TSTP Solution File: KLE150+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE150+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 : n007.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 10:44:56 EDT 2023
% Result : Theorem 24.67s 13.39s
% Output : CNFRefutation 25.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 84 ( 71 unt; 9 typ; 0 def)
% Number of atoms : 79 ( 68 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 13 ~; 2 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 102 (; 102 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > strong_iteration > star > zero > one > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(strong_iteration,type,
strong_iteration: $i > $i ).
tff(star,type,
star: $i > $i ).
tff(multiplication,type,
multiplication: ( $i * $i ) > $i ).
tff(addition,type,
addition: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_73,axiom,
! [A] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
tff(f_61,axiom,
! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
tff(f_76,axiom,
! [A] : ( addition(one,multiplication(A,star(A))) = star(A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(f_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+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/KLE004+0.ax',distributivity2) ).
tff(f_89,axiom,
! [A] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
tff(f_95,axiom,
! [A] : ( strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
tff(f_54,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
tff(f_100,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_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/KLE004+0.ax',distributivity1) ).
tff(f_107,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(c_20,plain,
! [A_19] : ( multiplication(zero,A_19) = zero ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_5319,plain,
! [A_136,B_137,C_138] : ( multiplication(multiplication(A_136,B_137),C_138) = multiplication(A_136,multiplication(B_137,C_138)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_22,plain,
! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = star(A_20) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_30823,plain,
! [A_428,B_429] : ( addition(one,multiplication(A_428,multiplication(B_429,star(multiplication(A_428,B_429))))) = star(multiplication(A_428,B_429)) ),
inference(superposition,[status(thm),theory(equality)],[c_5319,c_22]) ).
tff(c_31022,plain,
! [A_428] : ( addition(one,multiplication(A_428,zero)) = star(multiplication(A_428,zero)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_30823]) ).
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_114,plain,
! [B_40,A_41] : ( addition(B_40,A_41) = addition(A_41,B_40) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_130,plain,
! [A_41] : ( addition(zero,A_41) = A_41 ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_6]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_5610,plain,
! [A_146,C_147,B_148] : ( addition(multiplication(A_146,C_147),multiplication(B_148,C_147)) = multiplication(addition(A_146,B_148),C_147) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_5656,plain,
! [A_146,A_12] : ( multiplication(addition(A_146,one),A_12) = addition(multiplication(A_146,A_12),A_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_5610]) ).
tff(c_9540,plain,
! [A_211,A_212] : ( multiplication(addition(A_211,one),A_212) = addition(multiplication(A_211,A_212),A_212) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_5610]) ).
tff(c_68948,plain,
! [A_734,A_735] : ( multiplication(addition(A_734,one),A_735) = addition(A_735,multiplication(A_734,A_735)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_9540]) ).
tff(c_30,plain,
! [A_28] : ( addition(multiplication(A_28,strong_iteration(A_28)),one) = strong_iteration(A_28) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_31986,plain,
! [A_433,B_434] : ( addition(multiplication(A_433,multiplication(B_434,strong_iteration(multiplication(A_433,B_434)))),one) = strong_iteration(multiplication(A_433,B_434)) ),
inference(superposition,[status(thm),theory(equality)],[c_5319,c_30]) ).
tff(c_32188,plain,
! [A_433] : ( addition(multiplication(A_433,zero),one) = strong_iteration(multiplication(A_433,zero)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_31986]) ).
tff(c_69010,plain,
! [A_734] : ( addition(addition(zero,multiplication(A_734,zero)),one) = strong_iteration(multiplication(addition(A_734,one),zero)) ),
inference(superposition,[status(thm),theory(equality)],[c_68948,c_32188]) ).
tff(c_69647,plain,
! [A_734] : ( strong_iteration(multiplication(A_734,zero)) = star(multiplication(A_734,zero)) ),
inference(demodulation,[status(thm),theory(equality)],[c_31022,c_2,c_130,c_2,c_130,c_5656,c_69010]) ).
tff(c_34,plain,
! [A_32] : ( addition(star(A_32),multiplication(strong_iteration(A_32),zero)) = strong_iteration(A_32) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_5370,plain,
! [A_139,B_140,C_141] : ( addition(addition(A_139,B_140),C_141) = addition(A_139,addition(B_140,C_141)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_5469,plain,
! [A_142,C_143] : ( addition(A_142,addition(A_142,C_143)) = addition(A_142,C_143) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_5370]) ).
tff(c_5505,plain,
! [A_32] : ( addition(star(A_32),multiplication(strong_iteration(A_32),zero)) = addition(star(A_32),strong_iteration(A_32)) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_5469]) ).
