TSTP Solution File: KLE026+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE026+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/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 : n012.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 10:44:42 EDT 2023
% Result : Theorem 6.17s 2.49s
% Output : CNFRefutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 47 ( 23 unt; 12 typ; 0 def)
% Number of atoms : 53 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 12 ~; 9 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 48 (; 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > complement > test > multiplication > addition > #nlpp > c > zero > one > #skF_1 > #skF_2 > #skF_3 > #skF_4
%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('#skF_4',type,
'#skF_4': $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_80,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
tff(f_180,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) )
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_127,axiom,
! [X0,X1] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(f_121,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
tff(f_54,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
tff(f_61,axiom,
! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
tff(f_70,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
tff(c_279,plain,
! [A_53,B_54] :
( leq(A_53,B_54)
| ( addition(A_53,B_54) != B_54 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_50,plain,
~ leq(multiplication('#skF_3','#skF_2'),multiplication('#skF_2','#skF_4')),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_283,plain,
addition(multiplication('#skF_3','#skF_2'),multiplication('#skF_2','#skF_4')) != multiplication('#skF_2','#skF_4'),
inference(resolution,[status(thm)],[c_279,c_50]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_56,plain,
test('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_42,plain,
! [X0_29] :
( complement(X0_29,c(X0_29))
| ~ test(X0_29) ),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_269,plain,
! [X0_51,X1_52] :
( ( addition(X0_51,X1_52) = one )
| ~ complement(X1_52,X0_51) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_275,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_269]) ).
tff(c_278,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_275]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_386,plain,
! [A_65,B_66,C_67] : ( addition(addition(A_65,B_66),C_67) = addition(A_65,addition(B_66,C_67)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_696,plain,
! [A_75,C_76] : ( addition(A_75,addition(A_75,C_76)) = addition(A_75,C_76) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_386]) ).
tff(c_1694,plain,
! [X0_95] :
( ( addition(X0_95,c(X0_95)) = addition(X0_95,one) )
| ~ test(X0_95) ),
inference(superposition,[status(thm),theory(equality)],[c_278,c_696]) ).
tff(c_1828,plain,
! [X0_97] :
( ( addition(X0_97,one) = one )
| ~ test(X0_97)
| ~ test(X0_97) ),
inference(superposition,[status(thm),theory(equality)],[c_1694,c_278]) ).
tff(c_1836,plain,
( ( addition('#skF_3',one) = one )
| ~ test('#skF_3') ),
inference(resolution,[status(thm)],[c_56,c_1828]) ).
tff(c_1845,plain,
addition('#skF_3',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_1836]) ).
tff(c_503,plain,
! [A_69,B_70,C_71] : ( multiplication(multiplication(A_69,B_70),C_71) = multiplication(A_69,multiplication(B_70,C_71)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_52,plain,
multiplication(multiplication('#skF_3','#skF_2'),'#skF_4') = multiplication('#skF_3','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_520,plain,
multiplication('#skF_3',multiplication('#skF_2','#skF_4')) = multiplication('#skF_3','#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_503,c_52]) ).
tff(c_773,plain,
! [A_77,C_78,B_79] : ( addition(multiplication(A_77,C_78),multiplication(B_79,C_78)) = multiplication(addition(A_77,B_79),C_78) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_4221,plain,
! [B_127,A_128] : ( multiplication(addition(one,B_127),A_128) = addition(A_128,multiplication(B_127,A_128)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_773]) ).
tff(c_4390,plain,
multiplication(addition(one,'#skF_3'),multiplication('#skF_2','#skF_4')) = addition(multiplication('#skF_2','#skF_4'),multiplication('#skF_3','#skF_2')),
inference(superposition,[status(thm),theory(equality)],[c_520,c_4221]) ).
tff(c_4487,plain,
addition(multiplication('#skF_3','#skF_2'),multiplication('#skF_2','#skF_4')) = multiplication('#skF_2','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_1845,c_2,c_2,c_4390]) ).
tff(c_4489,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_283,c_4487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE026+2 : TPTP v8.1.2. Released v4.0.0.
% 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
% 0.14/0.36 % Computer : n012.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 23:22:52 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.17/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.17/2.50
% 6.17/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.17/2.53
% 6.17/2.53 Inference rules
% 6.17/2.53 ----------------------
% 6.17/2.53 #Ref : 0
% 6.17/2.53 #Sup : 1060
% 6.17/2.53 #Fact : 0
% 6.17/2.53 #Define : 0
% 6.17/2.53 #Split : 2
% 6.17/2.53 #Chain : 0
% 6.17/2.53 #Close : 0
% 6.17/2.53
% 6.17/2.53 Ordering : KBO
% 6.17/2.53
% 6.17/2.53 Simplification rules
% 6.17/2.53 ----------------------
% 6.17/2.53 #Subsume : 167
% 6.17/2.53 #Demod : 1093
% 6.17/2.53 #Tautology : 507
% 6.17/2.53 #SimpNegUnit : 4
% 6.17/2.53 #BackRed : 0
% 6.17/2.53
% 6.17/2.53 #Partial instantiations: 0
% 6.17/2.53 #Strategies tried : 1
% 6.17/2.53
% 6.17/2.53 Timing (in seconds)
% 6.17/2.53 ----------------------
% 6.17/2.53 Preprocessing : 0.52
% 6.17/2.53 Parsing : 0.28
% 6.17/2.53 CNF conversion : 0.03
% 6.17/2.53 Main loop : 0.94
% 6.17/2.53 Inferencing : 0.31
% 6.17/2.53 Reduction : 0.38
% 6.17/2.53 Demodulation : 0.31
% 6.17/2.53 BG Simplification : 0.04
% 6.17/2.53 Subsumption : 0.15
% 6.17/2.53 Abstraction : 0.04
% 6.17/2.53 MUC search : 0.00
% 6.17/2.53 Cooper : 0.00
% 6.17/2.53 Total : 1.51
% 6.17/2.53 Index Insertion : 0.00
% 6.17/2.53 Index Deletion : 0.00
% 6.17/2.53 Index Matching : 0.00
% 6.17/2.53 BG Taut test : 0.00
%------------------------------------------------------------------------------