%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE070+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 : n023.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 07:04:43 PM UTC 2025
% Result : Theorem 8.26s 2.94s
% Output : CNFRefutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 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; 4 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > zero > one > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(domain,type,
domain: $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(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/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_65,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(f_67,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_119,axiom,
! [X0] : ( addition(domain(X0),one) = one ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
tff(f_72,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(f_70,axiom,
! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
tff(f_127,negated_conjecture,
~ ! [X0,X1] : ( addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(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_54]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_32,plain,
! [X0_26] : ( addition(domain(X0_26),one) = one ),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_1244,plain,
! [A_67,C_68,B_69] : ( addition(multiplication(A_67,C_68),multiplication(B_69,C_68)) = multiplication(addition(A_67,B_69),C_68) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_1844,plain,
! [A_78,A_79] : ( multiplication(addition(A_78,one),A_79) = addition(multiplication(A_78,A_79),A_79) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1244]) ).
tff(c_1952,plain,
! [X0_26,A_79] : ( addition(multiplication(domain(X0_26),A_79),A_79) = multiplication(one,A_79) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_1844]) ).
tff(c_1989,plain,
! [X0_26,A_79] : ( addition(multiplication(domain(X0_26),A_79),A_79) = A_79 ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_1952]) ).
tff(c_1442,plain,
! [A_71,B_72,C_73] : ( addition(multiplication(A_71,B_72),multiplication(A_71,C_73)) = multiplication(A_71,addition(B_72,C_73)) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_9729,plain,
! [A_145,B_146] : ( multiplication(A_145,addition(B_146,one)) = addition(multiplication(A_145,B_146),A_145) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1442]) ).
tff(c_9916,plain,
! [A_145,X0_26] : ( addition(multiplication(A_145,multiplication(domain(X0_26),one)),A_145) = multiplication(A_145,one) ),
inference(superposition,[status(thm),theory(equality)],[c_1989,c_9729]) ).
tff(c_10011,plain,
! [A_145,X0_26] : ( addition(A_145,multiplication(A_145,domain(X0_26))) = A_145 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_12,c_12,c_9916]) ).
tff(c_38,plain,
addition(domain('#skF_1'),multiplication(domain('#skF_1'),domain('#skF_2'))) != domain('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_10308,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10011,c_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : KLE070+1 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.10 % 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
% 0.09/0.29 % Computer : n023.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 8 02:35:54 EDT 2025
% 0.09/0.29 % CPUTime :
% 8.26/2.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.26/2.95
% 8.26/2.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------