%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : FLD016-5 : 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 : n004.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 06:10:39 PM UTC 2025
% Result : Unsatisfiable 187.41s 168.67s
% Output : CNFRefutation 187.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 152 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 308 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 325 ( 169 ~; 156 |; 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 152 ( 152 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > v > u > r > q > 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(r,type,
r: $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(v,type,
v: $i ).
tff(add,type,
add: ( $i * $i ) > $i ).
tff(q,type,
q: $i ).
tff(f_258,axiom,
~ sum(additive_identity,u,v),
file(unknown,unknown) ).
tff(f_251,axiom,
defined(v),
file(unknown,unknown) ).
tff(f_252,axiom,
defined(q),
file(unknown,unknown) ).
tff(f_78,axiom,
! [X] :
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_159,axiom,
defined(additive_identity),
file(unknown,unknown) ).
tff(f_256,axiom,
sum(additive_identity,q,r),
file(unknown,unknown) ).
tff(f_83,axiom,
! [Y,X,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [X] :
( sum(additive_identity,X,X)
| ~ defined(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_164,axiom,
! [X] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file(unknown,unknown) ).
tff(f_249,axiom,
defined(a),
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_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_250,axiom,
defined(u),
file(unknown,unknown) ).
tff(f_254,axiom,
sum(a,u,q),
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_255,axiom,
sum(a,v,r),
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(c_70,plain,
~ sum(additive_identity,u,v),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_58,plain,
defined(v),
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_60,plain,
defined(q),
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_28,plain,
defined(additive_identity),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_68,plain,
sum(additive_identity,q,r),
inference(cnfTransformation,[status(thm)],[f_256]) ).
tff(c_75,plain,
! [X_78,Y_79,Z_80] :
( ~ sum(X_78,Y_79,Z_80)
| sum(Y_79,X_78,Z_80) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_89,plain,
sum(q,additive_identity,r),
inference(resolution,[status(thm)],[c_68,c_75]) ).
tff(c_6,plain,
! [X_13] :
( ~ defined(X_13)
| sum(additive_identity,X_13,X_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_241644,plain,
! [W_1562,X_1561,V_1559,U_1560,Y_1558,Z_1557] :
( ~ sum(U_1560,Z_1557,W_1562)
| ~ sum(Y_1558,Z_1557,V_1559)
| ~ sum(X_1561,Y_1558,U_1560)
| sum(X_1561,V_1559,W_1562) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_245746,plain,
! [Y_1686,X_1687,V_1688,X_1689] :
( ~ sum(Y_1686,X_1687,V_1688)
| ~ sum(X_1689,Y_1686,additive_identity)
| sum(X_1689,V_1688,X_1687)
| ~ defined(X_1687) ),
inference(resolution,[status(thm)],[c_6,c_241644]) ).
tff(c_245818,plain,
! [X_1689] :
( ~ sum(X_1689,q,additive_identity)
| sum(X_1689,r,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[c_89,c_245746]) ).
tff(c_248495,plain,
! [X_1742] :
( ~ sum(X_1742,q,additive_identity)
| sum(X_1742,r,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_245818]) ).
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_250386,plain,
! [X_1774] :
( sum(r,X_1774,additive_identity)
| ~ sum(X_1774,q,additive_identity) ),
inference(resolution,[status(thm)],[c_248495,c_10]) ).
tff(c_250392,plain,
( sum(r,additive_inverse(q),additive_identity)
| ~ defined(q) ),
inference(resolution,[status(thm)],[c_8,c_250386]) ).
tff(c_250398,plain,
sum(r,additive_inverse(q),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_250392]) ).
tff(c_250459,plain,
sum(additive_inverse(q),r,additive_identity),
inference(resolution,[status(thm)],[c_250398,c_10]) ).
tff(c_30,plain,
! [X_51] :
( ~ defined(X_51)
| defined(additive_inverse(X_51)) ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_54,plain,
defined(a),
inference(cnfTransformation,[status(thm)],[f_249]) ).
