TSTP Solution File: FLD026-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD026-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 : 600s
% DateTime : Sat Jul 16 02:28:22 EDT 2022
% Result : Unsatisfiable 15.43s 15.71s
% Output : Refutation 15.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 23
% Syntax : Number of clauses : 133 ( 39 unt; 12 nHn; 133 RR)
% Number of literals : 306 ( 0 equ; 175 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD026-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD026-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD026-3.p',unknown),
[] ).
cnf(4,axiom,
product(multiplicative_identity,a,b),
file('FLD026-3.p',unknown),
[] ).
cnf(5,axiom,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('FLD026-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD026-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD026-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(u)
| sum__dfg(additive_inverse(u),u,additive_identity) ),
file('FLD026-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD026-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD026-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD026-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD026-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD026-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD026-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD026-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,v)
| ~ product(z,y,u)
| ~ sum__dfg(z,x,x1)
| product(x1,y,w) ),
file('FLD026-3.p',unknown),
[] ).
cnf(19,axiom,
defined(additive_identity),
file('FLD026-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ defined(u)
| defined(additive_inverse(u)) ),
file('FLD026-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| ~ defined(v)
| defined(multiply(v,u)) ),
file('FLD026-3.p',unknown),
[] ).
cnf(22,axiom,
defined(multiplicative_identity),
file('FLD026-3.p',unknown),
[] ).
cnf(23,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD026-3.p',unknown),
[] ).
cnf(25,axiom,
( ~ defined(u)
| ~ defined(v)
| product(v,u,multiply(v,u)) ),
file('FLD026-3.p',unknown),
[] ).
cnf(31,axiom,
~ sum__dfg(additive_identity,additive_identity,multiplicative_identity),
file('FLD026-3.p',unknown),
[] ).
cnf(33,plain,
( ~ product(b,u,v)
| ~ product(a,u,w)
| product(multiplicative_identity,w,v) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.0,11.0')] ).
cnf(34,plain,
( ~ product(multiplicative_identity,u,v)
| ~ product(a,w,u)
| product(b,w,v) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.0')] ).
cnf(36,plain,
( ~ product(u,v,a)
| ~ product(multiplicative_identity,u,w)
| product(w,v,b) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.2')] ).
cnf(37,plain,
( ~ product(u,a,v)
| ~ product(w,multiplicative_identity,u)
| product(w,b,v) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.0,11.1')] ).
cnf(41,plain,
( ~ product(u,v,multiplicative_identity)
| ~ product(v,a,w)
| product(u,w,b) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.0,11.2')] ).
cnf(45,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[14,3]),
[iquote('0:Res:14.2,3.0')] ).
cnf(51,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,a)
| ~ product(u,x,additive_identity)
| ~ product(w,x,additive_identity) ),
inference(res,[status(thm),theory(equality)],[16,3]),
[iquote('0:Res:16.4,3.0')] ).
cnf(54,plain,
( ~ product(u,v,multiplicative_identity)
| ~ product(u,w,multiplicative_inverse(b))
| ~ product(v,multiplicative_inverse(a),w) ),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.3,5.0')] ).
cnf(57,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[45,1]),
[iquote('0:MRR:45.0,1.0')] ).
cnf(59,plain,
( ~ product(a,u,a)
| product(b,u,b) ),
inference(res,[status(thm),theory(equality)],[4,36]),
[iquote('0:Res:4.0,36.0')] ).
cnf(63,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,b,b) ),
inference(res,[status(thm),theory(equality)],[4,41]),
[iquote('0:Res:4.0,41.1')] ).
cnf(80,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('0:Res:8.1,10.0')] ).
cnf(86,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(b,u,b) ),
inference(res,[status(thm),theory(equality)],[63,15]),
[iquote('0:Res:63.1,15.0')] ).
cnf(87,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[57,15]),
[iquote('0:Res:57.0,15.0')] ).
cnf(88,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[13,15]),
[iquote('0:Res:13.1,15.0')] ).
cnf(92,plain,
( ~ defined(a)
| product(b,multiplicative_identity,b) ),
inference(res,[status(thm),theory(equality)],[88,59]),
[iquote('0:Res:88.1,59.0')] ).
cnf(94,plain,
product(b,multiplicative_identity,b),
inference(ssi,[status(thm)],[92,1]),
[iquote('0:SSi:92.0,1.0')] ).
cnf(101,plain,
( ~ defined(multiplicative_identity)
| sum__dfg(additive_identity,multiplicative_identity,additive_identity)
| product(b,multiplicative_inverse(multiplicative_identity),b) ),
inference(res,[status(thm),theory(equality)],[14,86]),
[iquote('0:Res:14.2,86.0')] ).
cnf(103,plain,
( sum__dfg(additive_identity,multiplicative_identity,additive_identity)
| product(b,multiplicative_inverse(multiplicative_identity),b) ),
inference(ssi,[status(thm)],[101,22]),
[iquote('0:SSi:101.0,22.0')] ).
