TSTP Solution File: KLE010+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE010+3 : 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 : n018.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 10:44:40 EDT 2023
% Result : Theorem 38.92s 22.50s
% Output : CNFRefutation 39.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 86 ( 45 unt; 11 typ; 0 def)
% Number of atoms : 121 ( 81 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 97 ( 51 ~; 38 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 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 : 81 (; 80 !; 1 ?; 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_177,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_112,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
tff(f_120,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_57,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
tff(f_53,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_51,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_126,axiom,
! [X0,X1] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(f_64,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_62,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(f_67,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_69,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_52,plain,
test('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_28,plain,
! [X0_23] :
( complement('#skF_1'(X0_23),X0_23)
| ~ test(X0_23) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_266,plain,
! [X0_51,X1_52] :
( ( addition(X0_51,X1_52) = one )
| ~ complement(X1_52,X0_51) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_275,plain,
! [X0_23] :
( ( addition(X0_23,'#skF_1'(X0_23)) = one )
| ~ test(X0_23) ),
inference(resolution,[status(thm)],[c_28,c_266]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_29084,plain,
! [A_231,B_232,C_233] : ( addition(addition(A_231,B_232),C_233) = addition(A_231,addition(B_232,C_233)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_29693,plain,
! [A_245,C_246] : ( addition(A_245,addition(A_245,C_246)) = addition(A_245,C_246) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_29084]) ).
tff(c_29884,plain,
! [X0_250] :
( ( addition(X0_250,'#skF_1'(X0_250)) = addition(X0_250,one) )
| ~ test(X0_250) ),
inference(superposition,[status(thm),theory(equality)],[c_275,c_29693]) ).
tff(c_30166,plain,
! [X0_255] :
( ( addition(X0_255,one) = one )
| ~ test(X0_255)
| ~ test(X0_255) ),
inference(superposition,[status(thm),theory(equality)],[c_275,c_29884]) ).
tff(c_30176,plain,
( ( addition('#skF_2',one) = one )
| ~ test('#skF_2') ),
inference(resolution,[status(thm)],[c_52,c_30166]) ).
tff(c_30190,plain,
addition('#skF_2',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_30176]) ).
tff(c_29725,plain,
! [X0_23] :
( ( addition(X0_23,'#skF_1'(X0_23)) = addition(X0_23,one) )
| ~ test(X0_23) ),
inference(superposition,[status(thm),theory(equality)],[c_275,c_29693]) ).
tff(c_291,plain,
! [X1_59,X0_60] :
( ( multiplication(X1_59,X0_60) = zero )
| ~ complement(X1_59,X0_60) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_299,plain,
! [X0_23] :
( ( multiplication('#skF_1'(X0_23),X0_23) = zero )
| ~ test(X0_23) ),
inference(resolution,[status(thm)],[c_28,c_291]) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_277,plain,
! [X0_55,X1_56] :
( ( multiplication(X0_55,X1_56) = zero )
| ~ complement(X1_56,X0_55) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_285,plain,
! [X0_23] :
( ( multiplication(X0_23,'#skF_1'(X0_23)) = zero )
| ~ test(X0_23) ),
inference(resolution,[status(thm)],[c_28,c_277]) ).
tff(c_30726,plain,
! [X1_263,X0_264] :
( complement(X1_263,X0_264)
| ( addition(X0_264,X1_263) != one )
| ( multiplication(X1_263,X0_264) != zero )
| ( multiplication(X0_264,X1_263) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_40,plain,
! [X0_29,X1_30] :
( ( c(X0_29) = X1_30 )
| ~ complement(X0_29,X1_30)
| ~ test(X0_29) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_64524,plain,
! [X1_410,X0_411] :
( ( c(X1_410) = X0_411 )
| ~ test(X1_410)
| ( addition(X0_411,X1_410) != one )
| ( multiplication(X1_410,X0_411) != zero )
| ( multiplication(X0_411,X1_410) != zero ) ),
inference(resolution,[status(thm)],[c_30726,c_40]) ).
tff(c_64645,plain,
! [X0_413] :
( ( c('#skF_2') = X0_413 )
| ( addition(X0_413,'#skF_2') != one )
| ( multiplication('#skF_2',X0_413) != zero )
| ( multiplication(X0_413,'#skF_2') != zero ) ),
inference(resolution,[status(thm)],[c_52,c_64524]) ).