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_139,plain,
! [Y_65] :
( ~ defined(Y_65)
| less_or_equal(Y_65,Y_65) ),
inference(factorization,[status(thm),theory(equality)],[c_46]) ).
tff(c_241306,plain,
! [Z_1526,X_1525,Y_1527,U_1524,V_1528] :
( ~ sum(Y_1527,Z_1526,V_1528)
| ~ sum(X_1525,Z_1526,U_1524)
| ~ less_or_equal(X_1525,Y_1527)
| less_or_equal(U_1524,V_1528) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_242087,plain,
! [X_1587,U_1588] :
( ~ sum(X_1587,q,U_1588)
| ~ less_or_equal(X_1587,additive_identity)
| less_or_equal(U_1588,r) ),
inference(resolution,[status(thm)],[c_68,c_241306]) ).
tff(c_242107,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(q,r)
| ~ defined(q) ),
inference(resolution,[status(thm)],[c_6,c_242087]) ).
tff(c_242123,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(q,r) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_242107]) ).
tff(c_242126,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_242123]) ).
tff(c_242135,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_139,c_242126]) ).
tff(c_242145,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_242135]) ).
tff(c_242146,plain,
less_or_equal(q,r),
inference(splitRight,[status(thm)],[c_242123]) ).
tff(c_152,plain,
! [Y_100,X_101] :
( ~ less_or_equal(Y_100,X_101)
| ~ less_or_equal(X_101,Y_100)
| sum(additive_identity,X_101,Y_100) ),
inference(cnfTransformation,[status(thm)],[f_204]) ).
tff(c_162,plain,
( ~ less_or_equal(v,u)
| ~ less_or_equal(u,v) ),
inference(resolution,[status(thm)],[c_152,c_70]) ).
tff(c_164,plain,
~ less_or_equal(u,v),
inference(splitLeft,[status(thm)],[c_162]) ).
tff(c_237,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_721,plain,
! [X_164,U_165] :
( ~ sum(X_164,q,U_165)
| ~ less_or_equal(X_164,additive_identity)
| less_or_equal(U_165,r) ),
inference(resolution,[status(thm)],[c_68,c_237]) ).
tff(c_741,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(q,r)
| ~ defined(q) ),
inference(resolution,[status(thm)],[c_6,c_721]) ).
tff(c_757,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(q,r) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_741]) ).
tff(c_802,plain,
~ less_or_equal(additive_identity,additive_identity),
inference(splitLeft,[status(thm)],[c_757]) ).
tff(c_811,plain,
~ defined(additive_identity),
inference(resolution,[status(thm)],[c_139,c_802]) ).
tff(c_821,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_28,c_811]) ).
tff(c_823,plain,
less_or_equal(additive_identity,additive_identity),
inference(splitRight,[status(thm)],[c_757]) ).
tff(c_56,plain,
defined(u),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_64,plain,
sum(a,u,q),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_88,plain,
sum(u,a,q),
inference(resolution,[status(thm)],[c_64,c_75]) ).
tff(c_489,plain,
! [Y_145,X_148,Z_144,U_147,W_149,V_146] :
( ~ sum(U_147,Z_144,W_149)
| ~ sum(Y_145,Z_144,V_146)
| ~ sum(X_148,Y_145,U_147)
| sum(X_148,V_146,W_149) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_3814,plain,
! [Y_247,X_248,V_249,X_250] :
( ~ sum(Y_247,X_248,V_249)
| ~ sum(X_250,Y_247,additive_identity)
| sum(X_250,V_249,X_248)
| ~ defined(X_248) ),
inference(resolution,[status(thm)],[c_6,c_489]) ).
tff(c_3884,plain,
! [X_250] :
( ~ sum(X_250,u,additive_identity)
| sum(X_250,q,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_88,c_3814]) ).
tff(c_4997,plain,
! [X_269] :
( ~ sum(X_269,u,additive_identity)
| sum(X_269,q,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_3884]) ).
tff(c_5005,plain,
( sum(additive_inverse(u),q,a)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_8,c_4997]) ).
tff(c_5011,plain,
sum(additive_inverse(u),q,a),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_5005]) ).
tff(c_5065,plain,
sum(q,additive_inverse(u),a),
inference(resolution,[status(thm)],[c_5011,c_10]) ).
tff(c_379,plain,
! [Y_136,W_132,V_134,U_133,X_135,Z_131] :
( ~ sum(X_135,V_134,W_132)
| ~ sum(Y_136,Z_131,V_134)
| ~ sum(X_135,Y_136,U_133)
| sum(U_133,Z_131,W_132) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_418,plain,
! [Y_136,Z_131,X_13,U_133] :
( ~ sum(Y_136,Z_131,X_13)
| ~ sum(additive_identity,Y_136,U_133)
| sum(U_133,Z_131,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_379]) ).
tff(c_5073,plain,
! [U_133] :
( ~ sum(additive_identity,q,U_133)
| sum(U_133,additive_inverse(u),a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_5065,c_418]) ).
