TSTP Solution File: KLE139+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE139+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 : n029.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 10:44:54 EDT 2023
% Result : Theorem 108.49s 90.40s
% Output : CNFRefutation 108.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 27
% Syntax : Number of formulae : 167 ( 113 unt; 8 typ; 0 def)
% Number of atoms : 205 ( 142 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 91 ( 45 ~; 42 |; 0 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 258 (; 258 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > strong_iteration > star > zero > one > #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_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
tff(f_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
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_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(f_73,axiom,
! [A] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
tff(f_86,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
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_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
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_78,axiom,
! [A] : ( addition(one,multiplication(star(A),A)) = star(A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
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_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_82,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
tff(f_93,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
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_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_105,negated_conjecture,
~ ! [X0] : ( strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),one) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
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_115,plain,
! [B_40,A_41] : ( addition(B_40,A_41) = addition(A_41,B_40) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_131,plain,
! [A_41] : ( addition(zero,A_41) = A_41 ),
inference(superposition,[status(thm),theory(equality)],[c_115,c_6]) ).
tff(c_20,plain,
! [A_19] : ( multiplication(zero,A_19) = zero ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1140,plain,
! [B_75,A_76,C_77] :
( leq(multiplication(B_75,star(A_76)),C_77)
| ~ leq(addition(multiplication(C_77,A_76),B_75),C_77) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_1181,plain,
! [B_75,A_19] :
( leq(multiplication(B_75,star(A_19)),zero)
| ~ leq(addition(zero,B_75),zero) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_1140]) ).
tff(c_1275,plain,
! [B_85,A_86] :
( leq(multiplication(B_85,star(A_86)),zero)
| ~ leq(B_85,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_131,c_1181]) ).
tff(c_36,plain,
! [A_33,B_34] :
( ( addition(A_33,B_34) = B_34 )
| ~ leq(A_33,B_34) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_1278,plain,
! [B_85,A_86] :
( ( addition(multiplication(B_85,star(A_86)),zero) = zero )
| ~ leq(B_85,zero) ),
inference(resolution,[status(thm)],[c_1275,c_36]) ).
tff(c_1350,plain,
! [B_90,A_91] :
( ( multiplication(B_90,star(A_91)) = zero )
| ~ leq(B_90,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1278]) ).
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_1397,plain,
! [A_91] :
( ( star(A_91) = addition(one,zero) )
| ~ leq(A_91,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_1350,c_22]) ).
tff(c_1462,plain,
! [A_93] :
( ( star(A_93) = one )
| ~ leq(A_93,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1397]) ).
tff(c_1473,plain,
! [A_33] :
( ( star(A_33) = one )
| ( addition(A_33,zero) != zero ) ),
inference(resolution,[status(thm)],[c_38,c_1462]) ).
tff(c_1478,plain,
! [A_33] :
( ( star(A_33) = one )
| ( zero != A_33 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1473]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_1480,plain,
star(zero) = one,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1473]) ).
tff(c_649,plain,
! [A_62,B_63,C_64] : ( addition(multiplication(A_62,B_63),multiplication(A_62,C_64)) = multiplication(A_62,addition(B_63,C_64)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_5364,plain,
! [A_135,B_136] : ( multiplication(A_135,addition(B_136,one)) = addition(multiplication(A_135,B_136),A_135) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_649]) ).
tff(c_5555,plain,
! [A_135] : ( addition(multiplication(A_135,zero),A_135) = multiplication(A_135,one) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_5364]) ).
tff(c_5617,plain,
! [A_135] : ( addition(multiplication(A_135,zero),A_135) = A_135 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_5555]) ).
