%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD067-3 : 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/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 : n016.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 24.67s 13.53s
% Output : CNFRefutation 24.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 61 ( 33 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > b > 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(b,type,
b: $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_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_251,axiom,
less_or_equal(a,b),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_188,axiom,
! [X,Y] :
( sum(X,Y,add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
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_253,axiom,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
file(unknown,unknown) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_58,plain,
less_or_equal(a,b),
inference(cnfTransformation,[status(thm)],[f_251]) ).
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_74,plain,
! [X_84,Y_85,Z_86] :
( ~ sum(X_84,Y_85,Z_86)
| sum(Y_85,X_84,Z_86) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_79,plain,
! [X_14] :
( sum(X_14,additive_inverse(X_14),additive_identity)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_74]) ).
tff(c_38,plain,
! [Y_56,X_55] :
( ~ defined(Y_56)
| ~ defined(X_55)
| sum(X_55,Y_56,add(X_55,Y_56)) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_277,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_4025,plain,
! [X_267,Y_268,U_269,X_270] :
( ~ sum(X_267,Y_268,U_269)
| ~ less_or_equal(X_267,X_270)
| less_or_equal(U_269,add(X_270,Y_268))
| ~ defined(Y_268)
| ~ defined(X_270) ),
inference(resolution,[status(thm)],[c_38,c_277]) ).
tff(c_66769,plain,
! [X_776,X_777] :
( ~ less_or_equal(X_776,X_777)
| less_or_equal(additive_identity,add(X_777,additive_inverse(X_776)))
| ~ defined(additive_inverse(X_776))
| ~ defined(X_777)
| ~ defined(X_776) ),
inference(resolution,[status(thm)],[c_79,c_4025]) ).
tff(c_60,plain,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_66799,plain,
( ~ less_or_equal(a,b)
| ~ defined(additive_inverse(a))
| ~ defined(b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_66769,c_60]) ).
tff(c_66821,plain,
~ defined(additive_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_56,c_58,c_66799]) ).
tff(c_66824,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_30,c_66821]) ).
tff(c_66828,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_66824]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD067-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 18:57:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 24.67/13.53 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.67/13.53
% 24.67/13.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------