%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD059-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 : n020.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 06:10:51 PM UTC 2025
% Result : Unsatisfiable 114.29s 99.33s
% Output : CNFRefutation 114.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 135 ( 69 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sum,type,
sum: ( $i * $i * $i ) > $o ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
tff(product,type,
product: ( $i * $i * $i ) > $o ).
tff(additive_identity,type,
additive_identity: $i ).
tff(multiplicative_identity,type,
multiplicative_identity: $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(additive_inverse,type,
additive_inverse: $i > $i ).
tff(defined,type,
defined: $i > $o ).
tff(multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_250,axiom,
less_or_equal(additive_identity,a),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_188,axiom,
! [X,Y] :
( sum(X,Y,add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_233,axiom,
! [U,Z,X,Y,V] :
( less_or_equal(U,V)
| ~ less_or_equal(X,Y)
| ~ sum(X,Z,U)
| ~ sum(Y,Z,V) ),
file(unknown,unknown) ).
tff(f_158,axiom,
! [X,Y] :
( defined(add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_222,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_212,axiom,
! [X,Z,Y] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) ),
file(unknown,unknown) ).
tff(f_204,axiom,
! [X,Y] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_252,axiom,
~ less_or_equal(additive_identity,add(a,a)),
file(unknown,unknown) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_56,plain,
less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_107,plain,
! [Y_100,X_101] :
( ~ defined(Y_100)
| ~ defined(X_101)
| sum(X_101,Y_100,add(X_101,Y_100)) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_10,plain,
! [X_16,Y_15,Z_17] :
( ~ sum(X_16,Y_15,Z_17)
| sum(Y_15,X_16,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_110,plain,
! [Y_100,X_101] :
( sum(Y_100,X_101,add(X_101,Y_100))
| ~ defined(Y_100)
| ~ defined(X_101) ),
inference(resolution,[status(thm)],[c_107,c_10]) ).
tff(c_302,plain,
! [X_125,U_124,Z_126,Y_127,V_128] :
( ~ sum(Y_127,Z_126,V_128)
| ~ sum(X_125,Z_126,U_124)
| ~ less_or_equal(X_125,Y_127)
| less_or_equal(U_124,V_128) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_76753,plain,
! [X_844,X_845,U_846,Y_847] :
( ~ sum(X_844,X_845,U_846)
| ~ less_or_equal(X_844,Y_847)
| less_or_equal(U_846,add(X_845,Y_847))
| ~ defined(Y_847)
| ~ defined(X_845) ),
inference(resolution,[status(thm)],[c_110,c_302]) ).
tff(c_77566,plain,
! [Y_847,X_13] :
( ~ less_or_equal(additive_identity,Y_847)
| less_or_equal(X_13,add(X_13,Y_847))
| ~ defined(Y_847)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_76753]) ).
tff(c_26,plain,
! [Y_50,X_49] :
( ~ defined(Y_50)
| ~ defined(X_49)
| defined(add(X_49,Y_50)) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_125,plain,
! [Y_102,X_103] :
( ~ defined(Y_102)
| ~ defined(X_103)
| less_or_equal(Y_102,X_103)
| less_or_equal(X_103,Y_102) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_88,plain,
! [Y_91,Z_92,X_93] :
( ~ less_or_equal(Y_91,Z_92)
| ~ less_or_equal(X_93,Y_91)
| less_or_equal(X_93,Z_92) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_91,plain,
! [X_93] :
( ~ less_or_equal(X_93,additive_identity)
| less_or_equal(X_93,a) ),
inference(resolution,[status(thm)],[c_56,c_88]) ).
tff(c_138,plain,
! [X_103] :
( less_or_equal(X_103,a)
| ~ defined(additive_identity)
| ~ defined(X_103)
| less_or_equal(additive_identity,X_103) ),
inference(resolution,[status(thm)],[c_125,c_91]) ).
tff(c_148,plain,
! [X_103] :
( less_or_equal(X_103,a)
| ~ defined(X_103)
| less_or_equal(additive_identity,X_103) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_138]) ).
tff(c_98,plain,
! [Y_98,X_99] :
( ~ less_or_equal(Y_98,X_99)
| ~ less_or_equal(X_99,Y_98)
| sum(additive_identity,X_99,Y_98) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_104,plain,
! [X_99,Y_98] :
( sum(X_99,additive_identity,Y_98)
| ~ less_or_equal(Y_98,X_99)
| ~ less_or_equal(X_99,Y_98) ),
inference(resolution,[status(thm)],[c_98,c_10]) ).
tff(c_74202,plain,
! [X_828,U_829,X_830,Y_831] :
( ~ sum(X_828,additive_identity,U_829)
| ~ less_or_equal(X_828,X_830)
| less_or_equal(U_829,Y_831)
| ~ less_or_equal(Y_831,X_830)
| ~ less_or_equal(X_830,Y_831) ),
inference(resolution,[status(thm)],[c_104,c_302]) ).
tff(c_74445,plain,
! [X_830,Y_831] :
( ~ less_or_equal(additive_identity,X_830)
| less_or_equal(additive_identity,Y_831)
| ~ less_or_equal(Y_831,X_830)
| ~ less_or_equal(X_830,Y_831)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_6,c_74202]) ).
tff(c_242538,plain,
! [X_1503,Y_1504] :
( ~ less_or_equal(additive_identity,X_1503)
| less_or_equal(additive_identity,Y_1504)
| ~ less_or_equal(Y_1504,X_1503)
| ~ less_or_equal(X_1503,Y_1504) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_74445]) ).
tff(c_250793,plain,
! [Y_1512] :
( less_or_equal(additive_identity,Y_1512)
| ~ less_or_equal(Y_1512,a)
| ~ less_or_equal(a,Y_1512) ),
inference(resolution,[status(thm)],[c_56,c_242538]) ).
tff(c_251432,plain,
! [X_1514] :
( ~ less_or_equal(a,X_1514)
| ~ defined(X_1514)
| less_or_equal(additive_identity,X_1514) ),
inference(resolution,[status(thm)],[c_148,c_250793]) ).
tff(c_58,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_252044,plain,
( ~ less_or_equal(a,add(a,a))
| ~ defined(add(a,a)) ),
inference(resolution,[status(thm)],[c_251432,c_58]) ).
tff(c_252045,plain,
~ defined(add(a,a)),
inference(splitLeft,[status(thm)],[c_252044]) ).
tff(c_252048,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_26,c_252045]) ).
tff(c_252052,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_252048]) ).
tff(c_252053,plain,
~ less_or_equal(a,add(a,a)),
inference(splitRight,[status(thm)],[c_252044]) ).
tff(c_252072,plain,
( ~ less_or_equal(additive_identity,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_77566,c_252053]) ).
tff(c_252087,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_56,c_252072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : FLD059-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.05/0.12 % 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
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 7 18:54:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 114.29/99.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 114.29/99.34
% 114.29/99.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------