%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE146+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 : n013.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 07:04:52 PM UTC 2025
% Result : Theorem 3.74s 2.01s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 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 : 24 ( 24 !; 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_89,axiom,
! [A] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
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_105,negated_conjecture,
~ ! [X0] : leq(one,strong_iteration(X0)),
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_269,plain,
! [A_49] : ( addition(multiplication(A_49,strong_iteration(A_49)),one) = strong_iteration(A_49) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_284,plain,
! [A_49] : ( addition(one,multiplication(A_49,strong_iteration(A_49))) = strong_iteration(A_49) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_269]) ).
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_463,plain,
! [A_55,C_56] : ( addition(A_55,addition(A_55,C_56)) = addition(A_55,C_56) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_371]) ).
tff(c_496,plain,
! [A_49] : ( addition(one,multiplication(A_49,strong_iteration(A_49))) = addition(one,strong_iteration(A_49)) ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_463]) ).
tff(c_546,plain,
! [A_49] : ( addition(one,strong_iteration(A_49)) = strong_iteration(A_49) ),
inference(demodulation,[status(thm),theory(equality)],[c_284,c_496]) ).
tff(c_209,plain,
! [A_43,B_44] :
( leq(A_43,B_44)
| ( addition(A_43,B_44) != B_44 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_40,plain,
~ leq(one,strong_iteration('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_213,plain,
addition(one,strong_iteration('#skF_1')) != strong_iteration('#skF_1'),
inference(resolution,[status(thm)],[c_209,c_40]) ).
tff(c_561,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_546,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE146+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 02:44:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.74/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.74/2.01
% 3.74/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------