TSTP Solution File: KLE048+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE048+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 : n002.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 10:44:45 EDT 2023
% Result : Theorem 16.59s 7.34s
% Output : CNFRefutation 16.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of formulae : 84 ( 50 unt; 11 typ; 0 def)
% Number of atoms : 100 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 20 ~; 18 |; 2 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 8 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 105 (; 105 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > complement > test > multiplication > addition > #nlpp > star > c > zero > one > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(c,type,
c: $i > $i ).
tff(star,type,
star: $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(test,type,
test: $i > $o ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_154,negated_conjecture,
~ ! [X0] :
( test(X0)
=> ( star(X0) = 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/KLE002+0.ax',additive_commutativity) ).
tff(f_142,axiom,
! [X0,X1] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(f_136,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/KLE002+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/KLE002+0.ax',additive_associativity) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
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/KLE002+0.ax',left_distributivity) ).
tff(f_80,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
tff(f_91,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
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/KLE002+0.ax',right_distributivity) ).
tff(f_95,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
tff(f_84,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
tff(c_54,plain,
star('#skF_2') != one,
inference(cnfTransformation,[status(thm)],[f_154]) ).
tff(c_56,plain,
test('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_154]) ).
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_50,plain,
! [X0_37] :
( complement(X0_37,c(X0_37))
| ~ test(X0_37) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_266,plain,
! [X0_57,X1_58] :
( ( addition(X0_57,X1_58) = one )
| ~ complement(X1_58,X0_57) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_272,plain,
! [X0_37] :
( ( addition(c(X0_37),X0_37) = one )
| ~ test(X0_37) ),
inference(resolution,[status(thm)],[c_50,c_266]) ).
tff(c_275,plain,
! [X0_37] :
( ( addition(X0_37,c(X0_37)) = one )
| ~ test(X0_37) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_272]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_24652,plain,
! [A_276,B_277,C_278] : ( addition(addition(A_276,B_277),C_278) = addition(A_276,addition(B_277,C_278)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_25186,plain,
! [A_290,C_291] : ( addition(A_290,addition(A_290,C_291)) = addition(A_290,C_291) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_24652]) ).
tff(c_27299,plain,
! [X0_339] :
( ( addition(X0_339,c(X0_339)) = addition(X0_339,one) )
| ~ test(X0_339) ),
inference(superposition,[status(thm),theory(equality)],[c_275,c_25186]) ).
tff(c_27390,plain,
! [X0_340] :
( ( addition(X0_340,one) = one )
| ~ test(X0_340)
| ~ test(X0_340) ),
inference(superposition,[status(thm),theory(equality)],[c_27299,c_275]) ).
tff(c_27400,plain,
( ( addition('#skF_2',one) = one )
| ~ test('#skF_2') ),
inference(resolution,[status(thm)],[c_56,c_27390]) ).
tff(c_27412,plain,
addition('#skF_2',one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_56,c_27400]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_25027,plain,
! [A_286,C_287,B_288] : ( addition(multiplication(A_286,C_287),multiplication(B_288,C_287)) = multiplication(addition(A_286,B_288),C_287) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_28462,plain,
! [A_350,A_351] : ( multiplication(addition(A_350,one),A_351) = addition(multiplication(A_350,A_351),A_351) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_25027]) ).
tff(c_28542,plain,
! [A_351] : ( addition(multiplication('#skF_2',A_351),A_351) = multiplication(one,A_351) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_28462]) ).
tff(c_28657,plain,
! [A_351] : ( addition(multiplication('#skF_2',A_351),A_351) = A_351 ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_28542]) ).
