%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE002+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/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 : n027.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 07:04:32 PM UTC 2025
% Result : Theorem 4.29s 2.03s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 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; 5 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > zero > one > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(multiplication,type,
multiplication: ( $i * $i ) > $i ).
tff(addition,type,
addition: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $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_86,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(f_79,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
tff(f_69,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
tff(c_30,plain,
leq('#skF_1','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_226,plain,
! [A_32,B_33] :
( ( addition(A_32,B_33) = B_33 )
| ~ leq(A_32,B_33) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_230,plain,
addition('#skF_1','#skF_2') = '#skF_2',
inference(resolution,[status(thm)],[c_30,c_226]) ).
tff(c_18,plain,
! [A_16,C_18,B_17] : ( addition(multiplication(A_16,C_18),multiplication(B_17,C_18)) = multiplication(addition(A_16,B_17),C_18) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_235,plain,
! [A_34,B_35] :
( leq(A_34,B_35)
| ( addition(A_34,B_35) != B_35 ) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_28,plain,
~ leq(multiplication('#skF_1','#skF_3'),multiplication('#skF_2','#skF_3')),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_243,plain,
addition(multiplication('#skF_1','#skF_3'),multiplication('#skF_2','#skF_3')) != multiplication('#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_235,c_28]) ).
tff(c_1842,plain,
multiplication(addition('#skF_1','#skF_2'),'#skF_3') != multiplication('#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_243]) ).
tff(c_1845,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_230,c_1842]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : KLE002+1 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.12 % 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
% 0.12/0.33 % Computer : n027.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 02:25:36 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.29/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.29/2.03
% 4.29/2.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------