tff(c_44500,plain,
! [U_591] :
( ~ sum(additive_identity,q,U_591)
| sum(U_591,additive_inverse(u),a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_5073]) ).
tff(c_44600,plain,
! [U_591] :
( sum(additive_inverse(u),U_591,a)
| ~ sum(additive_identity,q,U_591) ),
inference(resolution,[status(thm)],[c_44500,c_10]) ).
tff(c_66,plain,
sum(a,v,r),
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_3894,plain,
! [X_250] :
( ~ sum(X_250,a,additive_identity)
| sum(X_250,r,v)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_66,c_3814]) ).
tff(c_5651,plain,
! [X_283] :
( ~ sum(X_283,a,additive_identity)
| sum(X_283,r,v) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_3894]) ).
tff(c_8036,plain,
! [X_317] :
( sum(r,X_317,v)
| ~ sum(X_317,a,additive_identity) ),
inference(resolution,[status(thm)],[c_5651,c_10]) ).
tff(c_8042,plain,
( sum(r,additive_inverse(a),v)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8,c_8036]) ).
tff(c_8048,plain,
sum(r,additive_inverse(a),v),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_8042]) ).
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_75]) ).
tff(c_119753,plain,
! [Y_1023,X_1024,V_1025,X_1026] :
( ~ sum(Y_1023,additive_inverse(X_1024),V_1025)
| ~ sum(X_1026,Y_1023,X_1024)
| sum(X_1026,V_1025,additive_identity)
| ~ defined(X_1024) ),
inference(resolution,[status(thm)],[c_86,c_489]) ).
tff(c_119948,plain,
! [X_1026] :
( ~ sum(X_1026,r,a)
| sum(X_1026,v,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_8048,c_119753]) ).
tff(c_240144,plain,
! [X_1502] :
( ~ sum(X_1502,r,a)
| sum(X_1502,v,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_119948]) ).
tff(c_240491,plain,
! [X_1504] :
( sum(v,X_1504,additive_identity)
| ~ sum(X_1504,r,a) ),
inference(resolution,[status(thm)],[c_240144,c_10]) ).
tff(c_240507,plain,
( sum(v,additive_inverse(u),additive_identity)
| ~ sum(additive_identity,q,r) ),
inference(resolution,[status(thm)],[c_44600,c_240491]) ).
tff(c_240540,plain,
sum(v,additive_inverse(u),additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_240507]) ).
tff(c_3974,plain,
! [X_250,X_14] :
( ~ sum(X_250,additive_inverse(X_14),additive_identity)
| sum(X_250,additive_identity,X_14)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_3814]) ).
tff(c_240600,plain,
( sum(v,additive_identity,u)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_240540,c_3974]) ).
tff(c_240693,plain,
sum(v,additive_identity,u),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_240600]) ).
tff(c_240882,plain,
sum(additive_identity,v,u),
inference(resolution,[status(thm)],[c_240693,c_10]) ).
tff(c_276,plain,
! [X_119,X_13,U_118] :
( ~ sum(X_119,X_13,U_118)
| ~ less_or_equal(X_119,additive_identity)
| less_or_equal(U_118,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_237]) ).
tff(c_241092,plain,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(u,v)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_240882,c_276]) ).
tff(c_241185,plain,
less_or_equal(u,v),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_823,c_241092]) ).
tff(c_241187,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164,c_241185]) ).
tff(c_241189,plain,
less_or_equal(u,v),
inference(splitRight,[status(thm)],[c_162]) ).
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_241216,plain,
! [X_1508] :
( ~ less_or_equal(X_1508,u)
| less_or_equal(X_1508,v) ),
inference(resolution,[status(thm)],[c_241189,c_44]) ).
tff(c_241219,plain,
! [X_61,X_1508] :
( ~ less_or_equal(X_61,X_1508)
| less_or_equal(X_61,v)
| ~ less_or_equal(X_1508,u) ),
inference(resolution,[status(thm)],[c_241216,c_44]) ).
tff(c_242160,plain,
( less_or_equal(q,v)
| ~ less_or_equal(r,u) ),
inference(resolution,[status(thm)],[c_242146,c_241219]) ).
tff(c_242192,plain,
~ less_or_equal(r,u),
inference(splitLeft,[status(thm)],[c_242160]) ).
tff(c_241371,plain,
! [X_1530,U_1531] :
( ~ sum(X_1530,u,U_1531)
| ~ less_or_equal(X_1530,a)
| less_or_equal(U_1531,q) ),
inference(resolution,[status(thm)],[c_64,c_241306]) ).