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_1163,plain,
! [B_75,A_76,B_34] :
( leq(multiplication(B_75,star(A_76)),B_34)
| ( addition(addition(multiplication(B_34,A_76),B_75),B_34) != B_34 ) ),
inference(resolution,[status(thm)],[c_38,c_1140]) ).
tff(c_20809,plain,
! [B_331,A_332,B_333] :
( leq(multiplication(B_331,star(A_332)),B_333)
| ( addition(B_333,addition(multiplication(B_333,A_332),B_331)) != B_333 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1163]) ).
tff(c_20887,plain,
! [A_135] :
( leq(multiplication(A_135,star(zero)),A_135)
| ( addition(A_135,A_135) != A_135 ) ),
inference(superposition,[status(thm),theory(equality)],[c_5617,c_20809]) ).
tff(c_21012,plain,
! [A_135] : leq(A_135,A_135),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_12,c_1480,c_20887]) ).
tff(c_24,plain,
! [A_21] : ( addition(one,multiplication(star(A_21),A_21)) = star(A_21) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_421,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_511,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_421]) ).
tff(c_741,plain,
! [A_66,B_67] : ( addition(A_66,addition(B_67,A_66)) = addition(A_66,B_67) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_511]) ).
tff(c_806,plain,
! [A_21] : ( addition(multiplication(star(A_21),A_21),star(A_21)) = addition(multiplication(star(A_21),A_21),one) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_741]) ).
tff(c_853,plain,
! [A_21] : ( addition(multiplication(star(A_21),A_21),star(A_21)) = star(A_21) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_2,c_806]) ).
tff(c_6333,plain,
! [A_143] : ( multiplication(star(A_143),addition(A_143,one)) = star(A_143) ),
inference(superposition,[status(thm),theory(equality)],[c_853,c_5364]) ).
tff(c_6437,plain,
! [B_2] : ( multiplication(star(B_2),addition(one,B_2)) = star(B_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_6333]) ).
tff(c_553,plain,
! [A_21] : ( addition(one,multiplication(star(A_21),A_21)) = addition(one,star(A_21)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_511]) ).
tff(c_597,plain,
! [A_21] : ( addition(one,star(A_21)) = star(A_21) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_553]) ).
tff(c_488,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_421]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_864,plain,
! [A_68,C_69,B_70] : ( addition(multiplication(A_68,C_69),multiplication(B_70,C_69)) = multiplication(addition(A_68,B_70),C_69) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_7367,plain,
! [B_154,A_155] : ( multiplication(addition(one,B_154),A_155) = addition(A_155,multiplication(B_154,A_155)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_864]) ).
tff(c_7506,plain,
! [B_2] : ( multiplication(addition(one,star(B_2)),addition(one,B_2)) = addition(addition(one,B_2),star(B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_6437,c_7367]) ).
tff(c_7662,plain,
! [B_156] : ( addition(B_156,star(B_156)) = star(B_156) ),
inference(demodulation,[status(thm),theory(equality)],[c_6437,c_597,c_2,c_488,c_597,c_2,c_7506]) ).
tff(c_1956,plain,
! [A_103,A_101,B_102] : ( addition(A_103,addition(A_101,B_102)) = addition(A_101,addition(B_102,A_103)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_421]) ).
tff(c_2257,plain,
! [A_41,A_103] : ( addition(zero,addition(A_41,A_103)) = addition(A_103,A_41) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_1956]) ).
tff(c_7705,plain,
! [B_156] : ( addition(star(B_156),B_156) = addition(zero,star(B_156)) ),
inference(superposition,[status(thm),theory(equality)],[c_7662,c_2257]) ).
tff(c_7791,plain,
! [B_156] : ( addition(star(B_156),B_156) = star(B_156) ),
inference(demodulation,[status(thm),theory(equality)],[c_131,c_7705]) ).
tff(c_218,plain,
! [A_47] : ( addition(multiplication(A_47,strong_iteration(A_47)),one) = strong_iteration(A_47) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_244,plain,
addition(zero,one) = strong_iteration(zero),
inference(superposition,[status(thm),theory(equality)],[c_20,c_218]) ).
