%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE089+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 : 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 : Wed Apr 9 07:04:45 PM UTC 2025
% Result : Theorem 5.74s 2.38s
% Output : CNFRefutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 1 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > codomain > coantidomain > antidomain > zero > one > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(coantidomain,type,
coantidomain: $i > $i ).
tff(domain,type,
domain: $i > $i ).
tff(antidomain,type,
antidomain: $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(codomain,type,
codomain: $i > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_133,negated_conjecture,
~ ! [X0,X1] :
( ( multiplication(domain(X0),X1) = zero )
<= ( addition(domain(X0),antidomain(X1)) = antidomain(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_111,axiom,
! [X0] : ( multiplication(antidomain(X0),X0) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
tff(f_70,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
tff(c_44,plain,
multiplication(domain('#skF_1'),'#skF_2') != zero,
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_28,plain,
! [X0_23] : ( multiplication(antidomain(X0_23),X0_23) = zero ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_323,plain,
! [B_44,A_45] : ( addition(B_44,A_45) = addition(A_45,B_44) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_46,plain,
addition(domain('#skF_1'),antidomain('#skF_2')) = antidomain('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_344,plain,
addition(antidomain('#skF_2'),domain('#skF_1')) = antidomain('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_323,c_46]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_357,plain,
! [A_45] : ( addition(zero,A_45) = A_45 ),
inference(superposition,[status(thm),theory(equality)],[c_323,c_6]) ).
tff(c_1095,plain,
! [A_70,C_71,B_72] : ( addition(multiplication(A_70,C_71),multiplication(B_72,C_71)) = multiplication(addition(A_70,B_72),C_71) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_1159,plain,
! [X0_23,B_72] : ( multiplication(addition(antidomain(X0_23),B_72),X0_23) = addition(zero,multiplication(B_72,X0_23)) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_1095]) ).
tff(c_3804,plain,
! [X0_110,B_111] : ( multiplication(addition(antidomain(X0_110),B_111),X0_110) = multiplication(B_111,X0_110) ),
inference(demodulation,[status(thm),theory(equality)],[c_357,c_1159]) ).
tff(c_3893,plain,
multiplication(domain('#skF_1'),'#skF_2') = multiplication(antidomain('#skF_2'),'#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_344,c_3804]) ).
tff(c_3945,plain,
multiplication(domain('#skF_1'),'#skF_2') = zero,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_3893]) ).
tff(c_3947,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_3945]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE089+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
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 8 02:36:53 EDT 2025
% 0.15/0.35 % CPUTime :
% 5.74/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.74/2.38
% 5.74/2.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------