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_25776,plain,
! [A_306,C_307,B_308] :
( leq(multiplication(star(A_306),C_307),B_308)
| ~ leq(addition(multiplication(A_306,B_308),C_307),B_308) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_25807,plain,
! [A_306,C_307,B_22] :
( leq(multiplication(star(A_306),C_307),B_22)
| ( addition(addition(multiplication(A_306,B_22),C_307),B_22) != B_22 ) ),
inference(resolution,[status(thm)],[c_26,c_25776]) ).
tff(c_49124,plain,
! [A_460,C_461,B_462] :
( leq(multiplication(star(A_460),C_461),B_462)
| ( addition(B_462,addition(multiplication(A_460,B_462),C_461)) != B_462 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25807]) ).
tff(c_49257,plain,
! [A_351] :
( leq(multiplication(star('#skF_2'),A_351),A_351)
| ( addition(A_351,A_351) != A_351 ) ),
inference(superposition,[status(thm),theory(equality)],[c_28657,c_49124]) ).
tff(c_49409,plain,
! [A_463] : leq(multiplication(star('#skF_2'),A_463),A_463),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_49257]) ).
tff(c_49452,plain,
leq(star('#skF_2'),one),
inference(superposition,[status(thm),theory(equality)],[c_12,c_49409]) ).
tff(c_24,plain,
! [A_21,B_22] :
( ( addition(A_21,B_22) = B_22 )
| ~ leq(A_21,B_22) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_49470,plain,
addition(star('#skF_2'),one) = one,
inference(resolution,[status(thm)],[c_49452,c_24]) ).
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_27739,plain,
! [C_345] : ( addition('#skF_2',addition(one,C_345)) = addition(one,C_345) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_4]) ).
tff(c_27802,plain,
! [A_1] : ( addition('#skF_2',addition(A_1,one)) = addition(one,A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_27739]) ).
tff(c_49527,plain,
addition(one,star('#skF_2')) = addition('#skF_2',one),
inference(superposition,[status(thm),theory(equality)],[c_49470,c_27802]) ).
tff(c_49570,plain,
addition(one,star('#skF_2')) = one,
inference(demodulation,[status(thm),theory(equality)],[c_27412,c_49527]) ).
tff(c_25377,plain,
! [A_295,B_296,C_297] : ( addition(multiplication(A_295,B_296),multiplication(A_295,C_297)) = multiplication(A_295,addition(B_296,C_297)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_29419,plain,
! [A_357,B_358] : ( multiplication(A_357,addition(B_358,one)) = addition(multiplication(A_357,B_358),A_357) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_25377]) ).
tff(c_29533,plain,
! [A_357] : ( addition(multiplication(A_357,'#skF_2'),A_357) = multiplication(A_357,one) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_29419]) ).
tff(c_29659,plain,
! [A_357] : ( addition(multiplication(A_357,'#skF_2'),A_357) = A_357 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_29533]) ).
tff(c_25657,plain,
! [C_300,B_301,A_302] :
( leq(multiplication(C_300,star(B_301)),A_302)
| ~ leq(addition(multiplication(A_302,B_301),C_300),A_302) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_25688,plain,
! [C_300,B_301,B_22] :
( leq(multiplication(C_300,star(B_301)),B_22)
| ( addition(addition(multiplication(B_22,B_301),C_300),B_22) != B_22 ) ),
inference(resolution,[status(thm)],[c_26,c_25657]) ).
tff(c_49672,plain,
! [C_464,B_465,B_466] :
( leq(multiplication(C_464,star(B_465)),B_466)
| ( addition(B_466,addition(multiplication(B_466,B_465),C_464)) != B_466 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25688]) ).
tff(c_49790,plain,
! [A_357] :
( leq(multiplication(A_357,star('#skF_2')),A_357)
| ( addition(A_357,A_357) != A_357 ) ),
inference(superposition,[status(thm),theory(equality)],[c_29659,c_49672]) ).
tff(c_49975,plain,
! [A_467] : leq(multiplication(A_467,star('#skF_2')),A_467),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_49790]) ).
tff(c_50399,plain,
! [A_473] : ( addition(multiplication(A_473,star('#skF_2')),A_473) = A_473 ),
inference(resolution,[status(thm)],[c_49975,c_24]) ).
tff(c_27637,plain,
! [C_3] : ( addition('#skF_2',addition(one,C_3)) = addition(one,C_3) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_4]) ).
tff(c_24694,plain,
! [A_1,B_2,C_278] : ( addition(addition(A_1,B_2),C_278) = addition(B_2,addition(A_1,C_278)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_24652]) ).
tff(c_27644,plain,
! [C_344] : ( addition(one,addition('#skF_2',C_344)) = addition(one,C_344) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_24694]) ).
