%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE137+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 : n019.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 07:04:50 PM UTC 2025
% Result : Theorem 10.90s 3.67s
% Output : CNFRefutation 11.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 4 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 32 ( 32 !; 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_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_105,negated_conjecture,
~ ! [X0] : leq(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_63]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_371,plain,
! [A_52,B_53,C_54] : ( addition(addition(A_52,B_53),C_54) = addition(A_52,addition(B_53,C_54)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_448,plain,
! [A_7,C_54] : ( addition(A_7,addition(A_7,C_54)) = addition(A_7,C_54) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_371]) ).
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_1264,plain,
! [C_80,A_81,B_82] :
( leq(C_80,multiplication(strong_iteration(A_81),B_82))
| ~ leq(C_80,addition(multiplication(A_81,C_80),B_82)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_11851,plain,
! [A_203,B_204] :
( leq(A_203,multiplication(strong_iteration(one),B_204))
| ~ leq(A_203,addition(A_203,B_204)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1264]) ).
tff(c_11952,plain,
! [A_33,B_204] :
( leq(A_33,multiplication(strong_iteration(one),B_204))
| ( addition(A_33,addition(A_33,B_204)) != addition(A_33,B_204) ) ),
inference(resolution,[status(thm)],[c_38,c_11851]) ).
tff(c_11987,plain,
! [A_205,B_206] : leq(A_205,multiplication(strong_iteration(one),B_206)),
inference(demodulation,[status(thm),theory(equality)],[c_448,c_11952]) ).
tff(c_12022,plain,
! [A_205] : leq(A_205,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_11987]) ).
tff(c_40,plain,
~ leq('#skF_1',strong_iteration(one)),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_12038,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12022,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE137+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % 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
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 02:43:32 EDT 2025
% 0.12/0.33 % CPUTime :
% 10.90/3.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.90/3.68
% 10.90/3.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------