%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD007-3 : 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 : n015.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 06:10:36 PM UTC 2025
% Result : Unsatisfiable 10.66s 3.57s
% Output : CNFRefutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 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_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
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_57,axiom,
! [W,U,Z,X,Y,V] :
( sum(X,V,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_251,axiom,
~ sum(additive_identity,additive_inverse(additive_inverse(a)),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_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_403,plain,
! [Z_142,W_147,U_145,Y_143,X_146,V_144] :
( ~ sum(U_145,Z_142,W_147)
| ~ sum(Y_143,Z_142,V_144)
| ~ sum(X_146,Y_143,U_145)
| sum(X_146,V_144,W_147) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2028,plain,
! [Y_225,X_226,V_227,X_228] :
( ~ sum(Y_225,X_226,V_227)
| ~ sum(X_228,Y_225,additive_identity)
| sum(X_228,V_227,X_226)
| ~ defined(X_226) ),
inference(resolution,[status(thm)],[c_6,c_403]) ).
tff(c_6207,plain,
! [X_321,X_322] :
( ~ sum(X_321,additive_inverse(X_322),additive_identity)
| sum(X_321,additive_identity,X_322)
| ~ defined(X_322) ),
inference(resolution,[status(thm)],[c_8,c_2028]) ).
tff(c_11085,plain,
! [X_391] :
( sum(additive_inverse(additive_inverse(X_391)),additive_identity,X_391)
| ~ defined(X_391)
| ~ defined(additive_inverse(X_391)) ),
inference(resolution,[status(thm)],[c_8,c_6207]) ).
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_12824,plain,
! [X_406] :
( sum(additive_identity,additive_inverse(additive_inverse(X_406)),X_406)
| ~ defined(X_406)
| ~ defined(additive_inverse(X_406)) ),
inference(resolution,[status(thm)],[c_11085,c_10]) ).
tff(c_56,plain,
~ sum(additive_identity,additive_inverse(additive_inverse(a)),a),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_12868,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_12824,c_56]) ).
tff(c_12896,plain,
~ defined(additive_inverse(a)),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_12868]) ).
tff(c_12899,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_30,c_12896]) ).
tff(c_12903,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_12899]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : FLD007-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.13 % 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
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Apr 7 18:38:35 EDT 2025
% 0.14/0.34 % CPUTime :
% 10.66/3.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.66/3.57
% 10.66/3.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------