%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE085+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 : n017.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 4.30s 2.01s
% Output : CNFRefutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 26 ( 26 !; 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_54,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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_60,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
tff(f_56,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
tff(f_133,negated_conjecture,
~ ! [X0] : ( addition(domain(X0),one) = one ),
file('/export/starexec/sandbox2/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_54]) ).
tff(c_34,plain,
! [X0_27] : ( antidomain(antidomain(X0_27)) = domain(X0_27) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_195,plain,
! [X0_41] : ( antidomain(antidomain(X0_41)) = domain(X0_41) ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_207,plain,
! [X0_27] : ( domain(antidomain(X0_27)) = antidomain(domain(X0_27)) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_195]) ).
tff(c_32,plain,
! [X0_26] : ( addition(antidomain(antidomain(X0_26)),antidomain(X0_26)) = one ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_419,plain,
! [X0_47] : ( addition(domain(X0_47),antidomain(X0_47)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_32]) ).
tff(c_441,plain,
! [X0_27] : ( addition(domain(antidomain(X0_27)),domain(X0_27)) = one ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_419]) ).
tff(c_966,plain,
! [X0_27] : ( addition(domain(X0_27),antidomain(domain(X0_27))) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_207,c_441]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_709,plain,
! [A_60,B_61,C_62] : ( addition(addition(A_60,B_61),C_62) = addition(A_60,addition(B_61,C_62)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1381,plain,
! [A_78,C_79] : ( addition(A_78,addition(A_78,C_79)) = addition(A_78,C_79) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_709]) ).
tff(c_1413,plain,
! [X0_27] : ( addition(domain(X0_27),antidomain(domain(X0_27))) = addition(domain(X0_27),one) ),
inference(superposition,[status(thm),theory(equality)],[c_966,c_1381]) ).
tff(c_1467,plain,
! [X0_27] : ( addition(one,domain(X0_27)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_966,c_2,c_1413]) ).
tff(c_44,plain,
addition(domain('#skF_1'),one) != one,
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_49,plain,
addition(one,domain('#skF_1')) != one,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_44]) ).
tff(c_1482,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1467,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE085+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/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
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 02:36:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.30/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.30/2.02
% 4.30/2.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------