tff(c_247,plain,
strong_iteration(zero) = one,
inference(demodulation,[status(thm),theory(equality)],[c_131,c_244]) ).
tff(c_224,plain,
! [A_47] : ( addition(one,multiplication(A_47,strong_iteration(A_47))) = strong_iteration(A_47) ),
inference(superposition,[status(thm),theory(equality)],[c_218,c_2]) ).
tff(c_547,plain,
! [A_47] : ( addition(one,multiplication(A_47,strong_iteration(A_47))) = addition(one,strong_iteration(A_47)) ),
inference(superposition,[status(thm),theory(equality)],[c_224,c_511]) ).
tff(c_595,plain,
! [A_47] : ( addition(one,strong_iteration(A_47)) = strong_iteration(A_47) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_547]) ).
tff(c_498,plain,
! [A_7,C_57] : ( addition(A_7,addition(A_7,C_57)) = addition(A_7,C_57) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_421]) ).
tff(c_2305,plain,
! [A_7,A_103] : ( addition(A_7,addition(A_7,A_103)) = addition(A_103,A_7) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1956]) ).
tff(c_1304,plain,
! [A_87,B_88,C_89] :
( leq(multiplication(star(A_87),B_88),C_89)
| ~ leq(addition(multiplication(A_87,C_89),B_88),C_89) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_1327,plain,
! [A_87,B_88,B_34] :
( leq(multiplication(star(A_87),B_88),B_34)
| ( addition(addition(multiplication(A_87,B_34),B_88),B_34) != B_34 ) ),
inference(resolution,[status(thm)],[c_38,c_1304]) ).
tff(c_19837,plain,
! [A_317,B_318,B_319] :
( leq(multiplication(star(A_317),B_318),B_319)
| ( addition(B_319,addition(multiplication(A_317,B_319),B_318)) != B_319 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1327]) ).
tff(c_20004,plain,
! [B_318,A_19] :
( leq(multiplication(star(zero),B_318),A_19)
| ( addition(A_19,addition(zero,B_318)) != A_19 ) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_19837]) ).
tff(c_20342,plain,
! [B_326,A_327] :
( leq(B_326,A_327)
| ( addition(A_327,B_326) != A_327 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_131,c_14,c_1480,c_20004]) ).
tff(c_21150,plain,
! [B_336,A_337] :
( ( addition(B_336,A_337) = A_337 )
| ( addition(A_337,B_336) != A_337 ) ),
inference(resolution,[status(thm)],[c_20342,c_36]) ).
tff(c_21210,plain,
! [A_7,A_103] :
( ( addition(addition(A_7,A_103),A_7) = A_7 )
| ( addition(A_103,A_7) != A_7 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2305,c_21150]) ).
tff(c_29849,plain,
! [A_406,A_407] :
( ( addition(A_406,A_407) = A_406 )
| ( addition(A_407,A_406) != A_406 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_498,c_2,c_21210]) ).
tff(c_30701,plain,
! [A_414] : ( addition(strong_iteration(A_414),one) = strong_iteration(A_414) ),
inference(superposition,[status(thm),theory(equality)],[c_595,c_29849]) ).
tff(c_1171,plain,
! [B_75,A_11] :
( leq(multiplication(B_75,star(one)),A_11)
| ~ leq(addition(A_11,B_75),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1140]) ).
tff(c_30753,plain,
! [A_414] :
( leq(multiplication(one,star(one)),strong_iteration(A_414))
| ~ leq(strong_iteration(A_414),strong_iteration(A_414)) ),
inference(superposition,[status(thm),theory(equality)],[c_30701,c_1171]) ).
tff(c_31036,plain,
! [A_416] : leq(star(one),strong_iteration(A_416)),
inference(demodulation,[status(thm),theory(equality)],[c_21012,c_14,c_30753]) ).
tff(c_31046,plain,
leq(star(one),one),
inference(superposition,[status(thm),theory(equality)],[c_247,c_31036]) ).