tff(c_5556,plain,
! [A_32] : ( addition(star(A_32),strong_iteration(A_32)) = strong_iteration(A_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_5505]) ).
tff(c_7805,plain,
! [C_198,A_199,B_200] : ( addition(C_198,addition(A_199,B_200)) = addition(A_199,addition(B_200,C_198)) ),
inference(superposition,[status(thm),theory(equality)],[c_5370,c_2]) ).
tff(c_8289,plain,
! [A_201,C_202] : ( addition(zero,addition(A_201,C_202)) = addition(C_202,A_201) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_7805]) ).
tff(c_8402,plain,
! [A_32] : ( addition(strong_iteration(A_32),star(A_32)) = addition(zero,strong_iteration(A_32)) ),
inference(superposition,[status(thm),theory(equality)],[c_5556,c_8289]) ).
tff(c_8494,plain,
! [A_32] : ( addition(strong_iteration(A_32),star(A_32)) = strong_iteration(A_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_8402]) ).
tff(c_38,plain,
! [A_33,B_34] :
( leq(A_33,B_34)
| ( addition(A_33,B_34) != B_34 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_266,plain,
! [A_49] : ( addition(multiplication(A_49,strong_iteration(A_49)),one) = strong_iteration(A_49) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_284,plain,
! [A_49] : ( addition(one,multiplication(A_49,strong_iteration(A_49))) = strong_iteration(A_49) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_266]) ).
tff(c_426,plain,
! [A_55,B_56,C_57] : ( addition(addition(A_55,B_56),C_57) = addition(A_55,addition(B_56,C_57)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_516,plain,
! [A_58,C_59] : ( addition(A_58,addition(A_58,C_59)) = addition(A_58,C_59) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_426]) ).
tff(c_549,plain,
! [A_49] : ( addition(one,multiplication(A_49,strong_iteration(A_49))) = addition(one,strong_iteration(A_49)) ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_516]) ).
tff(c_599,plain,
! [A_49] : ( addition(one,strong_iteration(A_49)) = strong_iteration(A_49) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_549]) ).
tff(c_493,plain,
! [A_55,B_56,A_1] : ( addition(A_55,addition(B_56,A_1)) = addition(A_1,addition(A_55,B_56)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_426]) ).
tff(c_746,plain,
! [A_66,C_67,B_68] : ( addition(multiplication(A_66,C_67),multiplication(B_68,C_67)) = multiplication(addition(A_66,B_68),C_67) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_1700,plain,
! [B_98,A_99] : ( multiplication(addition(one,B_98),A_99) = addition(A_99,multiplication(B_98,A_99)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_746]) ).
tff(c_561,plain,
! [A_28] : ( addition(multiplication(A_28,strong_iteration(A_28)),strong_iteration(A_28)) = addition(multiplication(A_28,strong_iteration(A_28)),one) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_516]) ).
tff(c_949,plain,
! [A_71] : ( addition(multiplication(A_71,strong_iteration(A_71)),strong_iteration(A_71)) = strong_iteration(A_71) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_2,c_561]) ).
tff(c_983,plain,
! [A_71] : ( addition(strong_iteration(A_71),multiplication(A_71,strong_iteration(A_71))) = strong_iteration(A_71) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_949]) ).
tff(c_1728,plain,
! [B_98] : ( multiplication(addition(one,B_98),strong_iteration(B_98)) = strong_iteration(B_98) ),
inference(superposition,[status(thm),theory(equality)],[c_1700,c_983]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_632,plain,
! [A_61,B_62,C_63] : ( addition(multiplication(A_61,B_62),multiplication(A_61,C_63)) = multiplication(A_61,addition(B_62,C_63)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_4318,plain,
! [A_121,B_122] : ( multiplication(A_121,addition(B_122,one)) = addition(multiplication(A_121,B_122),A_121) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_632]) ).
tff(c_4460,plain,
! [B_98] : ( multiplication(addition(one,B_98),addition(strong_iteration(B_98),one)) = addition(strong_iteration(B_98),addition(one,B_98)) ),
inference(superposition,[status(thm),theory(equality)],[c_1728,c_4318]) ).
tff(c_4550,plain,
! [B_98] : ( addition(B_98,strong_iteration(B_98)) = strong_iteration(B_98) ),
inference(demodulation,[status(thm),theory(equality)],[c_599,c_2,c_493,c_1728,c_599,c_2,c_4460]) ).
