TSTP Solution File: KLE040+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE040+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 : n017.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 10:44:44 EDT 2023
% Result : Theorem 99.10s 82.19s
% Output : CNFRefutation 99.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 77 ( 54 unt; 7 typ; 0 def)
% Number of atoms : 86 ( 55 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 13 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 119 (; 119 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > star > zero > one > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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/KLE002+0.ax',multiplicative_right_identity) ).
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(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
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_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_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_80,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_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/KLE002+0.ax',right_distributivity) ).
tff(f_86,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
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_100,negated_conjecture,
~ ! [X0] : ( multiplication(star(X0),star(X0)) = star(X0) ),
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_28,plain,
! [A_23] : leq(addition(one,multiplication(A_23,star(A_23))),star(A_23)),
inference(cnfTransformation,[status(thm)],[f_84]) ).
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_1210,plain,
! [A_67,C_68,B_69] :
( leq(multiplication(star(A_67),C_68),B_69)
| ~ leq(addition(multiplication(A_67,B_69),C_68),B_69) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_9693,plain,
! [A_194,B_195,B_196] :
( leq(multiplication(star(A_194),B_195),B_196)
| ~ leq(addition(B_195,multiplication(A_194,B_196)),B_196) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1210]) ).
tff(c_9759,plain,
! [A_23] : leq(multiplication(star(A_23),one),star(A_23)),
inference(resolution,[status(thm)],[c_28,c_9693]) ).
tff(c_9791,plain,
! [A_23] : leq(star(A_23),star(A_23)),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_9759]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_618,plain,
! [A_56,C_57,B_58] : ( addition(multiplication(A_56,C_57),multiplication(B_58,C_57)) = multiplication(addition(A_56,B_58),C_57) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_668,plain,
! [B_58,A_12] : ( multiplication(addition(one,B_58),A_12) = addition(A_12,multiplication(B_58,A_12)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_618]) ).
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_252,plain,
! [A_45] : leq(addition(one,multiplication(A_45,star(A_45))),star(A_45)),
inference(cnfTransformation,[status(thm)],[f_84]) ).
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_4326,plain,
! [A_117] : ( addition(addition(one,multiplication(A_117,star(A_117))),star(A_117)) = star(A_117) ),
inference(resolution,[status(thm)],[c_252,c_24]) ).
tff(c_4401,plain,
! [A_117] : ( addition(one,addition(multiplication(A_117,star(A_117)),star(A_117))) = star(A_117) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_4326]) ).
tff(c_4431,plain,
! [A_117] : ( addition(one,multiplication(addition(one,A_117),star(A_117))) = star(A_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_668,c_2,c_4401]) ).
tff(c_4967,plain,
! [A_122] : ( addition(one,multiplication(addition(one,A_122),star(A_122))) = star(A_122) ),
inference(demodulation,[status(thm),theory(equality)],[c_668,c_2,c_4401]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_275,plain,
! [A_46,B_47,C_48] : ( addition(addition(A_46,B_47),C_48) = addition(A_46,addition(B_47,C_48)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_324,plain,
! [A_7,C_48] : ( addition(A_7,addition(A_7,C_48)) = addition(A_7,C_48) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_275]) ).
tff(c_5014,plain,
! [A_122] : ( addition(one,multiplication(addition(one,A_122),star(A_122))) = addition(one,star(A_122)) ),
inference(superposition,[status(thm),theory(equality)],[c_4967,c_324]) ).
tff(c_5086,plain,
! [A_122] : ( addition(one,star(A_122)) = star(A_122) ),
inference(demodulation,[status(thm),theory(equality)],[c_4431,c_5014]) ).
tff(c_310,plain,
! [B_2,A_1,C_48] : ( addition(addition(B_2,A_1),C_48) = addition(A_1,addition(B_2,C_48)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_275]) ).
tff(c_4335,plain,
! [A_117] : ( addition(multiplication(A_117,star(A_117)),addition(one,star(A_117))) = star(A_117) ),
inference(superposition,[status(thm),theory(equality)],[c_4326,c_310]) ).
tff(c_63683,plain,
! [A_117] : ( multiplication(addition(one,A_117),star(A_117)) = star(A_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_668,c_2,c_5086,c_4335]) ).
tff(c_11350,plain,
! [A_233,B_234] :
( leq(multiplication(star(A_233),multiplication(A_233,B_234)),B_234)
| ~ leq(multiplication(A_233,B_234),B_234) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1210]) ).