tff(c_31055,plain,
addition(star(one),one) = one,
inference(resolution,[status(thm)],[c_31046,c_36]) ).
tff(c_30019,plain,
! [A_21] : ( addition(star(A_21),one) = star(A_21) ),
inference(superposition,[status(thm),theory(equality)],[c_597,c_29849]) ).
tff(c_31061,plain,
star(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_31055,c_30019]) ).
tff(c_31236,plain,
! [B_75,A_11] :
( leq(multiplication(B_75,one),A_11)
| ~ leq(addition(A_11,B_75),A_11) ),
inference(demodulation,[status(thm),theory(equality)],[c_31061,c_1171]) ).
tff(c_51070,plain,
! [B_535,A_536] :
( leq(B_535,A_536)
| ~ leq(addition(A_536,B_535),A_536) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_31236]) ).
tff(c_51166,plain,
! [B_156] :
( leq(B_156,star(B_156))
| ~ leq(star(B_156),star(B_156)) ),
inference(superposition,[status(thm),theory(equality)],[c_7791,c_51070]) ).
tff(c_51368,plain,
! [B_538] : leq(B_538,star(B_538)),
inference(demodulation,[status(thm),theory(equality)],[c_21012,c_51166]) ).
tff(c_52653,plain,
! [A_545] :
( leq(A_545,one)
| ( zero != A_545 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1478,c_51368]) ).
tff(c_52716,plain,
! [A_545] :
( ( addition(A_545,one) = one )
| ( zero != A_545 ) ),
inference(resolution,[status(thm)],[c_52653,c_36]) ).
tff(c_680,plain,
! [A_62,C_64,B_63] : ( addition(multiplication(A_62,C_64),multiplication(A_62,B_63)) = multiplication(A_62,addition(B_63,C_64)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_649]) ).
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_32161,plain,
! [A_421,B_422,C_423,C_424] : ( addition(multiplication(A_421,B_422),addition(multiplication(A_421,C_423),C_424)) = addition(multiplication(A_421,addition(B_422,C_423)),C_424) ),
inference(superposition,[status(thm),theory(equality)],[c_649,c_4]) ).
tff(c_32648,plain,
! [A_421,B_422,C_423] : ( addition(multiplication(A_421,addition(B_422,C_423)),zero) = addition(multiplication(A_421,B_422),multiplication(A_421,C_423)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_32161]) ).
tff(c_72726,plain,
! [A_667,C_668,B_669] : ( multiplication(A_667,addition(C_668,B_669)) = multiplication(A_667,addition(B_669,C_668)) ),
inference(demodulation,[status(thm),theory(equality)],[c_131,c_2,c_680,c_32648]) ).
tff(c_73461,plain,
! [A_667,A_545] :
( ( multiplication(A_667,addition(one,A_545)) = multiplication(A_667,one) )
| ( zero != A_545 ) ),
inference(superposition,[status(thm),theory(equality)],[c_52716,c_72726]) ).
tff(c_174056,plain,
! [A_667] : ( multiplication(A_667,addition(one,zero)) = A_667 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_73461]) ).
tff(c_1224,plain,
! [C_82,A_83,B_84] :
( leq(C_82,multiplication(strong_iteration(A_83),B_84))
| ~ leq(C_82,addition(multiplication(A_83,C_82),B_84)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_11132,plain,
! [A_202,B_203] :
( leq(A_202,multiplication(strong_iteration(one),B_203))
| ~ leq(A_202,addition(A_202,B_203)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1224]) ).
tff(c_11228,plain,
! [A_33,B_203] :
( leq(A_33,multiplication(strong_iteration(one),B_203))
| ( addition(A_33,addition(A_33,B_203)) != addition(A_33,B_203) ) ),
inference(resolution,[status(thm)],[c_38,c_11132]) ).
