%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD059-2 : 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 : n032.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 5.51s 2.27s
% Output : CNFRefutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 76 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ less_or_equal > equalish > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > u > multiplicative_identity > additive_identity > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a,type,
a: $i ).
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(equalish,type,
equalish: ( $i * $i ) > $o ).
tff(f_238,axiom,
less_or_equal(additive_identity,a),
file(unknown,unknown) ).
tff(f_155,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,X) ),
file(unknown,unknown) ).
tff(f_236,axiom,
defined(a),
file(unknown,unknown) ).
tff(f_181,axiom,
! [X,Z,Y] :
( less_or_equal(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ less_or_equal(X,Y) ),
file(unknown,unknown) ).
tff(f_237,axiom,
defined(u),
file(unknown,unknown) ).
tff(f_173,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_239,axiom,
equalish(add(a,a),u),
file(unknown,unknown) ).
tff(f_199,axiom,
! [X,Y] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file(unknown,unknown) ).
tff(f_231,axiom,
! [Y,Z,X] :
( less_or_equal(Y,Z)
| ~ less_or_equal(X,Z)
| ~ equalish(X,Y) ),
file(unknown,unknown) ).
tff(f_241,axiom,
~ less_or_equal(additive_identity,u),
file(unknown,unknown) ).
tff(f_126,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_163,axiom,
! [X,Z,Y] :
( less_or_equal(X,Z)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,Z) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_215,axiom,
! [X,Z,Y] :
( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file(unknown,unknown) ).
tff(f_207,axiom,
! [X,Z,Y] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file(unknown,unknown) ).
tff(c_60,plain,
less_or_equal(additive_identity,a),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_211,plain,
! [Y_79,X_80] :
( ~ less_or_equal(Y_79,X_80)
| ~ less_or_equal(X_80,Y_79)
| equalish(X_80,Y_79) ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_217,plain,
( ~ less_or_equal(a,additive_identity)
| equalish(a,additive_identity) ),
inference(resolution,[status(thm)],[c_60,c_211]) ).
tff(c_218,plain,
~ less_or_equal(a,additive_identity),
inference(splitLeft,[status(thm)],[c_217]) ).
tff(c_56,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_785,plain,
! [X_105,Y_106,Z_107] :
( ~ less_or_equal(X_105,Y_106)
| ~ defined(Z_107)
| less_or_equal(add(X_105,Z_107),add(Y_106,Z_107)) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_58,plain,
defined(u),
inference(cnfTransformation,[status(thm)],[f_237]) ).
tff(c_36,plain,
! [Y_30,X_29] :
( ~ defined(Y_30)
| ~ defined(X_29)
| less_or_equal(Y_30,X_29)
| less_or_equal(X_29,Y_30) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_329,plain,
! [Y_30] :
( ~ defined(Y_30)
| less_or_equal(Y_30,Y_30) ),
inference(factorization,[status(thm),theory(equality)],[c_36]) ).
tff(c_62,plain,
equalish(add(a,a),u),
inference(cnfTransformation,[status(thm)],[f_239]) ).
tff(c_67,plain,
! [Y_53,X_54] :
( ~ equalish(Y_53,X_54)
| equalish(X_54,Y_53) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_72,plain,
equalish(u,add(a,a)),
inference(resolution,[status(thm)],[c_62,c_67]) ).
tff(c_105,plain,
! [X_66,Y_67,Z_68] :
( ~ equalish(X_66,Y_67)
| ~ less_or_equal(X_66,Z_68)
| less_or_equal(Y_67,Z_68) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_130,plain,
! [Z_68] :
( ~ less_or_equal(u,Z_68)
| less_or_equal(add(a,a),Z_68) ),
inference(resolution,[status(thm)],[c_72,c_105]) ).
tff(c_64,plain,
~ less_or_equal(additive_identity,u),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_22,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_248,plain,
! [Y_82,X_83] :
( ~ defined(Y_82)
| ~ defined(X_83)
| less_or_equal(Y_82,X_83)
| less_or_equal(X_83,Y_82) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_139,plain,
! [Y_71,Z_72,X_73] :
( ~ less_or_equal(Y_71,Z_72)
| ~ less_or_equal(X_73,Y_71)
| less_or_equal(X_73,Z_72) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_174,plain,
! [X_77] :
( ~ less_or_equal(X_77,additive_identity)
| less_or_equal(X_77,a) ),
inference(resolution,[status(thm)],[c_60,c_139]) ).
tff(c_179,plain,
( less_or_equal(add(a,a),a)
| ~ less_or_equal(u,additive_identity) ),
inference(resolution,[status(thm)],[c_130,c_174]) ).
tff(c_233,plain,
~ less_or_equal(u,additive_identity),
inference(splitLeft,[status(thm)],[c_179]) ).
tff(c_251,plain,
( ~ defined(u)
| ~ defined(additive_identity)
| less_or_equal(additive_identity,u) ),
inference(resolution,[status(thm)],[c_248,c_233]) ).
tff(c_285,plain,
less_or_equal(additive_identity,u),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_58,c_251]) ).
tff(c_287,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_285]) ).
tff(c_289,plain,
less_or_equal(u,additive_identity),
inference(splitRight,[status(thm)],[c_179]) ).
tff(c_34,plain,
! [Y_28,Z_27,X_26] :
( ~ less_or_equal(Y_28,Z_27)
| ~ less_or_equal(X_26,Y_28)
| less_or_equal(X_26,Z_27) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_391,plain,
! [X_87] :
( ~ less_or_equal(X_87,u)
| less_or_equal(X_87,additive_identity) ),
inference(resolution,[status(thm)],[c_289,c_34]) ).