tff(c_11357,plain,
! [A_233,B_234] :
( ( addition(multiplication(star(A_233),multiplication(A_233,B_234)),B_234) = B_234 )
| ~ leq(multiplication(A_233,B_234),B_234) ),
inference(resolution,[status(thm)],[c_11350,c_24]) ).
tff(c_106981,plain,
! [B_739,A_740] :
( ( addition(B_739,multiplication(star(A_740),multiplication(A_740,B_739))) = B_739 )
| ~ leq(multiplication(A_740,B_739),B_739) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_11357]) ).
tff(c_107546,plain,
! [A_117] :
( ( addition(star(A_117),multiplication(star(addition(one,A_117)),star(A_117))) = star(A_117) )
| ~ leq(multiplication(addition(one,A_117),star(A_117)),star(A_117)) ),
inference(superposition,[status(thm),theory(equality)],[c_63683,c_106981]) ).
tff(c_107968,plain,
! [A_117] : ( multiplication(star(addition(one,A_117)),star(A_117)) = star(A_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_9791,c_63683,c_5086,c_668,c_107546]) ).
tff(c_108038,plain,
! [A_741] : ( multiplication(star(addition(one,A_741)),star(A_741)) = star(A_741) ),
inference(demodulation,[status(thm),theory(equality)],[c_9791,c_63683,c_5086,c_668,c_107546]) ).
tff(c_701,plain,
! [A_59,B_60,C_61] : ( addition(multiplication(A_59,B_60),multiplication(A_59,C_61)) = multiplication(A_59,addition(B_60,C_61)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_753,plain,
! [A_11,C_61] : ( multiplication(A_11,addition(one,C_61)) = addition(A_11,multiplication(A_11,C_61)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_701]) ).
tff(c_108236,plain,
! [A_741] : ( multiplication(star(addition(one,A_741)),addition(one,star(A_741))) = addition(star(addition(one,A_741)),star(A_741)) ),
inference(superposition,[status(thm),theory(equality)],[c_108038,c_753]) ).
tff(c_108610,plain,
! [A_741] : ( addition(star(A_741),star(addition(one,A_741))) = star(A_741) ),
inference(demodulation,[status(thm),theory(equality)],[c_107968,c_5086,c_2,c_108236]) ).
tff(c_238,plain,
! [A_44] : leq(addition(one,multiplication(star(A_44),A_44)),star(A_44)),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_6086,plain,
! [A_141] : ( addition(addition(one,multiplication(star(A_141),A_141)),star(A_141)) = star(A_141) ),
inference(resolution,[status(thm)],[c_238,c_24]) ).
tff(c_6098,plain,
! [A_141] : ( addition(multiplication(star(A_141),A_141),addition(one,star(A_141))) = star(A_141) ),
inference(superposition,[status(thm),theory(equality)],[c_6086,c_310]) ).
tff(c_6195,plain,
! [A_141] : ( multiplication(star(A_141),addition(one,A_141)) = star(A_141) ),
inference(demodulation,[status(thm),theory(equality)],[c_753,c_2,c_5086,c_6098]) ).
tff(c_792,plain,
! [C_62,A_63,B_64] : ( addition(C_62,addition(A_63,B_64)) = addition(A_63,addition(B_64,C_62)) ),
inference(superposition,[status(thm),theory(equality)],[c_275,c_2]) ).
tff(c_1014,plain,
! [B_64,C_62,B_2] : ( addition(addition(B_64,C_62),B_2) = addition(C_62,addition(B_2,B_64)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_792]) ).
tff(c_4080,plain,
! [A_115,C_116] : ( multiplication(A_115,addition(one,C_116)) = addition(A_115,multiplication(A_115,C_116)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_701]) ).
tff(c_4269,plain,
! [A_115,A_1] : ( multiplication(A_115,addition(A_1,one)) = addition(A_115,multiplication(A_115,A_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_4080]) ).
tff(c_756,plain,
! [A_11,B_60] : ( multiplication(A_11,addition(B_60,one)) = addition(multiplication(A_11,B_60),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_701]) ).
tff(c_287,plain,
! [C_48,A_46,B_47] : ( addition(C_48,addition(A_46,B_47)) = addition(A_46,addition(B_47,C_48)) ),
inference(superposition,[status(thm),theory(equality)],[c_275,c_2]) ).