tff(c_11330,plain,
! [A_206,B_207] : leq(A_206,multiplication(strong_iteration(one),B_207)),
inference(demodulation,[status(thm),theory(equality)],[c_498,c_11228]) ).
tff(c_11427,plain,
! [A_210] : leq(A_210,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_11330]) ).
tff(c_11553,plain,
! [A_211] : ( addition(A_211,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_11427,c_36]) ).
tff(c_11597,plain,
star(strong_iteration(one)) = strong_iteration(one),
inference(superposition,[status(thm),theory(equality)],[c_11553,c_7791]) ).
tff(c_20958,plain,
! [B_331,A_332] :
( leq(multiplication(B_331,star(A_332)),zero)
| ( addition(multiplication(zero,A_332),B_331) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_20809]) ).
tff(c_23215,plain,
! [B_354,A_355] :
( leq(multiplication(B_354,star(A_355)),zero)
| ( zero != B_354 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_131,c_20,c_20958]) ).
tff(c_23230,plain,
! [B_354,A_355] :
( ( addition(multiplication(B_354,star(A_355)),zero) = zero )
| ( zero != B_354 ) ),
inference(resolution,[status(thm)],[c_23215,c_36]) ).
tff(c_23295,plain,
! [B_356,A_357] :
( ( multiplication(B_356,star(A_357)) = zero )
| ( zero != B_356 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_23230]) ).
tff(c_23512,plain,
! [B_356] :
( ( multiplication(B_356,strong_iteration(one)) = zero )
| ( zero != B_356 ) ),
inference(superposition,[status(thm),theory(equality)],[c_11597,c_23295]) ).
tff(c_921,plain,
! [A_68,A_12] : ( multiplication(addition(A_68,one),A_12) = addition(multiplication(A_68,A_12),A_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_864]) ).
tff(c_18081,plain,
! [A_305] : ( multiplication(addition(A_305,one),strong_iteration(one)) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_921,c_11553]) ).
tff(c_18230,plain,
! [B_2] : ( multiplication(addition(one,B_2),strong_iteration(one)) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_18081]) ).
tff(c_10,plain,
! [A_8,B_9,C_10] : ( multiplication(multiplication(A_8,B_9),C_10) = multiplication(A_8,multiplication(B_9,C_10)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_12843,plain,
! [A_219,C_220,B_221] : ( addition(multiplication(A_219,C_220),multiplication(A_219,B_221)) = multiplication(A_219,addition(B_221,C_220)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_649]) ).
tff(c_13040,plain,
! [A_11,C_220] : ( multiplication(A_11,addition(one,C_220)) = addition(multiplication(A_11,C_220),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_12843]) ).
tff(c_240,plain,
addition(strong_iteration(one),one) = strong_iteration(one),
inference(superposition,[status(thm),theory(equality)],[c_14,c_218]) ).
tff(c_61894,plain,
! [A_608] : ( addition(multiplication(A_608,strong_iteration(one)),A_608) = multiplication(A_608,strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_5364]) ).
tff(c_575,plain,
! [A_1,B_2] : ( addition(A_1,addition(B_2,A_1)) = addition(A_1,B_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_511]) ).
tff(c_2611,plain,
! [A_107,A_108] : ( addition(A_107,addition(A_107,A_108)) = addition(A_108,A_107) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1956]) ).
tff(c_2734,plain,
! [B_2,A_1] : ( addition(addition(B_2,A_1),A_1) = addition(A_1,addition(A_1,B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_575,c_2611]) ).
tff(c_3352,plain,
! [B_113,A_114] : ( addition(addition(B_113,A_114),A_114) = addition(A_114,B_113) ),
inference(demodulation,[status(thm),theory(equality)],[c_498,c_2734]) ).
tff(c_3525,plain,
! [B_2,A_1] : ( addition(addition(B_2,A_1),B_2) = addition(B_2,A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_3352]) ).