tff(c_27709,plain,
! [A_1] : ( addition(one,addition(A_1,'#skF_2')) = addition(one,A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_27644]) ).
tff(c_30741,plain,
! [A_370,A_368,B_369] : ( addition(A_370,addition(A_368,B_369)) = addition(A_368,addition(B_369,A_370)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_24652]) ).
tff(c_32205,plain,
! [A_375] : ( addition('#skF_2',addition(one,A_375)) = addition(A_375,one) ),
inference(superposition,[status(thm),theory(equality)],[c_27412,c_30741]) ).
tff(c_32303,plain,
! [A_1] : ( addition(addition(A_1,'#skF_2'),one) = addition('#skF_2',addition(one,A_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_27709,c_32205]) ).
tff(c_32400,plain,
! [A_1] : ( addition(addition(A_1,'#skF_2'),one) = addition(one,A_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_27637,c_32303]) ).
tff(c_50449,plain,
addition(one,multiplication('#skF_2',star('#skF_2'))) = addition('#skF_2',one),
inference(superposition,[status(thm),theory(equality)],[c_50399,c_32400]) ).
tff(c_50672,plain,
addition(one,multiplication('#skF_2',star('#skF_2'))) = one,
inference(demodulation,[status(thm),theory(equality)],[c_27412,c_50449]) ).
tff(c_24369,plain,
! [A_267] : leq(addition(one,multiplication(A_267,star(A_267))),star(A_267)),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_24381,plain,
! [A_267] : ( addition(addition(one,multiplication(A_267,star(A_267))),star(A_267)) = star(A_267) ),
inference(resolution,[status(thm)],[c_24369,c_24]) ).
tff(c_52955,plain,
addition(one,star('#skF_2')) = star('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_50672,c_24381]) ).
tff(c_53014,plain,
star('#skF_2') = one,
inference(demodulation,[status(thm),theory(equality)],[c_49570,c_52955]) ).
tff(c_53016,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54,c_53014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE048+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
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 23:40:01 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.59/7.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.83/7.35
% 16.83/7.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.83/7.38
% 16.83/7.38 Inference rules
% 16.83/7.38 ----------------------
% 16.83/7.38 #Ref : 0
% 16.83/7.38 #Sup : 12751
% 16.83/7.38 #Fact : 0
% 16.83/7.38 #Define : 0
% 16.83/7.38 #Split : 9
% 16.83/7.38 #Chain : 0
% 16.83/7.38 #Close : 0
% 16.83/7.38
% 16.83/7.38 Ordering : KBO
% 16.83/7.38
% 16.83/7.38 Simplification rules
% 16.83/7.38 ----------------------
% 16.83/7.38 #Subsume : 903
% 16.83/7.38 #Demod : 18835
% 16.83/7.38 #Tautology : 6265
% 16.83/7.38 #SimpNegUnit : 120
% 16.83/7.38 #BackRed : 89
% 16.83/7.38
% 16.83/7.38 #Partial instantiations: 0
% 16.83/7.38 #Strategies tried : 1
% 16.83/7.38
% 16.83/7.38 Timing (in seconds)
% 16.83/7.38 ----------------------
% 16.83/7.38 Preprocessing : 0.49
% 16.83/7.38 Parsing : 0.26
% 16.83/7.38 CNF conversion : 0.03
% 16.83/7.38 Main loop : 5.80
% 16.83/7.38 Inferencing : 1.08
% 16.83/7.38 Reduction : 3.41
% 16.83/7.38 Demodulation : 3.07
% 16.83/7.38 BG Simplification : 0.11
% 16.83/7.38 Subsumption : 0.91
% 16.83/7.38 Abstraction : 0.17
% 16.83/7.38 MUC search : 0.00
% 16.83/7.38 Cooper : 0.00
% 16.83/7.38 Total : 6.35
% 16.83/7.38 Index Insertion : 0.00
% 16.83/7.38 Index Deletion : 0.00
% 16.83/7.38 Index Matching : 0.00
% 16.83/7.38 BG Taut test : 0.00
%------------------------------------------------------------------------------