tff(c_64663,plain,
( ( c('#skF_2') = '#skF_1'('#skF_2') )
| ( addition('#skF_1'('#skF_2'),'#skF_2') != one )
| ( multiplication('#skF_1'('#skF_2'),'#skF_2') != zero )
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_285,c_64645]) ).
tff(c_64680,plain,
( ( c('#skF_2') = '#skF_1'('#skF_2') )
| ( addition('#skF_2','#skF_1'('#skF_2')) != one )
| ( multiplication('#skF_1'('#skF_2'),'#skF_2') != zero ) ),
inference(demodulation,[status(thm),theory(equality)],[c_52,c_2,c_64663]) ).
tff(c_66136,plain,
multiplication('#skF_1'('#skF_2'),'#skF_2') != zero,
inference(splitLeft,[status(thm)],[c_64680]) ).
tff(c_66139,plain,
~ test('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_299,c_66136]) ).
tff(c_66143,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_66139]) ).
tff(c_66144,plain,
( ( addition('#skF_2','#skF_1'('#skF_2')) != one )
| ( c('#skF_2') = '#skF_1'('#skF_2') ) ),
inference(splitRight,[status(thm)],[c_64680]) ).
tff(c_78246,plain,
addition('#skF_2','#skF_1'('#skF_2')) != one,
inference(splitLeft,[status(thm)],[c_66144]) ).
tff(c_78249,plain,
( ( addition('#skF_2',one) != one )
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_29725,c_78246]) ).
tff(c_78255,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_30190,c_78249]) ).
tff(c_78257,plain,
addition('#skF_2','#skF_1'('#skF_2')) = one,
inference(splitRight,[status(thm)],[c_66144]) ).
tff(c_32168,plain,
! [B_277,A_278,B_279] : ( addition(B_277,addition(A_278,B_279)) = addition(A_278,addition(B_279,B_277)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_29084]) ).
tff(c_32688,plain,
! [A_7,B_277] : ( addition(A_7,addition(A_7,B_277)) = addition(B_277,A_7) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_32168]) ).
tff(c_78644,plain,
addition('#skF_1'('#skF_2'),'#skF_2') = addition('#skF_2',one),
inference(superposition,[status(thm),theory(equality)],[c_78257,c_32688]) ).
tff(c_78697,plain,
addition('#skF_1'('#skF_2'),'#skF_2') = one,
inference(demodulation,[status(thm),theory(equality)],[c_30190,c_78644]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_54,plain,
test('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_30178,plain,
( ( addition('#skF_3',one) = one )
| ~ test('#skF_3') ),
inference(resolution,[status(thm)],[c_54,c_30166]) ).
tff(c_30193,plain,
addition('#skF_3',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_30178]) ).
tff(c_29497,plain,
! [A_241,B_242,C_243] : ( addition(multiplication(A_241,B_242),multiplication(A_241,C_243)) = multiplication(A_241,addition(B_242,C_243)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_38497,plain,
! [A_305,B_306] : ( multiplication(A_305,addition(B_306,one)) = addition(multiplication(A_305,B_306),A_305) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_29497]) ).
tff(c_38707,plain,
! [A_305] : ( addition(multiplication(A_305,'#skF_3'),A_305) = multiplication(A_305,one) ),
inference(superposition,[status(thm),theory(equality)],[c_30193,c_38497]) ).
tff(c_38839,plain,
! [A_307] : ( addition(multiplication(A_307,'#skF_3'),A_307) = A_307 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_38707]) ).
tff(c_29570,plain,
! [A_11,B_242] : ( multiplication(A_11,addition(B_242,one)) = addition(multiplication(A_11,B_242),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_29497]) ).
tff(c_38846,plain,
! [A_11] : ( addition(multiplication(A_11,multiplication(one,'#skF_3')),A_11) = multiplication(A_11,one) ),
inference(superposition,[status(thm),theory(equality)],[c_38839,c_29570]) ).
tff(c_38988,plain,
! [A_11] : ( addition(A_11,multiplication(A_11,'#skF_3')) = A_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14,c_12,c_38846]) ).
tff(c_78256,plain,
c('#skF_2') = '#skF_1'('#skF_2'),
inference(splitRight,[status(thm)],[c_66144]) ).
tff(c_42,plain,
! [X0_29] :
( complement(X0_29,c(X0_29))
| ~ test(X0_29) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_269,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_266]) ).
tff(c_274,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_269]) ).