tff(c_51202,plain,
! [B_2,A_1] :
( leq(B_2,addition(B_2,A_1))
| ~ leq(addition(B_2,A_1),addition(B_2,A_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_3525,c_51070]) ).
tff(c_51424,plain,
! [B_539,A_540] : leq(B_539,addition(B_539,A_540)),
inference(demodulation,[status(thm),theory(equality)],[c_21012,c_51202]) ).
tff(c_51580,plain,
! [A_55,A_1,B_56] : leq(A_55,addition(A_1,addition(A_55,B_56))),
inference(superposition,[status(thm),theory(equality)],[c_488,c_51424]) ).
tff(c_94259,plain,
! [A_831,B_832] : leq(A_831,multiplication(addition(A_831,B_832),strong_iteration(one))),
inference(superposition,[status(thm),theory(equality)],[c_61894,c_51580]) ).
tff(c_94333,plain,
! [A_11,C_220] : leq(multiplication(A_11,C_220),multiplication(multiplication(A_11,addition(one,C_220)),strong_iteration(one))),
inference(superposition,[status(thm),theory(equality)],[c_13040,c_94259]) ).
tff(c_115831,plain,
! [A_974,C_975] : leq(multiplication(A_974,C_975),multiplication(A_974,strong_iteration(one))),
inference(demodulation,[status(thm),theory(equality)],[c_18230,c_10,c_94333]) ).
tff(c_116118,plain,
! [B_976,C_977] :
( leq(multiplication(B_976,C_977),zero)
| ( zero != B_976 ) ),
inference(superposition,[status(thm),theory(equality)],[c_23512,c_115831]) ).
tff(c_256,plain,
! [A_48] : ( addition(one,multiplication(A_48,star(A_48))) = star(A_48) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_270,plain,
addition(one,zero) = star(zero),
inference(superposition,[status(thm),theory(equality)],[c_20,c_256]) ).
tff(c_273,plain,
star(zero) = one,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_270]) ).
tff(c_1414,plain,
! [B_90] :
( ( multiplication(B_90,one) = zero )
| ~ leq(B_90,zero) ),
inference(superposition,[status(thm),theory(equality)],[c_273,c_1350]) ).
tff(c_1441,plain,
! [B_90] :
( ( zero = B_90 )
| ~ leq(B_90,zero) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1414]) ).
tff(c_116378,plain,
! [C_977] : ( multiplication(zero,C_977) = zero ),
inference(resolution,[status(thm)],[c_116118,c_1441]) ).
tff(c_686,plain,
! [A_11,C_64] : ( multiplication(A_11,addition(one,C_64)) = addition(A_11,multiplication(A_11,C_64)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_649]) ).
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_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_16642,plain,
! [A_284,C_285] : ( addition(star(A_284),addition(multiplication(strong_iteration(A_284),zero),C_285)) = addition(strong_iteration(A_284),C_285) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_421]) ).
tff(c_16826,plain,
! [A_284,C_15] : ( addition(star(A_284),multiplication(strong_iteration(A_284),addition(zero,C_15))) = addition(strong_iteration(A_284),multiplication(strong_iteration(A_284),C_15)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_16642]) ).
tff(c_16882,plain,
! [A_284,C_15] : ( addition(star(A_284),multiplication(strong_iteration(A_284),C_15)) = multiplication(strong_iteration(A_284),addition(one,C_15)) ),
inference(demodulation,[status(thm),theory(equality)],[c_686,c_131,c_16826]) ).
tff(c_2357,plain,
! [A_104,A_105] : ( addition(zero,addition(A_104,A_105)) = addition(A_105,A_104) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_1956]) ).
tff(c_2471,plain,
! [A_32] : ( addition(multiplication(strong_iteration(A_32),zero),star(A_32)) = addition(zero,strong_iteration(A_32)) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_2357]) ).
tff(c_2538,plain,
! [A_32] : ( addition(multiplication(strong_iteration(A_32),zero),star(A_32)) = strong_iteration(A_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_131,c_2471]) ).
