%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD067-4 : 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 : n013.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 4.94s 2.74s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > u > 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(u,type,
u: $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_255,axiom,
~ less_or_equal(additive_identity,u),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_252,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_253,axiom,
sum(b,additive_inverse(a),u),
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_64,plain,
~ less_or_equal(additive_identity,u),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_60,plain,
less_or_equal(a,b),
inference(cnfTransformation,[status(thm)],[f_252]) ).
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_79,plain,
! [X_86,Y_87,Z_88] :
( ~ sum(X_86,Y_87,Z_88)
| sum(Y_87,X_86,Z_88) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_86,plain,
! [X_14] :
( sum(X_14,additive_inverse(X_14),additive_identity)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_79]) ).
tff(c_62,plain,
sum(b,additive_inverse(a),u),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_226,plain,
! [X_119,V_122,U_118,Y_121,Z_120] :
( ~ sum(Y_121,Z_120,V_122)
| ~ sum(X_119,Z_120,U_118)
| ~ less_or_equal(X_119,Y_121)
| less_or_equal(U_118,V_122) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_257,plain,
! [X_123,U_124] :
( ~ sum(X_123,additive_inverse(a),U_124)
| ~ less_or_equal(X_123,b)
| less_or_equal(U_124,u) ),
inference(resolution,[status(thm)],[c_62,c_226]) ).
tff(c_273,plain,
( ~ less_or_equal(a,b)
| less_or_equal(additive_identity,u)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_86,c_257]) ).
tff(c_290,plain,
less_or_equal(additive_identity,u),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_60,c_273]) ).
tff(c_292,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : FLD067-4 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.09 % 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
% 0.09/0.28 % Computer : n013.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 7 18:57:32 EDT 2025
% 0.09/0.29 % CPUTime :
% 4.94/2.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.94/2.75
% 4.94/2.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------