TSTP Solution File: KLE009+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE009+4 : 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 : n010.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 10:44:39 EDT 2023
% Result : Theorem 4.65s 2.21s
% Output : CNFRefutation 4.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 62 ( 27 unt; 11 typ; 0 def)
% Number of atoms : 80 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 35 ~; 20 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 49 (; 49 !; 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_180,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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_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(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(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_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(c_52,plain,
test('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_54,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_850,plain,
! [X0_87,X1_88] :
( ( addition(X0_87,X1_88) = one )
| ~ complement(X1_88,X0_87) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_856,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_850]) ).
tff(c_859,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_856]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_1107,plain,
! [X0_102] :
( ( addition(X0_102,c(X0_102)) = one )
| ~ test(X0_102) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_856]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
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_80]) ).
tff(c_276,plain,
! [X0_53,X1_54] :
( ( addition(X0_53,X1_54) = one )
| ~ complement(X1_54,X0_53) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_279,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_276]) ).
tff(c_284,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_279]) ).
tff(c_647,plain,
! [X0_74] :
( ( addition(X0_74,c(X0_74)) = one )
| ~ test(X0_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_279]) ).
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_70]) ).
tff(c_16,plain,
! [A_13,B_14,C_15] : ( addition(multiplication(A_13,B_14),multiplication(A_13,C_15)) = multiplication(A_13,addition(B_14,C_15)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_4,plain,
! [A_5,B_4,C_3] : ( addition(addition(A_5,B_4),C_3) = addition(A_5,addition(B_4,C_3)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_50,plain,
( ~ leq(addition(addition(addition(multiplication('#skF_2','#skF_3'),multiplication('#skF_2',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))),one)
| ~ leq(one,addition(addition(addition(multiplication('#skF_2','#skF_3'),multiplication('#skF_2',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3')))) ),
inference(cnfTransformation,[status(thm)],[f_180]) ).
tff(c_55,plain,
( ~ leq(addition(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))),one)
| ~ leq(one,addition(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_50]) ).
tff(c_56,plain,
( ~ leq(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),addition(multiplication(c('#skF_2'),'#skF_3'),multiplication(c('#skF_2'),c('#skF_3')))),one)
| ~ leq(one,addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),addition(multiplication(c('#skF_2'),'#skF_3'),multiplication(c('#skF_2'),c('#skF_3'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_55]) ).
tff(c_57,plain,
( ~ leq(multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3'))),one)
| ~ leq(one,multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_16,c_18,c_16,c_56]) ).
tff(c_157,plain,
~ leq(one,multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3')))),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_666,plain,
( ~ leq(one,multiplication(one,addition('#skF_3',c('#skF_3'))))
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_647,c_157]) ).
tff(c_697,plain,
~ leq(one,addition('#skF_3',c('#skF_3'))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_14,c_666]) ).
tff(c_707,plain,
( ~ leq(one,one)
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_697]) ).
tff(c_712,plain,
~ leq(one,one),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_707]) ).
tff(c_716,plain,
addition(one,one) != one,
inference(resolution,[status(thm)],[c_26,c_712]) ).
tff(c_720,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_716]) ).
tff(c_722,plain,
leq(one,multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3')))),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_1126,plain,
( leq(one,multiplication(one,addition('#skF_3',c('#skF_3'))))
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_1107,c_722]) ).
tff(c_1163,plain,
leq(one,addition('#skF_3',c('#skF_3'))),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_14,c_1126]) ).
tff(c_1180,plain,
( leq(one,one)
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_859,c_1163]) ).
tff(c_1183,plain,
leq(one,one),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_1180]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_721,plain,
~ leq(multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3'))),one),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_1139,plain,
( ~ leq(multiplication(addition('#skF_2',c('#skF_2')),one),one)
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_1107,c_721]) ).
tff(c_1170,plain,
~ leq(addition('#skF_2',c('#skF_2')),one),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_12,c_1139]) ).
tff(c_1200,plain,
( ~ leq(one,one)
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_859,c_1170]) ).
tff(c_1206,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_1183,c_1200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE009+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 23:20:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.65/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.65/2.21
% 4.65/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.65/2.26
% 4.65/2.26 Inference rules
% 4.65/2.26 ----------------------
% 4.65/2.26 #Ref : 0
% 4.65/2.26 #Sup : 268
% 4.65/2.26 #Fact : 0
% 4.65/2.26 #Define : 0
% 4.65/2.26 #Split : 5
% 4.65/2.26 #Chain : 0
% 4.65/2.26 #Close : 0
% 4.65/2.26
% 4.65/2.26 Ordering : KBO
% 4.65/2.26
% 4.65/2.26 Simplification rules
% 4.65/2.26 ----------------------
% 4.65/2.26 #Subsume : 42
% 4.65/2.26 #Demod : 115
% 4.65/2.26 #Tautology : 140
% 4.65/2.26 #SimpNegUnit : 2
% 4.65/2.26 #BackRed : 0
% 4.65/2.26
% 4.65/2.26 #Partial instantiations: 0
% 4.65/2.26 #Strategies tried : 1
% 4.65/2.26
% 4.65/2.26 Timing (in seconds)
% 4.65/2.26 ----------------------
% 4.65/2.26 Preprocessing : 0.56
% 4.65/2.26 Parsing : 0.30
% 4.65/2.26 CNF conversion : 0.03
% 4.65/2.26 Main loop : 0.56
% 4.65/2.26 Inferencing : 0.21
% 4.65/2.26 Reduction : 0.18
% 4.65/2.26 Demodulation : 0.14
% 4.65/2.26 BG Simplification : 0.03
% 4.65/2.26 Subsumption : 0.10
% 4.65/2.26 Abstraction : 0.02
% 4.65/2.26 MUC search : 0.00
% 4.65/2.26 Cooper : 0.00
% 4.65/2.26 Total : 1.18
% 4.65/2.26 Index Insertion : 0.00
% 4.65/2.26 Index Deletion : 0.00
% 4.65/2.26 Index Matching : 0.00
% 4.65/2.26 BG Taut test : 0.00
%------------------------------------------------------------------------------