tff(c_14633,plain,
! [B_240,C_241,A_242] : ( addition(multiplication(B_240,C_241),multiplication(A_242,C_241)) = multiplication(addition(A_242,B_240),C_241) ),
inference(superposition,[status(thm),theory(equality)],[c_864,c_2]) ).
tff(c_459,plain,
! [A_21,C_57] : ( addition(one,addition(multiplication(star(A_21),A_21),C_57)) = addition(star(A_21),C_57) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_421]) ).
tff(c_335918,plain,
! [A_1695,C_1696] : ( addition(one,multiplication(addition(A_1695,star(C_1696)),C_1696)) = addition(star(C_1696),multiplication(A_1695,C_1696)) ),
inference(superposition,[status(thm),theory(equality)],[c_14633,c_459]) ).
tff(c_336843,plain,
! [A_32] : ( addition(star(A_32),multiplication(multiplication(strong_iteration(A_32),zero),A_32)) = addition(one,multiplication(strong_iteration(A_32),A_32)) ),
inference(superposition,[status(thm),theory(equality)],[c_2538,c_335918]) ).
tff(c_337033,plain,
! [A_32] : ( addition(one,multiplication(strong_iteration(A_32),A_32)) = strong_iteration(A_32) ),
inference(demodulation,[status(thm),theory(equality)],[c_174056,c_116378,c_16882,c_10,c_336843]) ).
tff(c_40,plain,
addition(multiplication(strong_iteration('#skF_1'),'#skF_1'),one) != strong_iteration('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_41,plain,
addition(one,multiplication(strong_iteration('#skF_1'),'#skF_1')) != strong_iteration('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_40]) ).
tff(c_383132,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_337033,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE139+1 : 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 : n029.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 23:37:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 108.49/90.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.49/90.42
% 108.49/90.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 108.69/90.47
% 108.69/90.47 Inference rules
% 108.69/90.47 ----------------------
% 108.69/90.47 #Ref : 2
% 108.69/90.47 #Sup : 98625
% 108.69/90.47 #Fact : 0
% 108.69/90.47 #Define : 0
% 108.69/90.47 #Split : 10
% 108.69/90.47 #Chain : 0
% 108.69/90.47 #Close : 0
% 108.69/90.47
% 108.69/90.47 Ordering : KBO
% 108.69/90.47
% 108.69/90.47 Simplification rules
% 108.69/90.47 ----------------------
% 108.69/90.47 #Subsume : 29321
% 108.69/90.47 #Demod : 108311
% 108.69/90.47 #Tautology : 29165
% 108.69/90.47 #SimpNegUnit : 1707
% 108.69/90.47 #BackRed : 128
% 108.69/90.47
% 108.69/90.47 #Partial instantiations: 0
% 108.69/90.47 #Strategies tried : 1
% 108.69/90.47
% 108.69/90.47 Timing (in seconds)
% 108.69/90.47 ----------------------
% 108.69/90.47 Preprocessing : 0.48
% 108.69/90.47 Parsing : 0.27
% 108.69/90.47 CNF conversion : 0.03
% 108.69/90.47 Main loop : 88.89
% 108.69/90.47 Inferencing : 5.34
% 108.69/90.47 Reduction : 59.75
% 108.69/90.47 Demodulation : 53.06
% 108.69/90.47 BG Simplification : 0.55
% 108.69/90.47 Subsumption : 18.50
% 108.69/90.47 Abstraction : 1.00
% 108.69/90.47 MUC search : 0.00
% 108.69/90.47 Cooper : 0.00
% 108.69/90.47 Total : 89.46
% 108.69/90.47 Index Insertion : 0.00
% 108.69/90.47 Index Deletion : 0.00
% 108.69/90.47 Index Matching : 0.00
% 108.69/90.47 BG Taut test : 0.00
%------------------------------------------------------------------------------