition(X0_67,X1_68) = one )
| ~ complement(X1_68,X0_67) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_508,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_502]) ).
tff(c_702,plain,
! [X0_83] :
( ( addition(X0_83,c(X0_83)) = one )
| ~ test(X0_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_508]) ).
tff(c_268,plain,
! [X0_49,X1_50] :
( ( addition(X0_49,X1_50) = one )
| ~ complement(X1_50,X0_49) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_274,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_268]) ).
tff(c_354,plain,
! [X0_60] :
( ( addition(X0_60,c(X0_60)) = one )
| ~ test(X0_60) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_274]) ).
tff(c_18,plain,
! [A_16,C_18,B_17] : ( addition(multiplication(A_16,C_18),multiplication(B_17,C_18)) = multiplication(addition(A_16,B_17),C_18) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_46,plain,
( ~ leq(addition(multiplication('#skF_3','#skF_2'),multiplication(c('#skF_3'),'#skF_2')),'#skF_2')
| ~ leq('#skF_2',addition(multiplication('#skF_3','#skF_2'),multiplication(c('#skF_3'),'#skF_2'))) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_49,plain,
( ~ leq(multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'),'#skF_2')
| ~ leq('#skF_2',multiplication(addition('#skF_3',c('#skF_3')),'#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_18,c_46]) ).
tff(c_150,plain,
~ leq('#skF_2',multiplication(addition('#skF_3',c('#skF_3')),'#skF_2')),
inference(splitLeft,[status(thm)],[c_49]) ).
tff(c_363,plain,
( ~ leq('#skF_2',multiplication(one,'#skF_2'))
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_354,c_150]) ).
tff(c_382,plain,
~ leq('#skF_2','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_14,c_363]) ).
tff(c_387,plain,
addition('#skF_2','#skF_2') != '#skF_2',
inference(resolution,[status(thm)],[c_26,c_382]) ).
tff(c_391,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_387]) ).
tff(c_392,plain,
~ leq(multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'),'#skF_2'),
inference(splitRight,[status(thm)],[c_49]) ).
tff(c_711,plain,
( ~ leq(multiplication(one,'#skF_2'),'#skF_2')
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_702,c_392]) ).
tff(c_736,plain,
~ leq('#skF_2','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_14,c_711]) ).
tff(c_746,plain,
addition('#skF_2','#skF_2') != '#skF_2',
inference(resolution,[status(thm)],[c_26,c_736]) ).
tff(c_750,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE021+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Aug 3 23:28:51 EDT 2023
% 0.11/0.31 % CPUTime :
% 3.51/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/1.88
% 3.51/1.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.56/1.91
% 3.56/1.91 Inference rules
% 3.56/1.91 ----------------------
% 3.56/1.91 #Ref : 0
% 3.56/1.91 #Sup : 159
% 3.56/1.91 #Fact : 0
% 3.56/1.91 #Define : 0
% 3.56/1.91 #Split : 4
% 3.56/1.91 #Chain : 0
% 3.56/1.91 #Close : 0
% 3.56/1.91
% 3.56/1.91 Ordering : KBO
% 3.56/1.91
% 3.56/1.91 Simplification rules
% 3.56/1.91 ----------------------
% 3.56/1.91 #Subsume : 29
% 3.56/1.91 #Demod : 47
% 3.56/1.91 #Tautology : 94
% 3.56/1.91 #SimpNegUnit : 2
% 3.56/1.91 #BackRed : 0
% 3.56/1.91
% 3.56/1.91 #Partial instantiations: 0
% 3.56/1.91 #Strategies tried : 1
% 3.56/1.91
% 3.56/1.91 Timing (in seconds)
% 3.56/1.91 ----------------------
% 3.56/1.92 Preprocessing : 0.50
% 3.56/1.92 Parsing : 0.26
% 3.56/1.92 CNF conversion : 0.03
% 3.56/1.92 Main loop : 0.41
% 3.56/1.92 Inferencing : 0.16
% 3.56/1.92 Reduction : 0.12
% 3.56/1.92 Demodulation : 0.09
% 3.56/1.92 BG Simplification : 0.02
% 3.56/1.92 Subsumption : 0.08
% 3.56/1.92 Abstraction : 0.02
% 3.56/1.92 MUC search : 0.00
% 3.56/1.92 Cooper : 0.00
% 3.56/1.92 Total : 0.95
% 3.56/1.92 Index Insertion : 0.00
% 3.56/1.92 Index Deletion : 0.00
% 3.56/1.92 Index Matching : 0.00
% 3.56/1.92 BG Taut test : 0.00
%------------------------------------------------------------------------------