TSTP Solution File: KLE025+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE025+1 : 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 : n025.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 5.47s 2.42s
% Output : CNFRefutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 48 ( 24 unt; 12 typ; 0 def)
% Number of atoms : 54 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 13 ~; 10 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 47 (; 47 !; 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_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_143,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( ( multiplication(multiplication(X1,X0),c(X2)) = zero )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_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_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
tff(f_68,axiom,
! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
tff(c_10,plain,
! [A_8,B_9,C_10] : ( multiplication(multiplication(A_8,B_9),C_10) = multiplication(A_8,multiplication(B_9,C_10)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_46,plain,
multiplication(multiplication('#skF_3','#skF_2'),'#skF_4') != multiplication('#skF_3','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_53,plain,
multiplication('#skF_3',multiplication('#skF_2','#skF_4')) != multiplication('#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_46]) ).
tff(c_50,plain,
test('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
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_276,plain,
! [X0_51,X1_52] :
( ( addition(X0_51,X1_52) = one )
| ~ complement(X1_52,X0_51) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_282,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_276]) ).
tff(c_285,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_282]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_470,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_71,C_72] : ( addition(A_71,addition(A_71,C_72)) = addition(A_71,C_72) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_470]) ).
tff(c_1039,plain,
! [X0_80] :
( ( addition(X0_80,c(X0_80)) = addition(X0_80,one) )
| ~ test(X0_80) ),
inference(superposition,[status(thm),theory(equality)],[c_285,c_696]) ).
tff(c_1094,plain,
! [X0_81] :
( ( addition(X0_81,one) = one )
| ~ test(X0_81)
| ~ test(X0_81) ),
inference(superposition,[status(thm),theory(equality)],[c_1039,c_285]) ).
tff(c_1100,plain,
( ( addition('#skF_4',one) = one )
| ~ test('#skF_4') ),
inference(resolution,[status(thm)],[c_50,c_1094]) ).
tff(c_1108,plain,
addition('#skF_4',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_1100]) ).
tff(c_732,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = addition(X0_29,one) )
| ~ test(X0_29) ),
inference(superposition,[status(thm),theory(equality)],[c_285,c_696]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_48,plain,
multiplication(multiplication('#skF_3','#skF_2'),c('#skF_4')) = zero,
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_765,plain,
! [A_73,B_74,C_75] : ( addition(multiplication(A_73,B_74),multiplication(A_73,C_75)) = multiplication(A_73,addition(B_74,C_75)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_835,plain,
! [B_74] : ( multiplication(multiplication('#skF_3','#skF_2'),addition(B_74,c('#skF_4'))) = addition(multiplication(multiplication('#skF_3','#skF_2'),B_74),zero) ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_765]) ).
tff(c_3510,plain,
! [B_112] : ( multiplication(multiplication('#skF_3','#skF_2'),addition(B_112,c('#skF_4'))) = multiplication('#skF_3',multiplication('#skF_2',B_112)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_6,c_835]) ).
tff(c_3556,plain,
( ( multiplication(multiplication('#skF_3','#skF_2'),addition('#skF_4',one)) = multiplication('#skF_3',multiplication('#skF_2','#skF_4')) )
| ~ test('#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_732,c_3510]) ).
tff(c_3593,plain,
multiplication('#skF_3',multiplication('#skF_2','#skF_4')) = multiplication('#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_12,c_1108,c_10,c_3556]) ).
tff(c_3595,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_53,c_3593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE025+1 : 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 : n025.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 23:41:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 5.47/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.47/2.42
% 5.47/2.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.77/2.46
% 5.77/2.46 Inference rules
% 5.77/2.46 ----------------------
% 5.77/2.46 #Ref : 0
% 5.77/2.46 #Sup : 852
% 5.77/2.46 #Fact : 0
% 5.77/2.46 #Define : 0
% 5.77/2.46 #Split : 2
% 5.77/2.46 #Chain : 0
% 5.77/2.46 #Close : 0
% 5.77/2.46
% 5.77/2.46 Ordering : KBO
% 5.77/2.46
% 5.77/2.46 Simplification rules
% 5.77/2.46 ----------------------
% 5.77/2.46 #Subsume : 119
% 5.77/2.46 #Demod : 777
% 5.77/2.46 #Tautology : 412
% 5.77/2.46 #SimpNegUnit : 3
% 5.77/2.46 #BackRed : 0
% 5.77/2.46
% 5.77/2.46 #Partial instantiations: 0
% 5.77/2.46 #Strategies tried : 1
% 5.77/2.46
% 5.77/2.46 Timing (in seconds)
% 5.77/2.46 ----------------------
% 5.77/2.46 Preprocessing : 0.52
% 5.77/2.46 Parsing : 0.28
% 5.77/2.46 CNF conversion : 0.03
% 5.77/2.46 Main loop : 0.85
% 5.77/2.46 Inferencing : 0.29
% 5.77/2.46 Reduction : 0.34
% 5.77/2.46 Demodulation : 0.27
% 5.77/2.46 BG Simplification : 0.03
% 5.77/2.46 Subsumption : 0.14
% 5.77/2.46 Abstraction : 0.04
% 5.77/2.46 MUC search : 0.00
% 5.77/2.46 Cooper : 0.00
% 5.77/2.46 Total : 1.42
% 5.77/2.46 Index Insertion : 0.00
% 5.77/2.46 Index Deletion : 0.00
% 5.77/2.46 Index Matching : 0.00
% 5.77/2.46 BG Taut test : 0.00
%------------------------------------------------------------------------------