%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE083+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 : n009.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 5.63s 2.69s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > codomain > coantidomain > antidomain > zero > one > #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_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_67,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_119,axiom,
! [X0] : ( domain(X0) = antidomain(antidomain(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
tff(f_117,axiom,
! [X0] : ( addition(antidomain(antidomain(X0)),antidomain(X0)) = one ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
tff(f_58,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
tff(f_113,axiom,
! [X0] : ( multiplication(antidomain(X0),X0) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
tff(f_72,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(f_133,negated_conjecture,
~ ! [X0] : ( X0 = multiplication(domain(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_34,plain,
! [X0_27] : ( antidomain(antidomain(X0_27)) = domain(X0_27) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_32,plain,
! [X0_26] : ( addition(antidomain(antidomain(X0_26)),antidomain(X0_26)) = one ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_47,plain,
! [X0_26] : ( addition(domain(X0_26),antidomain(X0_26)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_32]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_28,plain,
! [X0_23] : ( multiplication(antidomain(X0_23),X0_23) = zero ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_754,plain,
! [A_62,C_63,B_64] : ( addition(multiplication(A_62,C_63),multiplication(B_64,C_63)) = multiplication(addition(A_62,B_64),C_63) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_791,plain,
! [A_62,X0_23] : ( multiplication(addition(A_62,antidomain(X0_23)),X0_23) = addition(multiplication(A_62,X0_23),zero) ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_754]) ).
tff(c_3401,plain,
! [A_110,X0_111] : ( multiplication(addition(A_110,antidomain(X0_111)),X0_111) = multiplication(A_110,X0_111) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_791]) ).
tff(c_3471,plain,
! [X0_26] : ( multiplication(domain(X0_26),X0_26) = multiplication(one,X0_26) ),
inference(superposition,[status(thm),theory(equality)],[c_47,c_3401]) ).
tff(c_3515,plain,
! [X0_26] : ( multiplication(domain(X0_26),X0_26) = X0_26 ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_3471]) ).
tff(c_44,plain,
multiplication(domain('#skF_1'),'#skF_1') != '#skF_1',
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_3523,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3515,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : KLE083+1 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.09 % 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
% 0.09/0.30 % Computer : n009.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Apr 8 02:36:26 EDT 2025
% 0.09/0.30 % CPUTime :
% 5.63/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.63/2.70
% 5.63/2.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------