%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE141+1 : TPTP v9.0.0. 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 : n008.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 : Wed Apr 9 07:04:51 PM UTC 2025
% Result : Theorem 13.13s 4.23s
% Output : CNFRefutation 13.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 8 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 67 ( 67 !; 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_64,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
tff(f_59,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
tff(f_101,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
tff(f_66,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
tff(f_53,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(f_57,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
tff(f_74,axiom,
! [A] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
tff(f_62,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_106,negated_conjecture,
~ ! [X0] : ( multiplication(strong_iteration(one),X0) = strong_iteration(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_64]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
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_55]) ).
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_101]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
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_94]) ).
tff(c_10048,plain,
! [A_188,B_189] :
( leq(A_188,multiplication(strong_iteration(one),B_189))
| ~ leq(A_188,addition(A_188,B_189)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1299]) ).
tff(c_10144,plain,
! [A_33,B_189] :
( leq(A_33,multiplication(strong_iteration(one),B_189))
| ( addition(A_33,addition(A_33,B_189)) != addition(A_33,B_189) ) ),
inference(resolution,[status(thm)],[c_38,c_10048]) ).
tff(c_10173,plain,
! [A_190,B_191] : leq(A_190,multiplication(strong_iteration(one),B_191)),
inference(demodulation,[status(thm),theory(equality)],[c_417,c_10144]) ).
tff(c_10204,plain,
! [A_192] : leq(A_192,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_10173]) ).
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_101]) ).
tff(c_10219,plain,
! [A_193] : ( addition(A_193,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_10204,c_36]) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_10377,plain,
! [A_193] : ( addition(strong_iteration(one),A_193) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_10219,c_2]) ).
tff(c_10197,plain,
! [A_190] : leq(A_190,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_10173]) ).
tff(c_32,plain,
! [C_31,A_29,B_30] :
( leq(C_31,multiplication(strong_iteration(A_29),B_30))
| ~ leq(C_31,addition(multiplication(A_29,C_31),B_30)) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_10339,plain,
! [C_31,A_29] :
( leq(C_31,multiplication(strong_iteration(A_29),strong_iteration(one)))
| ~ leq(C_31,strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_10219,c_32]) ).
tff(c_11417,plain,
! [C_203,A_204] : leq(C_203,multiplication(strong_iteration(A_204),strong_iteration(one))),
inference(demodulation,[status(thm),theory(equality)],[c_10197,c_10339]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1338,plain,
! [C_87,A_88] :
( leq(C_87,multiplication(strong_iteration(A_88),zero))
| ~ leq(C_87,multiplication(A_88,C_87)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_1299]) ).
tff(c_17715,plain,
! [A_294] : leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A_294)),zero)),
inference(resolution,[status(thm)],[c_11417,c_1338]) ).
tff(c_17718,plain,
! [A_294] : ( addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A_294)),zero)) = multiplication(strong_iteration(strong_iteration(A_294)),zero) ),
inference(resolution,[status(thm)],[c_17715,c_36]) ).
tff(c_17726,plain,
! [A_294] : ( multiplication(strong_iteration(strong_iteration(A_294)),zero) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_10377,c_17718]) ).
tff(c_20,plain,
! [A_19] : ( multiplication(zero,A_19) = zero ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_17909,plain,
! [A_298] : ( multiplication(strong_iteration(strong_iteration(A_298)),zero) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_10377,c_17718]) ).
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_62]) ).
tff(c_17978,plain,
! [A_298,C_10] : ( multiplication(strong_iteration(strong_iteration(A_298)),multiplication(zero,C_10)) = multiplication(strong_iteration(one),C_10) ),
inference(superposition,[status(thm),theory(equality)],[c_17909,c_10]) ).
tff(c_18017,plain,
! [C_10] : ( multiplication(strong_iteration(one),C_10) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_17726,c_20,c_17978]) ).
tff(c_40,plain,
multiplication(strong_iteration(one),'#skF_1') != strong_iteration(one),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_18299,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18017,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE141+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % 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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 02:44:02 EDT 2025
% 0.14/0.34 % CPUTime :
% 13.13/4.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.13/4.24
% 13.13/4.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------