tff(c_417,plain,
( less_or_equal(add(a,a),additive_identity)
| ~ less_or_equal(u,u) ),
inference(resolution,[status(thm)],[c_130,c_391]) ).
tff(c_549,plain,
~ less_or_equal(u,u),
inference(splitLeft,[status(thm)],[c_417]) ).
tff(c_552,plain,
~ defined(u),
inference(resolution,[status(thm)],[c_329,c_549]) ).
tff(c_558,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_552]) ).
tff(c_559,plain,
less_or_equal(add(a,a),additive_identity),
inference(splitRight,[status(thm)],[c_417]) ).
tff(c_599,plain,
! [X_26] :
( ~ less_or_equal(X_26,add(a,a))
| less_or_equal(X_26,additive_identity) ),
inference(resolution,[status(thm)],[c_559,c_34]) ).
tff(c_789,plain,
! [X_105] :
( less_or_equal(add(X_105,a),additive_identity)
| ~ less_or_equal(X_105,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_785,c_599]) ).
tff(c_804,plain,
! [X_105] :
( less_or_equal(add(X_105,a),additive_identity)
| ~ less_or_equal(X_105,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_789]) ).
tff(c_4,plain,
! [X_4] :
( ~ defined(X_4)
| equalish(add(additive_identity,X_4),X_4) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_1300,plain,
! [X_139,Z_140] :
( ~ less_or_equal(add(additive_identity,X_139),Z_140)
| less_or_equal(X_139,Z_140)
| ~ defined(X_139) ),
inference(resolution,[status(thm)],[c_4,c_105]) ).
tff(c_1304,plain,
( less_or_equal(a,additive_identity)
| ~ defined(a)
| ~ less_or_equal(additive_identity,a) ),
inference(resolution,[status(thm)],[c_804,c_1300]) ).
tff(c_1343,plain,
less_or_equal(a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_56,c_1304]) ).
tff(c_1345,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_218,c_1343]) ).
tff(c_1346,plain,
equalish(a,additive_identity),
inference(splitRight,[status(thm)],[c_217]) ).
tff(c_52,plain,
! [X_50,Y_48,Z_49] :
( ~ equalish(X_50,Y_48)
| ~ less_or_equal(X_50,Z_49)
| less_or_equal(Y_48,Z_49) ),
inference(cnfTransformation,[status(thm)],[f_231]) ).
tff(c_1480,plain,
! [Z_146] :
( ~ less_or_equal(a,Z_146)
| less_or_equal(additive_identity,Z_146) ),
inference(resolution,[status(thm)],[c_1346,c_52]) ).
tff(c_1497,plain,
~ less_or_equal(a,u),
inference(resolution,[status(thm)],[c_1480,c_64]) ).
tff(c_1391,plain,
! [Y_30] :
( ~ defined(Y_30)
| less_or_equal(Y_30,Y_30) ),
inference(factorization,[status(thm),theory(equality)],[c_36]) ).
tff(c_44,plain,
! [Y_38,X_37] :
( ~ equalish(Y_38,X_37)
| equalish(X_37,Y_38) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_1356,plain,
equalish(additive_identity,a),
inference(resolution,[status(thm)],[c_1346,c_44]) ).
tff(c_1886,plain,
! [X_163,Y_164,Z_165] :
( ~ equalish(X_163,Y_164)
| ~ defined(Z_165)
| equalish(add(X_163,Z_165),add(Y_164,Z_165)) ),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_146,plain,
! [Y_74,Z_75,X_76] :
( ~ equalish(Y_74,Z_75)
| ~ equalish(X_76,Y_74)
| equalish(X_76,Z_75) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_172,plain,
! [X_76] :
( ~ equalish(X_76,add(a,a))
| equalish(X_76,u) ),
inference(resolution,[status(thm)],[c_62,c_146]) ).
tff(c_1890,plain,
! [X_163] :
( equalish(add(X_163,a),u)
| ~ equalish(X_163,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_1886,c_172]) ).
tff(c_1966,plain,
! [X_172] :
( equalish(add(X_172,a),u)
| ~ equalish(X_172,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_1890]) ).
tff(c_1975,plain,
! [X_172] :
( equalish(u,add(X_172,a))
| ~ equalish(X_172,a) ),
inference(resolution,[status(thm)],[c_1966,c_44]) ).
tff(c_2201,plain,
! [X_184,X_185] :
( ~ equalish(X_184,add(additive_identity,X_185))
| equalish(X_184,X_185)
| ~ defined(X_185) ),
inference(resolution,[status(thm)],[c_4,c_146]) ).
tff(c_2209,plain,
( equalish(u,a)
| ~ defined(a)
| ~ equalish(additive_identity,a) ),
inference(resolution,[status(thm)],[c_1975,c_2201]) ).
tff(c_2252,plain,
equalish(u,a),
inference(demodulation,[status(thm),theory(equality)],[c_1356,c_56,c_2209]) ).
tff(c_2322,plain,
! [Z_186] :
( ~ less_or_equal(u,Z_186)
| less_or_equal(a,Z_186) ),
inference(resolution,[status(thm)],[c_2252,c_52]) ).
tff(c_2343,plain,
( less_or_equal(a,u)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_1391,c_2322]) ).
tff(c_2366,plain,
less_or_equal(a,u),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_2343]) ).
tff(c_2368,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1497,c_2366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : FLD059-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.10 % 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
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 7 18:54:31 EDT 2025
% 0.10/0.30 % CPUTime :
% 5.51/2.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/2.28
% 5.91/2.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------