TSTP Solution File: KLE010+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE010+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 34.74s 21.52s
% Output : CNFRefutation 34.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 87 ( 43 unt; 11 typ; 0 def)
% Number of atoms : 125 ( 82 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 105 ( 56 ~; 41 |; 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 : 83 (; 82 !; 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_140,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/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(f_112,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
tff(f_57,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
tff(f_51,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_64,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_69,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
tff(f_126,axiom,
! [X0,X1] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(f_62,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
tff(c_48,plain,
test('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_50,plain,
test('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_28,plain,
! [X0_23] :
( complement('#skF_1'(X0_23),X0_23)
| ~ test(X0_23) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_212,plain,
! [X0_46,X1_47] :
( ( addition(X0_46,X1_47) = one )
| ~ complement(X1_47,X0_46) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_221,plain,
! [X0_23] :
( ( addition(X0_23,'#skF_1'(X0_23)) = one )
| ~ test(X0_23) ),
inference(resolution,[status(thm)],[c_28,c_212]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_14233,plain,
! [A_168,B_169,C_170] : ( addition(addition(A_168,B_169),C_170) = addition(A_168,addition(B_169,C_170)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_14685,plain,
! [A_178,C_179] : ( addition(A_178,addition(A_178,C_179)) = addition(A_178,C_179) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_14233]) ).
tff(c_15140,plain,
! [X0_189] :
( ( addition(X0_189,'#skF_1'(X0_189)) = addition(X0_189,one) )
| ~ test(X0_189) ),
inference(superposition,[status(thm),theory(equality)],[c_221,c_14685]) ).
tff(c_15343,plain,
! [X0_193] :
( ( addition(X0_193,one) = one )
| ~ test(X0_193)
| ~ test(X0_193) ),
inference(superposition,[status(thm),theory(equality)],[c_15140,c_221]) ).
tff(c_15355,plain,
( ( addition('#skF_3',one) = one )
| ~ test('#skF_3') ),
inference(resolution,[status(thm)],[c_50,c_15343]) ).
tff(c_15370,plain,
addition('#skF_3',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_15355]) ).
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_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_15353,plain,
( ( addition('#skF_2',one) = one )
| ~ test('#skF_2') ),
inference(resolution,[status(thm)],[c_48,c_15343]) ).
tff(c_15367,plain,
addition('#skF_2',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_15353]) ).
tff(c_15199,plain,
! [A_190,C_191,B_192] : ( addition(multiplication(A_190,C_191),multiplication(B_192,C_191)) = multiplication(addition(A_190,B_192),C_191) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_22539,plain,
! [A_236,A_237] : ( multiplication(addition(A_236,one),A_237) = addition(multiplication(A_236,A_237),A_237) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_15199]) ).
tff(c_22762,plain,
! [A_237] : ( addition(multiplication('#skF_2',A_237),A_237) = multiplication(one,A_237) ),
inference(superposition,[status(thm),theory(equality)],[c_15367,c_22539]) ).
tff(c_23077,plain,
! [A_239] : ( addition(multiplication('#skF_2',A_239),A_239) = A_239 ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_22762]) ).
tff(c_16167,plain,
! [A_206,A_204,B_205] : ( addition(A_206,addition(A_204,B_205)) = addition(A_204,addition(B_205,A_206)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_14233]) ).
tff(c_16460,plain,
! [A_204] : ( addition(one,addition(A_204,'#skF_3')) = addition(A_204,one) ),
inference(superposition,[status(thm),theory(equality)],[c_15370,c_16167]) ).
tff(c_23115,plain,
addition(multiplication('#skF_2','#skF_3'),one) = addition(one,'#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_23077,c_16460]) ).
tff(c_23240,plain,
addition(multiplication('#skF_2','#skF_3'),one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_15370,c_2,c_23115]) ).
tff(c_14298,plain,
! [A_168,B_169,A_1] : ( addition(A_168,addition(B_169,A_1)) = addition(A_1,addition(A_168,B_169)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_14233]) ).
tff(c_16534,plain,
! [X0_23,A_204] :
( ( addition('#skF_1'(X0_23),addition(A_204,X0_23)) = addition(A_204,one) )
| ~ test(X0_23) ),
inference(superposition,[status(thm),theory(equality)],[c_221,c_16167]) ).
tff(c_16656,plain,
! [X0_23,A_204] :
( ( addition(X0_23,addition('#skF_1'(X0_23),A_204)) = addition(A_204,one) )
| ~ test(X0_23) ),
inference(demodulation,[status(thm),theory(equality)],[c_14298,c_16534]) ).
tff(c_14724,plain,
! [X0_23] :
( ( addition(X0_23,'#skF_1'(X0_23)) = addition(X0_23,one) )
| ~ test(X0_23) ),
inference(superposition,[status(thm),theory(equality)],[c_221,c_14685]) ).
tff(c_271,plain,
! [X1_49,X0_50] :
( ( multiplication(X1_49,X0_50) = zero )
| ~ complement(X1_49,X0_50) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_279,plain,
! [X0_23] :
( ( multiplication('#skF_1'(X0_23),X0_23) = zero )
| ~ test(X0_23) ),
inference(resolution,[status(thm)],[c_28,c_271]) ).
tff(c_287,plain,
! [X0_55,X1_56] :
( ( multiplication(X0_55,X1_56) = zero )
| ~ complement(X1_56,X0_55) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_295,plain,
! [X0_23] :
( ( multiplication(X0_23,'#skF_1'(X0_23)) = zero )
| ~ test(X0_23) ),
inference(resolution,[status(thm)],[c_28,c_287]) ).