cnf(108,plain,
( ~ defined(u)
| ~ defined(v)
| product(u,v,multiply(v,u)) ),
inference(res,[status(thm),theory(equality)],[25,15]),
[iquote('0:Res:25.2,15.0')] ).
cnf(130,plain,
( ~ defined(u)
| ~ sum__dfg(v,u,w)
| ~ sum__dfg(x,v,additive_identity)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[8,6]),
[iquote('0:Res:8.1,6.0')] ).
cnf(157,plain,
( ~ defined(u)
| ~ product(v,w,u)
| ~ product(multiplicative_identity,v,x)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[13,12]),
[iquote('0:Res:13.1,12.0')] ).
cnf(187,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,v,multiplicative_identity)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[13,11]),
[iquote('0:Res:13.1,11.0')] ).
cnf(189,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,v,multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity)
| product(x,w,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[14,11]),
[iquote('0:Res:14.2,11.0')] ).
cnf(305,plain,
( ~ defined(u)
| ~ product(v,w,u)
| ~ product(x,w,additive_inverse(u))
| ~ sum__dfg(x,v,y)
| product(y,w,additive_identity) ),
inference(res,[status(thm),theory(equality)],[9,17]),
[iquote('0:Res:9.1,17.0')] ).
cnf(346,plain,
( ~ defined(u)
| ~ product(a,v,u)
| product(b,v,u) ),
inference(res,[status(thm),theory(equality)],[13,34]),
[iquote('0:Res:13.1,34.0')] ).
cnf(373,plain,
( ~ defined(multiplicative_identity)
| product(b,multiplicative_inverse(a),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[87,346]),
[iquote('0:Res:87.0,346.1')] ).
cnf(376,plain,
( ~ defined(a)
| ~ defined(a)
| product(b,multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[88,346]),
[iquote('0:Res:88.1,346.1')] ).
cnf(380,plain,
product(b,multiplicative_inverse(a),multiplicative_identity),
inference(ssi,[status(thm)],[373,22]),
[iquote('0:SSi:373.0,22.0')] ).
cnf(381,plain,
( ~ defined(a)
| product(b,multiplicative_identity,a) ),
inference(obv,[status(thm),theory(equality)],[376]),
[iquote('0:Obv:376.0')] ).
cnf(382,plain,
product(b,multiplicative_identity,a),
inference(ssi,[status(thm)],[381,1]),
[iquote('0:SSi:381.0,1.0')] ).
cnf(436,plain,
( ~ product(a,multiplicative_inverse(multiplicative_identity),u)
| sum__dfg(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_identity,u,b) ),
inference(res,[status(thm),theory(equality)],[103,33]),
[iquote('0:Res:103.1,33.0')] ).
cnf(511,plain,
( ~ defined(a)
| ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,b,a) ),
inference(res,[status(thm),theory(equality)],[13,37]),
[iquote('0:Res:13.1,37.0')] ).
cnf(518,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,b,a) ),
inference(ssi,[status(thm)],[511,1]),
[iquote('0:SSi:511.0,1.0')] ).
cnf(670,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(b,u,a) ),
inference(res,[status(thm),theory(equality)],[518,15]),
[iquote('0:Res:518.1,15.0')] ).
cnf(738,plain,
( ~ defined(multiplicative_inverse(b))
| ~ product(multiplicative_inverse(b),u,multiplicative_identity)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[88,54]),
[iquote('0:Res:88.1,54.1')] ).
cnf(748,plain,
( ~ defined(multiplicative_identity)
| sum__dfg(additive_identity,multiplicative_identity,additive_identity)
| product(b,multiplicative_inverse(multiplicative_identity),a) ),
inference(res,[status(thm),theory(equality)],[14,670]),
[iquote('0:Res:14.2,670.0')] ).
cnf(751,plain,
( sum__dfg(additive_identity,multiplicative_identity,additive_identity)
| product(b,multiplicative_inverse(multiplicative_identity),a) ),
inference(ssi,[status(thm)],[748,22]),
[iquote('0:SSi:748.0,22.0')] ).
cnf(752,plain,
sum__dfg(additive_identity,multiplicative_identity,additive_identity),
inference(spt,[spt(split,[position(s1)])],[751]),
[iquote('1:Spt:751.0')] ).
cnf(853,plain,
( ~ defined(multiplicative_identity)
| ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,additive_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[752,130]),
[iquote('1:Res:752.0,130.1')] ).
cnf(875,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,additive_identity,multiplicative_identity) ),
inference(ssi,[status(thm)],[853,22]),
[iquote('1:SSi:853.0,22.0')] ).
cnf(962,plain,
( ~ defined(u)
| ~ defined(u)
| ~ product(multiplicative_identity,u,v)
| product(v,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[88,157]),
[iquote('0:Res:88.1,157.1')] ).
cnf(968,plain,
( ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,b,u)
| product(u,multiplicative_inverse(a),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[380,157]),
[iquote('0:Res:380.0,157.1')] ).
