TSTP Solution File: KLE025+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE025+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 : n031.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 5.01s 2.38s
% Output : CNFRefutation 5.53s
% 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_180,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_50,plain,
multiplication(multiplication('#skF_3','#skF_2'),'#skF_4') != multiplication('#skF_3','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_57,plain,
multiplication('#skF_3',multiplication('#skF_2','#skF_4')) != multiplication('#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_50]) ).
tff(c_54,plain,
test('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_180]) ).
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_271,plain,
! [X0_53,X1_54] :
( ( addition(X0_53,X1_54) = one )
| ~ complement(X1_54,X0_53) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_277,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_271]) ).
tff(c_280,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_277]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_346,plain,
! [A_64,B_65,C_66] : ( addition(addition(A_64,B_65),C_66) = addition(A_64,addition(B_65,C_66)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_704,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_346]) ).
tff(c_1236,plain,
! [X0_88] :
( ( addition(X0_88,c(X0_88)) = addition(X0_88,one) )
| ~ test(X0_88) ),
inference(superposition,[status(thm),theory(equality)],[c_280,c_704]) ).
tff(c_1296,plain,
! [X0_89] :
( ( addition(X0_89,one) = one )
| ~ test(X0_89)
| ~ test(X0_89) ),
inference(superposition,[status(thm),theory(equality)],[c_1236,c_280]) ).
tff(c_1302,plain,
( ( addition('#skF_4',one) = one )
| ~ test('#skF_4') ),
inference(resolution,[status(thm)],[c_54,c_1296]) ).
tff(c_1310,plain,
addition('#skF_4',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_1302]) ).
tff(c_730,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = addition(X0_29,one) )
| ~ test(X0_29) ),
inference(superposition,[status(thm),theory(equality)],[c_280,c_704]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_52,plain,
multiplication(multiplication('#skF_3','#skF_2'),c('#skF_4')) = zero,
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_1314,plain,
! [A_90,B_91,C_92] : ( addition(multiplication(A_90,B_91),multiplication(A_90,C_92)) = multiplication(A_90,addition(B_91,C_92)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_1423,plain,
! [B_91] : ( multiplication(multiplication('#skF_3','#skF_2'),addition(B_91,c('#skF_4'))) = addition(multiplication(multiplication('#skF_3','#skF_2'),B_91),zero) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_1314]) ).
tff(c_2492,plain,
! [B_107] : ( multiplication(multiplication('#skF_3','#skF_2'),addition(B_107,c('#skF_4'))) = multiplication('#skF_3',multiplication('#skF_2',B_107)) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_6,c_1423]) ).
tff(c_2535,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_730,c_2492]) ).
tff(c_2573,plain,
multiplication('#skF_3',multiplication('#skF_2','#skF_4')) = multiplication('#skF_3','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_12,c_1310,c_10,c_2535]) ).
tff(c_2575,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57,c_2573]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % 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
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 23:47:15 EDT 2023
% 0.16/0.37 % CPUTime :
% 5.01/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/2.39
% 5.44/2.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.53/2.42
% 5.53/2.42 Inference rules
% 5.53/2.42 ----------------------
% 5.53/2.42 #Ref : 0
% 5.53/2.42 #Sup : 602
% 5.53/2.42 #Fact : 0
% 5.53/2.42 #Define : 0
% 5.53/2.42 #Split : 2
% 5.53/2.42 #Chain : 0
% 5.53/2.42 #Close : 0
% 5.53/2.42
% 5.53/2.42 Ordering : KBO
% 5.53/2.42
% 5.53/2.42 Simplification rules
% 5.53/2.42 ----------------------
% 5.53/2.42 #Subsume : 56
% 5.53/2.42 #Demod : 588
% 5.53/2.42 #Tautology : 318
% 5.53/2.42 #SimpNegUnit : 2
% 5.53/2.42 #BackRed : 0
% 5.53/2.42
% 5.53/2.42 #Partial instantiations: 0
% 5.53/2.42 #Strategies tried : 1
% 5.53/2.42
% 5.53/2.42 Timing (in seconds)
% 5.53/2.42 ----------------------
% 5.53/2.42 Preprocessing : 0.52
% 5.53/2.42 Parsing : 0.28
% 5.53/2.42 CNF conversion : 0.03
% 5.53/2.42 Main loop : 0.73
% 5.53/2.42 Inferencing : 0.25
% 5.53/2.42 Reduction : 0.28
% 5.53/2.42 Demodulation : 0.22
% 5.53/2.42 BG Simplification : 0.03
% 5.53/2.42 Subsumption : 0.12
% 5.53/2.42 Abstraction : 0.03
% 5.53/2.42 MUC search : 0.00
% 5.53/2.42 Cooper : 0.00
% 5.53/2.42 Total : 1.30
% 5.53/2.42 Index Insertion : 0.00
% 5.53/2.42 Index Deletion : 0.00
% 5.53/2.42 Index Matching : 0.00
% 5.53/2.42 BG Taut test : 0.00
%------------------------------------------------------------------------------