TSTP Solution File: KLE144+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE144+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 : n015.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 10:44:55 EDT 2023
% Result : Theorem 13.91s 4.49s
% Output : CNFRefutation 13.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 56 ( 39 unt; 8 typ; 0 def)
% Number of atoms : 57 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 7 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 76 (; 76 !; 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_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
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_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
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_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_105,negated_conjecture,
~ ! [X0] : ( strong_iteration(star(X0)) = strong_iteration(one) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_343,plain,
! [A_51,B_52,C_53] : ( addition(addition(A_51,B_52),C_53) = addition(A_51,addition(B_52,C_53)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_417,plain,
! [A_7,C_53] : ( addition(A_7,addition(A_7,C_53)) = addition(A_7,C_53) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_343]) ).
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_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_1299,plain,
! [C_87,A_88,B_89] :
( leq(C_87,multiplication(strong_iteration(A_88),B_89))
| ~ leq(C_87,addition(multiplication(A_88,C_87),B_89)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_10731,plain,
! [A_195,B_196] :
( leq(A_195,multiplication(strong_iteration(one),B_196))
| ~ leq(A_195,addition(A_195,B_196)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1299]) ).
tff(c_10827,plain,
! [A_33,B_196] :
( leq(A_33,multiplication(strong_iteration(one),B_196))
| ( addition(A_33,addition(A_33,B_196)) != addition(A_33,B_196) ) ),
inference(resolution,[status(thm)],[c_38,c_10731]) ).
tff(c_10856,plain,
! [A_197,B_198] : leq(A_197,multiplication(strong_iteration(one),B_198)),
inference(demodulation,[status(thm),theory(equality)],[c_417,c_10827]) ).
tff(c_10887,plain,
! [A_199] : leq(A_199,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_10856]) ).
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_10902,plain,
! [A_200] : ( addition(A_200,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_10887,c_36]) ).
tff(c_11138,plain,
! [A_1] : ( addition(strong_iteration(one),A_1) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_10902]) ).
tff(c_10880,plain,
! [A_197] : leq(A_197,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_10856]) ).
tff(c_10901,plain,
! [A_199] : ( addition(A_199,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_10887,c_36]) ).
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_22,plain,
! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = star(A_20) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_3677,plain,
! [B_126,A_127,B_128] : ( addition(B_126,addition(A_127,B_128)) = addition(A_127,addition(B_128,B_126)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_343]) ).
tff(c_4191,plain,
! [A_129,B_130] : ( addition(zero,addition(A_129,B_130)) = addition(B_130,A_129) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_3677]) ).
tff(c_4341,plain,
! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = addition(zero,star(A_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_4191]) ).
tff(c_4406,plain,
! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = star(A_20) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_4341]) ).
tff(c_648,plain,
! [A_62,C_63,B_64] : ( addition(multiplication(A_62,C_63),multiplication(B_64,C_63)) = multiplication(addition(A_62,B_64),C_63) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_694,plain,
! [A_62,A_12] : ( multiplication(addition(A_62,one),A_12) = addition(multiplication(A_62,A_12),A_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_648]) ).
tff(c_18341,plain,
! [A_301] : ( multiplication(addition(A_301,one),strong_iteration(one)) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_694,c_10902]) ).
tff(c_18447,plain,
! [A_20] : ( multiplication(star(A_20),strong_iteration(one)) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_4406,c_18341]) ).
tff(c_20482,plain,
! [C_319,A_320,A_321] :
( leq(C_319,multiplication(strong_iteration(A_320),A_321))
| ~ leq(C_319,addition(A_321,multiplication(A_320,C_319))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1299]) ).
tff(c_20494,plain,
! [A_20,A_321] :
( leq(strong_iteration(one),multiplication(strong_iteration(star(A_20)),A_321))
| ~ leq(strong_iteration(one),addition(A_321,strong_iteration(one))) ),
inference(superposition,[status(thm),theory(equality)],[c_18447,c_20482]) ).
tff(c_21852,plain,
! [A_331,A_332] : leq(strong_iteration(one),multiplication(strong_iteration(star(A_331)),A_332)),
inference(demodulation,[status(thm),theory(equality)],[c_10880,c_10901,c_20494]) ).
tff(c_21892,plain,
! [A_333] : leq(strong_iteration(one),strong_iteration(star(A_333))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_21852]) ).
tff(c_21895,plain,
! [A_333] : ( addition(strong_iteration(one),strong_iteration(star(A_333))) = strong_iteration(star(A_333)) ),
inference(resolution,[status(thm)],[c_21892,c_36]) ).
tff(c_21905,plain,
! [A_333] : ( strong_iteration(star(A_333)) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_11138,c_21895]) ).
tff(c_40,plain,
strong_iteration(star('#skF_1')) != strong_iteration(one),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_21918,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_21905,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE144+1 : 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
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 23:47:29 EDT 2023
% 0.15/0.36 % CPUTime :
% 13.91/4.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.91/4.49
% 13.91/4.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.91/4.53
% 13.91/4.53 Inference rules
% 13.91/4.53 ----------------------
% 13.91/4.53 #Ref : 0
% 13.91/4.53 #Sup : 5724
% 13.91/4.53 #Fact : 0
% 13.91/4.53 #Define : 0
% 13.91/4.53 #Split : 3
% 13.91/4.53 #Chain : 0
% 13.91/4.53 #Close : 0
% 13.91/4.53
% 13.91/4.53 Ordering : KBO
% 13.91/4.53
% 13.91/4.53 Simplification rules
% 13.91/4.53 ----------------------
% 13.91/4.53 #Subsume : 1650
% 13.91/4.53 #Demod : 4850
% 13.91/4.53 #Tautology : 1836
% 13.91/4.53 #SimpNegUnit : 43
% 13.91/4.53 #BackRed : 16
% 13.91/4.53
% 13.91/4.53 #Partial instantiations: 0
% 13.91/4.53 #Strategies tried : 1
% 13.91/4.53
% 13.91/4.53 Timing (in seconds)
% 13.91/4.53 ----------------------
% 13.91/4.53 Preprocessing : 0.49
% 13.91/4.53 Parsing : 0.26
% 13.91/4.53 CNF conversion : 0.03
% 13.91/4.53 Main loop : 2.96
% 13.91/4.53 Inferencing : 0.71
% 13.91/4.53 Reduction : 1.44
% 13.91/4.53 Demodulation : 1.21
% 13.91/4.53 BG Simplification : 0.07
% 13.91/4.53 Subsumption : 0.52
% 13.91/4.53 Abstraction : 0.10
% 13.91/4.53 MUC search : 0.00
% 13.91/4.53 Cooper : 0.00
% 13.91/4.53 Total : 3.50
% 13.91/4.53 Index Insertion : 0.00
% 13.91/4.53 Index Deletion : 0.00
% 13.91/4.53 Index Matching : 0.00
% 13.91/4.53 BG Taut test : 0.00
%------------------------------------------------------------------------------