tff(c_15702,plain,
! [X1_198,X0_199] :
( complement(X1_198,X0_199)
| ( addition(X0_199,X1_198) != one )
| ( multiplication(X1_198,X0_199) != zero )
| ( multiplication(X0_199,X1_198) != 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_35912,plain,
! [X1_303,X0_304] :
( ( c(X1_303) = X0_304 )
| ~ test(X1_303)
| ( addition(X0_304,X1_303) != one )
| ( multiplication(X1_303,X0_304) != zero )
| ( multiplication(X0_304,X1_303) != zero ) ),
inference(resolution,[status(thm)],[c_15702,c_40]) ).
tff(c_35936,plain,
! [X0_305] :
( ( c('#skF_2') = X0_305 )
| ( addition(X0_305,'#skF_2') != one )
| ( multiplication('#skF_2',X0_305) != zero )
| ( multiplication(X0_305,'#skF_2') != zero ) ),
inference(resolution,[status(thm)],[c_48,c_35912]) ).
tff(c_35951,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_295,c_35936]) ).
tff(c_35969,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_48,c_2,c_35951]) ).
tff(c_36796,plain,
multiplication('#skF_1'('#skF_2'),'#skF_2') != zero,
inference(splitLeft,[status(thm)],[c_35969]) ).
tff(c_36799,plain,
~ test('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_279,c_36796]) ).
tff(c_36803,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_36799]) ).
tff(c_36804,plain,
( ( addition('#skF_2','#skF_1'('#skF_2')) != one )
| ( c('#skF_2') = '#skF_1'('#skF_2') ) ),
inference(splitRight,[status(thm)],[c_35969]) ).
tff(c_54921,plain,
addition('#skF_2','#skF_1'('#skF_2')) != one,
inference(splitLeft,[status(thm)],[c_36804]) ).
tff(c_54924,plain,
( ( addition('#skF_2',one) != one )
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_14724,c_54921]) ).
tff(c_54930,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_15367,c_54924]) ).
tff(c_54931,plain,
c('#skF_2') = '#skF_1'('#skF_2'),
inference(splitRight,[status(thm)],[c_36804]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_42,plain,
! [X0_29] :
( complement(X0_29,c(X0_29))
| ~ test(X0_29) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_215,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_212]) ).
tff(c_220,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_215]) ).
tff(c_14178,plain,
! [X0_167] :
( ( addition(X0_167,c(X0_167)) = one )
| ~ test(X0_167) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_215]) ).
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_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_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_46,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_140]) ).
tff(c_51,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_46]) ).
tff(c_52,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_51]) ).
tff(c_53,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_52]) ).
tff(c_14188,plain,
( ( addition(multiplication(one,'#skF_2'),addition(multiplication('#skF_2','#skF_3'),multiplication(c('#skF_2'),addition('#skF_3',c('#skF_3'))))) != one )
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_14178,c_53]) ).
tff(c_14206,plain,
addition('#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_50,c_14,c_14188]) ).
tff(c_14855,plain,
( ( addition('#skF_2',addition(multiplication('#skF_2','#skF_3'),multiplication(c('#skF_2'),one))) != one )
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_220,c_14206]) ).
tff(c_14857,plain,
addition('#skF_2',addition(c('#skF_2'),multiplication('#skF_2','#skF_3'))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_2,c_12,c_14855]) ).
tff(c_124504,plain,
addition('#skF_2',addition('#skF_1'('#skF_2'),multiplication('#skF_2','#skF_3'))) != one,
inference(demodulation,[status(thm),theory(equality)],[c_54931,c_14857]) ).
tff(c_124507,plain,
( ( addition(multiplication('#skF_2','#skF_3'),one) != one )
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_16656,c_124504]) ).
tff(c_124510,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_23240,c_124507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE010+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Aug 3 23:29:06 EDT 2023
% 0.12/0.32 % CPUTime :
% 34.74/21.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.74/21.53
% 34.74/21.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.87/21.57
% 34.87/21.57 Inference rules
% 34.87/21.57 ----------------------
% 34.87/21.57 #Ref : 0
% 34.87/21.57 #Sup : 28518
% 34.87/21.57 #Fact : 2
% 34.87/21.57 #Define : 0
% 34.87/21.57 #Split : 11
% 34.87/21.57 #Chain : 0
% 34.87/21.57 #Close : 0
% 34.87/21.57
% 34.87/21.57 Ordering : KBO
% 34.87/21.57
% 34.87/21.57 Simplification rules
% 34.87/21.57 ----------------------
% 34.87/21.57 #Subsume : 3629
% 34.87/21.57 #Demod : 48378
% 34.87/21.57 #Tautology : 12835
% 34.87/21.57 #SimpNegUnit : 59
% 34.87/21.57 #BackRed : 121
% 34.87/21.57
% 34.87/21.57 #Partial instantiations: 0
% 34.87/21.57 #Strategies tried : 1
% 34.87/21.57
% 34.87/21.57 Timing (in seconds)
% 34.87/21.57 ----------------------
% 34.87/21.57 Preprocessing : 0.51
% 34.87/21.57 Parsing : 0.27
% 34.87/21.57 CNF conversion : 0.03
% 34.87/21.57 Main loop : 20.02
% 34.87/21.57 Inferencing : 2.05
% 34.87/21.57 Reduction : 14.32
% 34.87/21.57 Demodulation : 13.50
% 34.87/21.57 BG Simplification : 0.24
% 34.87/21.57 Subsumption : 2.64
% 34.87/21.57 Abstraction : 0.41
% 34.87/21.57 MUC search : 0.00
% 34.87/21.57 Cooper : 0.00
% 34.87/21.57 Total : 20.59
% 34.87/21.57 Index Insertion : 0.00
% 34.87/21.57 Index Deletion : 0.00
% 34.87/21.57 Index Matching : 0.00
% 34.87/21.57 BG Taut test : 0.00
%------------------------------------------------------------------------------