%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD013-3 : 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 : n018.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 06:10:38 PM UTC 2025
% Result : Unsatisfiable 284.07s 253.21s
% Output : CNFRefutation 284.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 127 ( 65 ~; 62 |; 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > d > c > 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(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(d,type,
d: $i ).
tff(c,type,
c: $i ).
tff(f_252,axiom,
defined(d),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_222,axiom,
! [X,Y] :
( less_or_equal(X,Y)
| less_or_equal(Y,X)
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_251,axiom,
defined(c),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_254,axiom,
sum(additive_identity,c,d),
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_204,axiom,
! [X,Y] :
( sum(additive_identity,X,Y)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,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_250,axiom,
defined(b),
file(unknown,unknown) ).
tff(f_253,axiom,
sum(additive_identity,a,b),
file(unknown,unknown) ).
tff(f_188,axiom,
! [X,Y] :
( sum(X,Y,add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [W,U,Z,X,Y,V] :
( sum(U,Z,W)
| ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W) ),
file(unknown,unknown) ).
tff(f_256,axiom,
~ sum(a,c,add(d,b)),
file(unknown,unknown) ).
tff(c_60,plain,
defined(d),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_46,plain,
! [Y_65,X_64] :
( ~ defined(Y_65)
| ~ defined(X_64)
| less_or_equal(Y_65,X_64)
| less_or_equal(X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_222]) ).
tff(c_133,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_58,plain,
defined(c),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_64,plain,
sum(additive_identity,c,d),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_209,plain,
! [V_119,X_116,Y_118,Z_117,U_115] :
( ~ sum(Y_118,Z_117,V_119)
| ~ sum(X_116,Z_117,U_115)
| ~ less_or_equal(X_116,Y_118)
| less_or_equal(U_115,V_119) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_246,plain,
! [X_120,U_121] :
( ~ sum(X_120,c,U_121)
| ~ less_or_equal(X_120,additive_identity)
| less_or_equal(U_121,d) ),
inference(resolution,[status(thm)],[c_64,c_209]) ).
tff(c_266,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(c,d)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c_6,c_246]) ).
tff(c_282,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(c,d) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_266]) ).
tff(c_284,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_282]) ).
tff(c_287,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_133,c_284]) ).
tff(c_293,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_287]) ).
tff(c_295,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_282]) ).
tff(c_42,plain,
! [Y_60,X_59] :
( ~ less_or_equal(Y_60,X_59)
| ~ less_or_equal(X_59,Y_60)
| sum(additive_identity,X_59,Y_60) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_393,plain,
! [U_138,Y_136,W_140,V_137,X_139,Z_135] :
( ~ sum(U_138,Z_135,W_140)
| ~ sum(Y_136,Z_135,V_137)
| ~ sum(X_139,Y_136,U_138)
| sum(X_139,V_137,W_140) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_3745,plain,
! [Y_240,X_241,V_242,X_243] :
( ~ sum(Y_240,X_241,V_242)
| ~ sum(X_243,Y_240,additive_identity)
| sum(X_243,V_242,X_241)
| ~ defined(X_241) ),
inference(resolution,[status(thm)],[c_6,c_393]) ).
tff(c_3817,plain,
! [X_243] :
( ~ sum(X_243,additive_identity,additive_identity)
| sum(X_243,d,c)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c_64,c_3745]) ).
tff(c_4153,plain,
! [X_254] :
( ~ sum(X_254,additive_identity,additive_identity)
| sum(X_254,d,c) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_3817]) ).
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_4683,plain,
! [X_262] :
( sum(d,X_262,c)
| ~ sum(X_262,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_4153,c_10]) ).
tff(c_4689,plain,
( sum(d,additive_identity,c)
| ~ less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_42,c_4683]) ).
tff(c_4702,plain,
sum(d,additive_identity,c),
inference(demodulation,[status(thm),theory(equality)],[c_295,c_4689]) ).
tff(c_56,plain,
defined(b),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_62,plain,
sum(additive_identity,a,b),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_38,plain,
! [Y_56,X_55] :
( ~ defined(Y_56)
| ~ defined(X_55)
| sum(X_55,Y_56,add(X_55,Y_56)) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_331,plain,
! [X_133,Y_134,Z_129,V_132,W_130,U_131] :
( ~ sum(X_133,V_132,W_130)
| ~ sum(Y_134,Z_129,V_132)
| ~ sum(X_133,Y_134,U_131)
| sum(U_131,Z_129,W_130) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_8044,plain,
! [Y_321,U_319,Z_317,X_320,Y_318] :
( ~ sum(Y_318,Z_317,Y_321)
| ~ sum(X_320,Y_318,U_319)
| sum(U_319,Z_317,add(X_320,Y_321))
| ~ defined(Y_321)
| ~ defined(X_320) ),
inference(resolution,[status(thm)],[c_38,c_331]) ).
tff(c_8162,plain,
! [X_320,U_319] :
( ~ sum(X_320,additive_identity,U_319)
| sum(U_319,a,add(X_320,b))
| ~ defined(b)
| ~ defined(X_320) ),
inference(resolution,[status(thm)],[c_62,c_8044]) ).
tff(c_43532,plain,
! [X_581,U_582] :
( ~ sum(X_581,additive_identity,U_582)
| sum(U_582,a,add(X_581,b))
| ~ defined(X_581) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_8162]) ).
tff(c_396922,plain,
! [U_1964,X_1965] :
( sum(a,U_1964,add(X_1965,b))
| ~ sum(X_1965,additive_identity,U_1964)
| ~ defined(X_1965) ),
inference(resolution,[status(thm)],[c_43532,c_10]) ).
tff(c_66,plain,
~ sum(a,c,add(d,b)),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_397151,plain,
( ~ sum(d,additive_identity,c)
| ~ defined(d) ),
inference(resolution,[status(thm)],[c_396922,c_66]) ).
tff(c_397266,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_60,c_4702,c_397151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD013-3 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 18:41:02 EDT 2025
% 0.14/0.34 % CPUTime :
% 284.07/253.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 284.07/253.22
% 284.07/253.22 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------