%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD059-4 : 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 : n019.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 4.28s 1.94s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 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 : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > u > 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(u,type,
u: $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_251,axiom,
less_or_equal(additive_identity,a),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_252,axiom,
sum(a,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(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_254,axiom,
~ less_or_equal(additive_identity,u),
file(unknown,unknown) ).
tff(c_58,plain,
less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_60,plain,
sum(a,a,u),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_421,plain,
! [Z_130,Y_131,U_128,V_132,X_129] :
( ~ sum(Y_131,Z_130,V_132)
| ~ sum(X_129,Z_130,U_128)
| ~ less_or_equal(X_129,Y_131)
| less_or_equal(U_128,V_132) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_449,plain,
! [X_133,U_134] :
( ~ sum(X_133,a,U_134)
| ~ less_or_equal(X_133,a)
| less_or_equal(U_134,u) ),
inference(resolution,[status(thm)],[c_60,c_421]) ).
tff(c_469,plain,
( ~ less_or_equal(additive_identity,a)
| less_or_equal(a,u)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_6,c_449]) ).
tff(c_488,plain,
less_or_equal(a,u),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_58,c_469]) ).
tff(c_44,plain,
! [Y_63,Z_62,X_61] :
( ~ less_or_equal(Y_63,Z_62)
| ~ less_or_equal(X_61,Y_63)
| less_or_equal(X_61,Z_62) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_591,plain,
! [X_141] :
( ~ less_or_equal(X_141,a)
| less_or_equal(X_141,u) ),
inference(resolution,[status(thm)],[c_488,c_44]) ).
tff(c_62,plain,
~ less_or_equal(additive_identity,u),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_600,plain,
~ less_or_equal(additive_identity,a),
inference(resolution,[status(thm)],[c_591,c_62]) ).
tff(c_612,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : FLD059-4 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.10 % 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
% 0.09/0.29 % Computer : n019.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 7 18:55:02 EDT 2025
% 0.09/0.29 % CPUTime :
% 4.28/1.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/1.94
% 4.28/1.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------