tff(c_241391,plain,
( ~ less_or_equal(additive_identity,a)
| less_or_equal(u,q)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_6,c_241371]) ).
tff(c_241407,plain,
( ~ less_or_equal(additive_identity,a)
| less_or_equal(u,q) ),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_241391]) ).
tff(c_241409,plain,
~ less_or_equal(additive_identity,a),
inference(splitLeft,[status(thm)],[c_241407]) ).
tff(c_241412,plain,
( ~ defined(additive_identity)
| ~ defined(a)
| less_or_equal(a,additive_identity) ),
inference(resolution,[status(thm)],[c_46,c_241409]) ).
tff(c_241418,plain,
less_or_equal(a,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_28,c_241412]) ).
tff(c_241521,plain,
! [V_1548,Z_1545,X_1549,Y_1550,W_1546,U_1547] :
( ~ sum(X_1549,V_1548,W_1546)
| ~ sum(Y_1550,Z_1545,V_1548)
| ~ sum(X_1549,Y_1550,U_1547)
| sum(U_1547,Z_1545,W_1546) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_242321,plain,
! [Y_1595,Z_1596,U_1597] :
( ~ sum(Y_1595,Z_1596,q)
| ~ sum(additive_identity,Y_1595,U_1597)
| sum(U_1597,Z_1596,r) ),
inference(resolution,[status(thm)],[c_68,c_241521]) ).
tff(c_242374,plain,
! [U_1598] :
( ~ sum(additive_identity,a,U_1598)
| sum(U_1598,u,r) ),
inference(resolution,[status(thm)],[c_64,c_242321]) ).
tff(c_242386,plain,
( sum(a,u,r)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_6,c_242374]) ).
tff(c_242396,plain,
sum(a,u,r),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_242386]) ).
tff(c_242464,plain,
! [X_1599,X_1600,U_1601] :
( ~ sum(X_1599,X_1600,U_1601)
| ~ less_or_equal(X_1599,additive_identity)
| less_or_equal(U_1601,X_1600)
| ~ defined(X_1600) ),
inference(resolution,[status(thm)],[c_6,c_241306]) ).
tff(c_242470,plain,
( ~ less_or_equal(a,additive_identity)
| less_or_equal(r,u)
| ~ defined(u) ),
inference(resolution,[status(thm)],[c_242396,c_242464]) ).
tff(c_242519,plain,
less_or_equal(r,u),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_241418,c_242470]) ).
tff(c_242521,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_242192,c_242519]) ).
tff(c_242523,plain,
less_or_equal(r,u),
inference(splitRight,[status(thm)],[c_242160]) ).
tff(c_242568,plain,
! [X_1603] :
( ~ less_or_equal(X_1603,r)
| less_or_equal(X_1603,u) ),
inference(resolution,[status(thm)],[c_242523,c_44]) ).
tff(c_241431,plain,
( less_or_equal(a,v)
| ~ less_or_equal(additive_identity,u) ),
inference(resolution,[status(thm)],[c_241418,c_241219]) ).
tff(c_241506,plain,
~ less_or_equal(additive_identity,u),
inference(splitLeft,[status(thm)],[c_241431]) ).
tff(c_242588,plain,
~ less_or_equal(additive_identity,r),
inference(resolution,[status(thm)],[c_242568,c_241506]) ).
tff(c_241997,plain,
! [X_1585,U_1586] :
( ~ sum(X_1585,v,U_1586)
| ~ less_or_equal(X_1585,a)
| less_or_equal(U_1586,r) ),
inference(resolution,[status(thm)],[c_66,c_241306]) ).
tff(c_242013,plain,
( ~ less_or_equal(additive_inverse(v),a)
| less_or_equal(additive_identity,r)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_8,c_241997]) ).
tff(c_242030,plain,
( ~ less_or_equal(additive_inverse(v),a)
| less_or_equal(additive_identity,r) ),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_242013]) ).
tff(c_244032,plain,
~ less_or_equal(additive_inverse(v),a),
inference(negUnitSimplification,[status(thm)],[c_242588,c_242030]) ).
tff(c_244038,plain,
( ~ defined(additive_inverse(v))
| ~ defined(a)
| less_or_equal(a,additive_inverse(v)) ),
inference(resolution,[status(thm)],[c_46,c_244032]) ).
tff(c_244045,plain,
( ~ defined(additive_inverse(v))
| less_or_equal(a,additive_inverse(v)) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_244038]) ).
