%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD019-3 : 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 : n012.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 06:10:40 PM UTC 2025
% Result : Unsatisfiable 5.09s 2.18s
% Output : CNFRefutation 5.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 42 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 51 ( 51 !; 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,
~ sum(additive_identity,a,additive_identity),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
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_250,axiom,
sum(additive_identity,additive_inverse(a),additive_identity),
file(unknown,unknown) ).
tff(f_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ 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(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(c_58,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
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_72,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_72]) ).
tff(c_56,plain,
sum(additive_identity,additive_inverse(a),additive_identity),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_81,plain,
sum(additive_inverse(a),additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_56,c_72]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_214,plain,
! [V_123,Z_121,Y_122,U_119,X_120] :
( ~ sum(Y_122,Z_121,V_123)
| ~ sum(X_120,Z_121,U_119)
| ~ less_or_equal(X_120,Y_122)
| less_or_equal(U_119,V_123) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_245,plain,
! [X_124,U_125] :
( ~ sum(X_124,additive_inverse(a),U_125)
| ~ less_or_equal(X_124,additive_identity)
| less_or_equal(U_125,additive_identity) ),
inference(resolution,[status(thm)],[c_56,c_214]) ).
tff(c_280,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_inverse(a),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_6,c_245]) ).
tff(c_282,plain,
~ defined(additive_inverse(a)),
inference(splitLeft,[status(thm)],[c_280]) ).
tff(c_285,plain,
~ defined(a),
inference(resolution,[status(thm)],[c_30,c_282]) ).
tff(c_289,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_54,c_285]) ).
tff(c_291,plain,
defined(additive_inverse(a)),
inference(splitRight,[status(thm)],[c_280]) ).
tff(c_513,plain,
! [U_153,Z_150,W_155,V_152,X_154,Y_151] :
( ~ sum(U_153,Z_150,W_155)
| ~ sum(Y_151,Z_150,V_152)
| ~ sum(X_154,Y_151,U_153)
| sum(X_154,V_152,W_155) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1526,plain,
! [Y_201,V_202,X_203] :
( ~ sum(Y_201,additive_inverse(a),V_202)
| ~ sum(X_203,Y_201,additive_identity)
| sum(X_203,V_202,additive_identity) ),
inference(resolution,[status(thm)],[c_56,c_513]) ).
tff(c_1549,plain,
! [X_203] :
( ~ sum(X_203,additive_identity,additive_identity)
| sum(X_203,additive_inverse(a),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[c_6,c_1526]) ).
tff(c_1622,plain,
! [X_206] :
( ~ sum(X_206,additive_identity,additive_identity)
| sum(X_206,additive_inverse(a),additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_291,c_1549]) ).
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_1659,plain,
! [X_207] :
( sum(additive_inverse(a),X_207,additive_identity)
| ~ sum(X_207,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_1622,c_10]) ).
tff(c_543,plain,
! [Y_151,V_152,X_154] :
( ~ sum(Y_151,additive_inverse(a),V_152)
| ~ sum(X_154,Y_151,additive_identity)
| sum(X_154,V_152,additive_identity) ),
inference(resolution,[status(thm)],[c_56,c_513]) ).
tff(c_1665,plain,
! [X_154] :
( ~ sum(X_154,additive_inverse(a),additive_identity)
| sum(X_154,additive_identity,additive_identity)
| ~ sum(additive_inverse(a),additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_1659,c_543]) ).
tff(c_1705,plain,
! [X_208] :
( ~ sum(X_208,additive_inverse(a),additive_identity)
| sum(X_208,additive_identity,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_81,c_1665]) ).
tff(c_1727,plain,
( sum(a,additive_identity,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_79,c_1705]) ).
tff(c_1747,plain,
sum(a,additive_identity,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_1727]) ).
tff(c_1767,plain,
sum(additive_identity,a,additive_identity),
inference(resolution,[status(thm)],[c_1747,c_10]) ).
tff(c_1780,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_1767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : FLD019-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.10/0.13 % 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 : n012.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 18:41:45 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.09/2.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.09/2.18
% 5.09/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------