tff(c_40,plain,
( ~ leq(strong_iteration(multiplication('#skF_2',zero)),addition(one,multiplication('#skF_2',zero)))
| ~ leq(addition(one,multiplication('#skF_1',zero)),strong_iteration(multiplication('#skF_1',zero))) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_210,plain,
~ leq(addition(one,multiplication('#skF_1',zero)),strong_iteration(multiplication('#skF_1',zero))),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_306,plain,
addition(addition(one,multiplication('#skF_1',zero)),strong_iteration(multiplication('#skF_1',zero))) != strong_iteration(multiplication('#skF_1',zero)),
inference(resolution,[status(thm)],[c_38,c_210]) ).
tff(c_308,plain,
addition(strong_iteration(multiplication('#skF_1',zero)),addition(one,multiplication('#skF_1',zero))) != strong_iteration(multiplication('#skF_1',zero)),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_306]) ).
tff(c_2099,plain,
addition(one,addition(multiplication('#skF_1',zero),strong_iteration(multiplication('#skF_1',zero)))) != strong_iteration(multiplication('#skF_1',zero)),
inference(demodulation,[status(thm),theory(equality)],[c_493,c_493,c_308]) ).
tff(c_5130,plain,
addition(one,strong_iteration(multiplication('#skF_1',zero))) != strong_iteration(multiplication('#skF_1',zero)),
inference(demodulation,[status(thm),theory(equality)],[c_4550,c_2099]) ).
tff(c_5133,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_599,c_5130]) ).
tff(c_5134,plain,
~ leq(strong_iteration(multiplication('#skF_2',zero)),addition(one,multiplication('#skF_2',zero))),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_63924,plain,
~ leq(strong_iteration(multiplication('#skF_2',zero)),star(multiplication('#skF_2',zero))),
inference(demodulation,[status(thm),theory(equality)],[c_31022,c_5134]) ).
tff(c_64204,plain,
addition(strong_iteration(multiplication('#skF_2',zero)),star(multiplication('#skF_2',zero))) != star(multiplication('#skF_2',zero)),
inference(resolution,[status(thm)],[c_38,c_63924]) ).
tff(c_64208,plain,
strong_iteration(multiplication('#skF_2',zero)) != star(multiplication('#skF_2',zero)),
inference(demodulation,[status(thm),theory(equality)],[c_8494,c_64204]) ).
tff(c_82667,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_69647,c_64208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % 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
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 23:07:54 EDT 2023
% 0.15/0.37 % CPUTime :
% 24.67/13.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.67/13.40
% 24.67/13.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.01/13.45
% 25.01/13.45 Inference rules
% 25.01/13.45 ----------------------
% 25.01/13.45 #Ref : 0
% 25.01/13.45 #Sup : 21117
% 25.01/13.45 #Fact : 0
% 25.01/13.45 #Define : 0
% 25.01/13.45 #Split : 16
% 25.01/13.45 #Chain : 0
% 25.01/13.45 #Close : 0
% 25.01/13.45
% 25.01/13.45 Ordering : KBO
% 25.01/13.45
% 25.01/13.45 Simplification rules
% 25.01/13.45 ----------------------
% 25.01/13.45 #Subsume : 5407
% 25.01/13.45 #Demod : 21983
% 25.01/13.45 #Tautology : 6790
% 25.01/13.45 #SimpNegUnit : 301
% 25.01/13.45 #BackRed : 101
% 25.01/13.45
% 25.01/13.45 #Partial instantiations: 0
% 25.01/13.45 #Strategies tried : 1
% 25.01/13.45
% 25.01/13.45 Timing (in seconds)
% 25.01/13.45 ----------------------
% 25.01/13.46 Preprocessing : 0.50
% 25.01/13.46 Parsing : 0.27
% 25.01/13.46 CNF conversion : 0.03
% 25.01/13.46 Main loop : 11.83
% 25.01/13.46 Inferencing : 1.55
% 25.01/13.46 Reduction : 7.43
% 25.01/13.46 Demodulation : 6.49
% 25.01/13.46 BG Simplification : 0.14
% 25.01/13.46 Subsumption : 2.08
% 25.01/13.46 Abstraction : 0.24
% 25.01/13.46 MUC search : 0.00
% 25.01/13.46 Cooper : 0.00
% 25.01/13.46 Total : 12.40
% 25.01/13.46 Index Insertion : 0.00
% 25.01/13.46 Index Deletion : 0.00
% 25.01/13.46 Index Matching : 0.00
% 25.01/13.46 BG Taut test : 0.00
%------------------------------------------------------------------------------