TSTP Solution File: KLE141+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE141+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 13.49s 4.29s
% Output : CNFRefutation 13.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 38 ( 18 unt; 9 typ; 0 def)
% Number of atoms : 40 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 8 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 46 (; 46 !; 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_64,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
tff(f_59,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
tff(f_55,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
tff(f_101,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
tff(f_66,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
tff(f_94,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
tff(f_108,negated_conjecture,
~ ! [X0] :
( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
& leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_11310,plain,
! [A_215,B_216,C_217] : ( addition(addition(A_215,B_216),C_217) = addition(A_215,addition(B_216,C_217)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_11390,plain,
! [A_7,C_217] : ( addition(A_7,addition(A_7,C_217)) = addition(A_7,C_217) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_11310]) ).
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_101]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_12410,plain,
! [C_249,A_250,B_251] :
( leq(C_249,multiplication(strong_iteration(A_250),B_251))
| ~ leq(C_249,addition(multiplication(A_250,C_249),B_251)) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_22777,plain,
! [A_351,B_352] :
( leq(A_351,multiplication(strong_iteration(one),B_352))
| ~ leq(A_351,addition(A_351,B_352)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_12410]) ).
tff(c_22899,plain,
! [A_33,B_352] :
( leq(A_33,multiplication(strong_iteration(one),B_352))
| ( addition(A_33,addition(A_33,B_352)) != addition(A_33,B_352) ) ),
inference(resolution,[status(thm)],[c_38,c_22777]) ).
tff(c_22931,plain,
! [A_353,B_354] : leq(A_353,multiplication(strong_iteration(one),B_354)),
inference(demodulation,[status(thm),theory(equality)],[c_11390,c_22899]) ).
tff(c_22950,plain,
! [A_353] : leq(A_353,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_22931]) ).
tff(c_425,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_55]) ).
tff(c_502,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_425]) ).
tff(c_1180,plain,
! [C_84,A_85,B_86] :
( leq(C_84,multiplication(strong_iteration(A_85),B_86))
| ~ leq(C_84,addition(multiplication(A_85,C_84),B_86)) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_10953,plain,
! [A_201,B_202] :
( leq(A_201,multiplication(strong_iteration(one),B_202))
| ~ leq(A_201,addition(A_201,B_202)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1180]) ).
tff(c_11053,plain,
! [A_33,B_202] :
( leq(A_33,multiplication(strong_iteration(one),B_202))
| ( addition(A_33,addition(A_33,B_202)) != addition(A_33,B_202) ) ),
inference(resolution,[status(thm)],[c_38,c_10953]) ).
tff(c_11078,plain,
! [A_33,B_202] : leq(A_33,multiplication(strong_iteration(one),B_202)),
inference(demodulation,[status(thm),theory(equality)],[c_502,c_11053]) ).
tff(c_40,plain,
( ~ leq(multiplication(strong_iteration(one),'#skF_2'),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),'#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_210,plain,
~ leq(strong_iteration(one),multiplication(strong_iteration(one),'#skF_1')),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_11084,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11078,c_210]) ).
tff(c_11085,plain,
~ leq(multiplication(strong_iteration(one),'#skF_2'),strong_iteration(one)),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_22959,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22950,c_11085]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KLE141+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n004.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 23:24:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 13.49/4.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.50/4.29
% 13.50/4.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.50/4.32
% 13.50/4.32 Inference rules
% 13.50/4.32 ----------------------
% 13.50/4.32 #Ref : 0
% 13.50/4.32 #Sup : 5916
% 13.50/4.32 #Fact : 0
% 13.50/4.32 #Define : 0
% 13.50/4.32 #Split : 9
% 13.50/4.32 #Chain : 0
% 13.50/4.32 #Close : 0
% 13.50/4.32
% 13.50/4.32 Ordering : KBO
% 13.50/4.32
% 13.50/4.32 Simplification rules
% 13.50/4.32 ----------------------
% 13.50/4.32 #Subsume : 1103
% 13.50/4.32 #Demod : 5076
% 13.50/4.32 #Tautology : 2117
% 13.50/4.32 #SimpNegUnit : 33
% 13.50/4.32 #BackRed : 12
% 13.50/4.32
% 13.50/4.32 #Partial instantiations: 0
% 13.50/4.32 #Strategies tried : 1
% 13.50/4.32
% 13.50/4.32 Timing (in seconds)
% 13.50/4.32 ----------------------
% 13.50/4.32 Preprocessing : 0.49
% 13.50/4.32 Parsing : 0.26
% 13.50/4.32 CNF conversion : 0.03
% 13.50/4.32 Main loop : 2.80
% 13.50/4.32 Inferencing : 0.74
% 13.50/4.32 Reduction : 1.40
% 13.50/4.32 Demodulation : 1.19
% 13.50/4.32 BG Simplification : 0.08
% 13.50/4.32 Subsumption : 0.42
% 13.50/4.32 Abstraction : 0.10
% 13.50/4.32 MUC search : 0.00
% 13.50/4.32 Cooper : 0.00
% 13.50/4.32 Total : 3.33
% 13.50/4.32 Index Insertion : 0.00
% 13.50/4.32 Index Deletion : 0.00
% 13.50/4.32 Index Matching : 0.00
% 13.50/4.32 BG Taut test : 0.00
%------------------------------------------------------------------------------