%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE055+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 : n022.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 07:04:41 PM UTC 2025
% Result : Theorem 9.68s 3.36s
% Output : CNFRefutation 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > zero > one > #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_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_127,negated_conjecture,
~ ! [X0] :
( ( addition(X0,one) = one )
=> ( addition(X0,domain(X0)) = domain(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(f_117,axiom,
! [X0] : ( addition(domain(X0),one) = one ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
tff(f_68,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_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(f_113,axiom,
! [X0] : ( addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
tff(c_38,plain,
addition('#skF_1',domain('#skF_1')) != domain('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_32,plain,
! [X0_26] : ( addition(domain(X0_26),one) = one ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_1667,plain,
! [A_75,B_76,C_77] : ( addition(multiplication(A_75,B_76),multiplication(A_75,C_77)) = multiplication(A_75,addition(B_76,C_77)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_7929,plain,
! [A_121,B_122] : ( multiplication(A_121,addition(B_122,one)) = addition(multiplication(A_121,B_122),A_121) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1667]) ).
tff(c_8117,plain,
! [A_121,X0_26] : ( addition(multiplication(A_121,domain(X0_26)),A_121) = multiplication(A_121,one) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_7929]) ).
tff(c_8167,plain,
! [A_121,X0_26] : ( addition(multiplication(A_121,domain(X0_26)),A_121) = A_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_8117]) ).
tff(c_1221,plain,
! [A_66,C_67,B_68] : ( addition(multiplication(A_66,C_67),multiplication(B_68,C_67)) = multiplication(addition(A_66,B_68),C_67) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_11279,plain,
! [A_142,A_143] : ( multiplication(addition(A_142,one),A_143) = addition(multiplication(A_142,A_143),A_143) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1221]) ).
tff(c_11428,plain,
! [X0_26,A_143] : ( addition(multiplication(multiplication(one,domain(X0_26)),A_143),A_143) = multiplication(one,A_143) ),
inference(superposition,[status(thm),theory(equality)],[c_8167,c_11279]) ).
tff(c_11565,plain,
! [A_143,X0_26] : ( addition(A_143,multiplication(domain(X0_26),A_143)) = A_143 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14,c_14,c_11428]) ).
tff(c_28,plain,
! [X0_23] : ( addition(X0_23,multiplication(domain(X0_23),X0_23)) = multiplication(domain(X0_23),X0_23) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_12747,plain,
! [X0_151] : ( multiplication(domain(X0_151),X0_151) = X0_151 ),
inference(demodulation,[status(thm),theory(equality)],[c_11565,c_28]) ).
tff(c_40,plain,
addition('#skF_1',one) = one,
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_8138,plain,
! [A_121] : ( addition(multiplication(A_121,'#skF_1'),A_121) = multiplication(A_121,one) ),
inference(superposition,[status(thm),theory(equality)],[c_40,c_7929]) ).
tff(c_8173,plain,
! [A_121] : ( addition(multiplication(A_121,'#skF_1'),A_121) = A_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_8138]) ).
tff(c_12786,plain,
addition('#skF_1',domain('#skF_1')) = domain('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_12747,c_8173]) ).
tff(c_12882,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_12786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : KLE055+1 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.13 % 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
% 0.12/0.34 % Computer : n022.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 02:34:51 EDT 2025
% 0.12/0.34 % CPUTime :
% 9.68/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.68/3.36
% 9.68/3.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------