%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE009+3 : 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 07:04:33 PM UTC 2025
% Result : Theorem 4.24s 2.14s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 35 ~; 18 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > complement > test > multiplication > addition > #nlpp > c > zero > one > #skF_1 > #skF_2 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(c,type,
c: $i > $i ).
tff(multiplication,type,
multiplication: ( $i * $i ) > $i ).
tff(addition,type,
addition: ( $i * $i ) > $i ).
tff(complement,type,
complement: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(test,type,
test: $i > $o ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_57,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
tff(f_79,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
tff(f_142,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_51,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_126,axiom,
! [X0,X1] :
( test(X0)
=> ( ( c(X0) = X1 )
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
tff(f_120,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( ( multiplication(X0,X1) = zero )
& ( multiplication(X1,X0) = zero )
& ( addition(X0,X1) = one ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
tff(f_64,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_62,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(f_69,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_67,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_53,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_26,plain,
! [A_21,B_22] :
( leq(A_21,B_22)
| ( addition(A_21,B_22) != B_22 ) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_50,plain,
test('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_42,plain,
! [X0_29] :
( complement(X0_29,c(X0_29))
| ~ test(X0_29) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_519,plain,
! [X0_73,X1_74] :
( ( addition(X0_73,X1_74) = one )
| ~ complement(X1_74,X0_73) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_525,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_519]) ).
tff(c_528,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_525]) ).
tff(c_48,plain,
test('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_807,plain,
! [X0_87] :
( ( addition(X0_87,c(X0_87)) = one )
| ~ test(X0_87) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_525]) ).
tff(c_281,plain,
! [X0_51,X1_52] :
( ( addition(X0_51,X1_52) = one )
| ~ complement(X1_52,X0_51) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_287,plain,
! [X0_29] :
( ( addition(c(X0_29),X0_29) = one )
| ~ test(X0_29) ),
inference(resolution,[status(thm)],[c_42,c_281]) ).
tff(c_290,plain,
! [X0_29] :
( ( addition(X0_29,c(X0_29)) = one )
| ~ test(X0_29) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_287]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_311,plain,
! [X0_59] :
( ( addition(X0_59,c(X0_59)) = one )
| ~ test(X0_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_287]) ).
tff(c_18,plain,
! [A_16,C_18,B_17] : ( addition(multiplication(A_16,C_18),multiplication(B_17,C_18)) = multiplication(addition(A_16,B_17),C_18) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_16,plain,
! [A_13,B_14,C_15] : ( addition(multiplication(A_13,B_14),multiplication(A_13,C_15)) = multiplication(A_13,addition(B_14,C_15)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4,plain,
! [A_5,B_4,C_3] : ( addition(addition(A_5,B_4),C_3) = addition(A_5,addition(B_4,C_3)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_46,plain,
( ~ leq(addition(addition(addition(multiplication('#skF_2','#skF_3'),multiplication('#skF_2',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))),one)
| ~ leq(one,addition(addition(addition(multiplication('#skF_2','#skF_3'),multiplication('#skF_2',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3')))) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_51,plain,
( ~ leq(addition(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3'))),one)
| ~ leq(one,addition(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),multiplication(c('#skF_2'),'#skF_3')),multiplication(c('#skF_2'),c('#skF_3')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_46]) ).
tff(c_52,plain,
( ~ leq(addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),addition(multiplication(c('#skF_2'),'#skF_3'),multiplication(c('#skF_2'),c('#skF_3')))),one)
| ~ leq(one,addition(multiplication('#skF_2',addition('#skF_3',c('#skF_3'))),addition(multiplication(c('#skF_2'),'#skF_3'),multiplication(c('#skF_2'),c('#skF_3'))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_51]) ).
tff(c_53,plain,
( ~ leq(multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3'))),one)
| ~ leq(one,multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_16,c_18,c_16,c_52]) ).
tff(c_153,plain,
~ leq(one,multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3')))),
inference(splitLeft,[status(thm)],[c_53]) ).
tff(c_320,plain,
( ~ leq(one,multiplication(addition('#skF_2',c('#skF_2')),one))
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_311,c_153]) ).
tff(c_336,plain,
~ leq(one,addition('#skF_2',c('#skF_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_12,c_320]) ).
tff(c_371,plain,
( ~ leq(one,one)
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_290,c_336]) ).
tff(c_376,plain,
~ leq(one,one),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_371]) ).
tff(c_380,plain,
addition(one,one) != one,
inference(resolution,[status(thm)],[c_26,c_376]) ).
tff(c_384,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_380]) ).
tff(c_385,plain,
~ leq(multiplication(addition('#skF_2',c('#skF_2')),addition('#skF_3',c('#skF_3'))),one),
inference(splitRight,[status(thm)],[c_53]) ).
tff(c_819,plain,
( ~ leq(multiplication(one,addition('#skF_3',c('#skF_3'))),one)
| ~ test('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_807,c_385]) ).
tff(c_852,plain,
~ leq(addition('#skF_3',c('#skF_3')),one),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_14,c_819]) ).
tff(c_866,plain,
( ~ leq(one,one)
| ~ test('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_528,c_852]) ).
tff(c_871,plain,
~ leq(one,one),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_866]) ).
tff(c_876,plain,
addition(one,one) != one,
inference(resolution,[status(thm)],[c_26,c_871]) ).
tff(c_880,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE009+3 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.14 % 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
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 02:26:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.24/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.40/2.15
% 4.40/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------