tff(c_244086,plain,
~ defined(additive_inverse(v)),
inference(splitLeft,[status(thm)],[c_244045]) ).
tff(c_244110,plain,
~ defined(v),
inference(resolution,[status(thm)],[c_30,c_244086]) ).
tff(c_244114,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_244110]) ).
tff(c_244116,plain,
defined(additive_inverse(v)),
inference(splitRight,[status(thm)],[c_244045]) ).
tff(c_90,plain,
sum(v,a,r),
inference(resolution,[status(thm)],[c_66,c_75]) ).
tff(c_245816,plain,
! [X_1689] :
( ~ sum(X_1689,v,additive_identity)
| sum(X_1689,r,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c_90,c_245746]) ).
tff(c_247589,plain,
! [X_1726] :
( ~ sum(X_1726,v,additive_identity)
| sum(X_1726,r,a) ),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_245816]) ).
tff(c_247597,plain,
( sum(additive_inverse(v),r,a)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_8,c_247589]) ).
tff(c_247601,plain,
sum(additive_inverse(v),r,a),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_247597]) ).
tff(c_247941,plain,
sum(r,additive_inverse(v),a),
inference(resolution,[status(thm)],[c_247601,c_10]) ).
tff(c_241683,plain,
! [Y_1558,X_13,V_1559,X_1561] :
( ~ sum(Y_1558,X_13,V_1559)
| ~ sum(X_1561,Y_1558,additive_identity)
| sum(X_1561,V_1559,X_13)
| ~ defined(X_13) ),
inference(resolution,[status(thm)],[c_6,c_241644]) ).
tff(c_247949,plain,
! [X_1561] :
( ~ sum(X_1561,r,additive_identity)
| sum(X_1561,a,additive_inverse(v))
| ~ defined(additive_inverse(v)) ),
inference(resolution,[status(thm)],[c_247941,c_241683]) ).
tff(c_343627,plain,
! [X_2415] :
( ~ sum(X_2415,r,additive_identity)
| sum(X_2415,a,additive_inverse(v)) ),
inference(demodulation,[status(thm),theory(equality)],[c_244116,c_247949]) ).
tff(c_247602,plain,
! [Y_1727,Z_1728,X_1729,U_1730] :
( ~ sum(Y_1727,Z_1728,X_1729)
| ~ sum(additive_inverse(X_1729),Y_1727,U_1730)
| sum(U_1730,Z_1728,additive_identity)
| ~ defined(X_1729) ),
inference(resolution,[status(thm)],[c_8,c_241521]) ).
tff(c_247720,plain,
! [U_1730] :
( ~ sum(additive_inverse(q),a,U_1730)
| sum(U_1730,u,additive_identity)
| ~ defined(q) ),
inference(resolution,[status(thm)],[c_64,c_247602]) ).
tff(c_247889,plain,
! [U_1730] :
( ~ sum(additive_inverse(q),a,U_1730)
| sum(U_1730,u,additive_identity) ),
inference(demodulation,[status(thm),theory(equality)],[c_60,c_247720]) ).
tff(c_343682,plain,
( sum(additive_inverse(v),u,additive_identity)
| ~ sum(additive_inverse(q),r,additive_identity) ),
inference(resolution,[status(thm)],[c_343627,c_247889]) ).
tff(c_343774,plain,
sum(additive_inverse(v),u,additive_identity),
inference(demodulation,[status(thm),theory(equality)],[c_250459,c_343682]) ).
tff(c_343933,plain,
sum(u,additive_inverse(v),additive_identity),
inference(resolution,[status(thm)],[c_343774,c_10]) ).
tff(c_245916,plain,
! [X_1689,X_14] :
( ~ sum(X_1689,additive_inverse(X_14),additive_identity)
| sum(X_1689,additive_identity,X_14)
| ~ defined(X_14) ),
inference(resolution,[status(thm)],[c_8,c_245746]) ).
tff(c_344051,plain,
( sum(u,additive_identity,v)
| ~ defined(v) ),
inference(resolution,[status(thm)],[c_343933,c_245916]) ).
tff(c_344103,plain,
sum(u,additive_identity,v),
inference(demodulation,[status(thm),theory(equality)],[c_58,c_344051]) ).
tff(c_344305,plain,
sum(additive_identity,u,v),
inference(resolution,[status(thm)],[c_344103,c_10]) ).
tff(c_344364,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_344305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD016-5 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % 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
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 18:40:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 187.41/168.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 187.41/168.68
% 187.41/168.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------