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_53]) ).
tff(c_29636,plain,
! [X0_244] :
( ( addition(X0_244,c(X0_244)) = one )
| ~ test(X0_244) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_269]) ).
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_67]) ).
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_69]) ).
tff(c_50,plain,
addition(addition(addition(addition(multiplication('#skF_3','#skF_2'),multiplication(c('#skF_3'),'#skF_2')),multiplication('#skF_2','#skF_3')),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))) != one,
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_55,plain,
addition(addition(addition(multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'),multiplication('#skF_2','#skF_3')),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_18,c_50]) ).
tff(c_56,plain,
addition(multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'),addition(multiplication('#skF_2','#skF_3'),addition(multiplication(c('#skF_2'),'#skF_3'),multiplication(c('#skF_2'),c('#skF_3'))))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_4,c_55]) ).
tff(c_57,plain,
addition(multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'),addition(multiplication('#skF_2','#skF_3'),multiplication(c('#skF_2'),addition('#skF_3',c('#skF_3'))))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_56]) ).
tff(c_29656,plain,
( ( addition(multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'),addition(multiplication('#skF_2','#skF_3'),multiplication(c('#skF_2'),one))) != one )
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_29636,c_57]) ).
tff(c_29680,plain,
addition(c('#skF_2'),addition(multiplication('#skF_2','#skF_3'),multiplication(addition('#skF_3',c('#skF_3')),'#skF_2'))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_4,c_2,c_2,c_12,c_29656]) ).
tff(c_29690,plain,
( ( addition(c('#skF_2'),addition(multiplication('#skF_2','#skF_3'),multiplication(one,'#skF_2'))) != one )
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_274,c_29680]) ).
tff(c_29692,plain,
addition(c('#skF_2'),addition('#skF_2',multiplication('#skF_2','#skF_3'))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_2,c_14,c_29690]) ).
tff(c_135083,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_78697,c_38988,c_78256,c_29692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE010+3 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % 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
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 23:39:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 38.92/22.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.92/22.51
% 38.92/22.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.02/22.55
% 39.02/22.55 Inference rules
% 39.02/22.55 ----------------------
% 39.02/22.55 #Ref : 0
% 39.02/22.55 #Sup : 31123
% 39.02/22.55 #Fact : 2
% 39.02/22.55 #Define : 0
% 39.02/22.55 #Split : 10
% 39.02/22.55 #Chain : 0
% 39.02/22.55 #Close : 0
% 39.02/22.55
% 39.02/22.55 Ordering : KBO
% 39.02/22.55
% 39.02/22.55 Simplification rules
% 39.02/22.55 ----------------------
% 39.02/22.55 #Subsume : 3490
% 39.02/22.55 #Demod : 51159
% 39.02/22.55 #Tautology : 14135
% 39.02/22.55 #SimpNegUnit : 73
% 39.02/22.55 #BackRed : 107
% 39.02/22.55
% 39.02/22.55 #Partial instantiations: 0
% 39.02/22.55 #Strategies tried : 1
% 39.02/22.55
% 39.02/22.55 Timing (in seconds)
% 39.02/22.55 ----------------------
% 39.02/22.55 Preprocessing : 0.53
% 39.02/22.55 Parsing : 0.28
% 39.02/22.55 CNF conversion : 0.03
% 39.02/22.55 Main loop : 20.93
% 39.02/22.55 Inferencing : 2.28
% 39.02/22.55 Reduction : 14.80
% 39.02/22.55 Demodulation : 13.88
% 39.02/22.55 BG Simplification : 0.25
% 39.02/22.55 Subsumption : 2.84
% 39.02/22.55 Abstraction : 0.48
% 39.02/22.55 MUC search : 0.00
% 39.02/22.55 Cooper : 0.00
% 39.02/22.55 Total : 21.52
% 39.02/22.55 Index Insertion : 0.00
% 39.02/22.55 Index Deletion : 0.00
% 39.02/22.55 Index Matching : 0.00
% 39.02/22.55 BG Taut test : 0.00
%------------------------------------------------------------------------------