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_1315,plain,
! [C_74,B_75,A_76] :
( leq(multiplication(C_74,star(B_75)),A_76)
| ~ leq(addition(multiplication(A_76,B_75),C_74),A_76) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1336,plain,
! [C_74,B_75,B_22] :
( leq(multiplication(C_74,star(B_75)),B_22)
| ( addition(addition(multiplication(B_22,B_75),C_74),B_22) != B_22 ) ),
inference(resolution,[status(thm)],[c_26,c_1315]) ).
tff(c_12285,plain,
! [C_249,B_250,B_251] :
( leq(multiplication(C_249,star(B_250)),B_251)
| ( addition(B_251,addition(multiplication(B_251,B_250),C_249)) != B_251 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_287,c_4,c_1336]) ).
tff(c_330755,plain,
! [A_1241,B_1242] :
( leq(multiplication(A_1241,star(B_1242)),A_1241)
| ( addition(A_1241,multiplication(A_1241,addition(B_1242,one))) != A_1241 ) ),
inference(superposition,[status(thm),theory(equality)],[c_756,c_12285]) ).
tff(c_330904,plain,
! [A_117] :
( leq(star(A_117),star(addition(one,A_117)))
| ( addition(star(addition(one,A_117)),multiplication(star(addition(one,A_117)),addition(A_117,one))) != star(addition(one,A_117)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_107968,c_330755]) ).
tff(c_331167,plain,
! [A_1243] : leq(star(A_1243),star(addition(one,A_1243))),
inference(demodulation,[status(thm),theory(equality)],[c_6195,c_1014,c_4269,c_330904]) ).
tff(c_331170,plain,
! [A_1243] : ( addition(star(A_1243),star(addition(one,A_1243))) = star(addition(one,A_1243)) ),
inference(resolution,[status(thm)],[c_331167,c_24]) ).
tff(c_331594,plain,
! [A_1243] : ( star(addition(one,A_1243)) = star(A_1243) ),
inference(demodulation,[status(thm),theory(equality)],[c_108610,c_331170]) ).
tff(c_331700,plain,
! [A_117] : ( multiplication(star(A_117),star(A_117)) = star(A_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_331594,c_107968]) ).
tff(c_36,plain,
multiplication(star('#skF_1'),star('#skF_1')) != star('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_334261,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_331700,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE040+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 : n017.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 22:59:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 99.10/82.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.10/82.20
% 99.10/82.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 99.10/82.24
% 99.10/82.24 Inference rules
% 99.10/82.24 ----------------------
% 99.10/82.24 #Ref : 7
% 99.10/82.24 #Sup : 86973
% 99.10/82.24 #Fact : 0
% 99.10/82.24 #Define : 0
% 99.10/82.24 #Split : 6
% 99.10/82.24 #Chain : 0
% 99.10/82.24 #Close : 0
% 99.10/82.24
% 99.10/82.24 Ordering : KBO
% 99.10/82.24
% 99.10/82.24 Simplification rules
% 99.10/82.24 ----------------------
% 99.10/82.24 #Subsume : 30797
% 99.10/82.24 #Demod : 100037
% 99.10/82.24 #Tautology : 14175
% 99.10/82.24 #SimpNegUnit : 589
% 99.10/82.24 #BackRed : 56
% 99.10/82.24
% 99.10/82.24 #Partial instantiations: 0
% 99.10/82.24 #Strategies tried : 1
% 99.10/82.24
% 99.10/82.24 Timing (in seconds)
% 99.10/82.24 ----------------------
% 99.10/82.24 Preprocessing : 0.46
% 99.10/82.24 Parsing : 0.26
% 99.10/82.24 CNF conversion : 0.03
% 99.10/82.24 Main loop : 80.72
% 99.10/82.24 Inferencing : 5.04
% 99.10/82.24 Reduction : 59.39
% 99.10/82.24 Demodulation : 54.70
% 99.10/82.24 BG Simplification : 0.70
% 99.10/82.24 Subsumption : 12.58
% 99.10/82.24 Abstraction : 1.25
% 99.10/82.24 MUC search : 0.00
% 99.10/82.24 Cooper : 0.00
% 99.10/82.24 Total : 81.24
% 99.10/82.24 Index Insertion : 0.00
% 99.10/82.24 Index Deletion : 0.00
% 99.10/82.24 Index Matching : 0.00
% 99.10/82.24 BG Taut test : 0.00
%------------------------------------------------------------------------------