%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD065-3 : 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 06:10:53 PM UTC 2025
% Result : Unsatisfiable 4.01s 1.97s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 18 ( 18 !; 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_252,axiom,
~ less_or_equal(additive_identity,a),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_250,axiom,
less_or_equal(additive_inverse(a),additive_identity),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
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(c_58,plain,
~ less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_56,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_8,plain,
! [X_14] :
( ~ defined(X_14)
| sum(additive_inverse(X_14),X_14,additive_identity) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_325,plain,
! [Y_130,U_127,Z_129,X_128,V_131] :
( ~ sum(Y_130,Z_129,V_131)
| ~ sum(X_128,Z_129,U_127)
| ~ less_or_equal(X_128,Y_130)
| less_or_equal(U_127,V_131) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_350,plain,
! [X_132,X_133,U_134] :
( ~ sum(X_132,X_133,U_134)
| ~ less_or_equal(X_132,additive_identity)
| less_or_equal(U_134,X_133)
| ~ defined(X_133) ),
inference(resolution,[status(thm)],[c_6,c_325]) ).
tff(c_387,plain,
! [X_135] :
( ~ less_or_equal(additive_inverse(X_135),additive_identity)
| less_or_equal(additive_identity,X_135)
| ~ defined(X_135) ),
inference(resolution,[status(thm)],[c_8,c_350]) ).
tff(c_403,plain,
( less_or_equal(additive_identity,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_56,c_387]) ).
tff(c_417,plain,
less_or_equal(additive_identity,a),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_403]) ).
tff(c_419,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD065-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.13 % 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 : n020.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 : Mon Apr 7 18:56:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 4.01/1.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.01/1.97
% 4.01/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------