cnf(991,plain,
( ~ product(multiplicative_identity,b,u)
| product(u,multiplicative_inverse(a),multiplicative_identity) ),
inference(ssi,[status(thm)],[968,22]),
[iquote('0:SSi:968.0,22.0')] ).
cnf(1005,plain,
( ~ defined(u)
| ~ product(multiplicative_identity,u,v)
| product(v,multiplicative_identity,u) ),
inference(obv,[status(thm),theory(equality)],[962]),
[iquote('0:Obv:962.0')] ).
cnf(1032,plain,
( ~ defined(additive_identity)
| sum__dfg(additive_identity,additive_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[80,875]),
[iquote('1:Res:80.1,875.0')] ).
cnf(1038,plain,
sum__dfg(additive_identity,additive_identity,multiplicative_identity),
inference(ssi,[status(thm)],[1032,19]),
[iquote('1:SSi:1032.0,19.0')] ).
cnf(1039,plain,
$false,
inference(mrr,[status(thm)],[1038,31]),
[iquote('1:MRR:1038.0,31.0')] ).
cnf(1045,plain,
~ sum__dfg(additive_identity,multiplicative_identity,additive_identity),
inference(spt,[spt(split,[position(sa)])],[1039,752]),
[iquote('1:Spt:1039.0,751.0,752.0')] ).
cnf(1046,plain,
product(b,multiplicative_inverse(multiplicative_identity),a),
inference(spt,[spt(split,[position(s2)])],[751]),
[iquote('1:Spt:1039.0,751.1')] ).
cnf(1050,plain,
( ~ product(a,multiplicative_inverse(multiplicative_identity),u)
| product(multiplicative_identity,u,b) ),
inference(mrr,[status(thm)],[436,1045]),
[iquote('1:MRR:436.1,1045.0')] ).
cnf(1067,plain,
( ~ defined(multiplicative_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(res,[status(thm),theory(equality)],[23,1045]),
[iquote('1:Res:23.2,1045.0')] ).
cnf(1069,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(ssi,[status(thm)],[1067,22]),
[iquote('1:SSi:1067.0,22.0')] ).
cnf(1097,plain,
( ~ defined(multiplicative_identity)
| ~ product(u,b,multiplicative_identity)
| product(u,a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[382,187]),
[iquote('0:Res:382.0,187.1')] ).
cnf(1118,plain,
( ~ product(u,b,multiplicative_identity)
| product(u,a,multiplicative_identity) ),
inference(ssi,[status(thm)],[1097,22]),
[iquote('0:SSi:1097.0,22.0')] ).
cnf(1271,plain,
( ~ product(u,b,multiplicative_identity)
| product(a,u,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[1118,15]),
[iquote('0:Res:1118.1,15.0')] ).
cnf(1341,plain,
( ~ defined(b)
| sum__dfg(additive_identity,b,additive_identity)
| product(a,multiplicative_inverse(b),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[14,1271]),
[iquote('0:Res:14.2,1271.0')] ).
cnf(1343,plain,
( sum__dfg(additive_identity,b,additive_identity)
| product(a,multiplicative_inverse(b),multiplicative_identity) ),
inference(ssi,[status(thm)],[1341,2]),
[iquote('0:SSi:1341.0,2.0')] ).
cnf(1344,plain,
sum__dfg(additive_identity,b,additive_identity),
inference(spt,[spt(split,[position(s2s1)])],[1343]),
[iquote('2:Spt:1343.0')] ).
cnf(1348,plain,
sum__dfg(b,additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[1344,10]),
[iquote('2:Res:1344.0,10.0')] ).
cnf(1349,plain,
( ~ defined(b)
| ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,additive_identity,b) ),
inference(res,[status(thm),theory(equality)],[1344,130]),
[iquote('2:Res:1344.0,130.1')] ).
cnf(1353,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,additive_identity,b) ),
inference(ssi,[status(thm)],[1349,2]),
[iquote('2:SSi:1349.0,2.0')] ).
cnf(1364,plain,
( ~ defined(additive_identity)
| ~ sum__dfg(u,b,additive_identity)
| sum__dfg(u,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1348,130]),
[iquote('2:Res:1348.0,130.1')] ).
cnf(1368,plain,
( ~ sum__dfg(u,b,additive_identity)
| sum__dfg(u,additive_identity,additive_identity) ),
inference(ssi,[status(thm)],[1364,19]),
[iquote('2:SSi:1364.0,19.0')] ).
cnf(1457,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(additive_identity,u,b) ),
inference(res,[status(thm),theory(equality)],[1353,10]),
[iquote('2:Res:1353.1,10.0')] ).
cnf(1544,plain,
( ~ defined(b)
| sum__dfg(additive_inverse(b),additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[9,1368]),
[iquote('2:Res:9.1,1368.0')] ).
cnf(1546,plain,
sum__dfg(additive_identity,additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[1344,1368]),
[iquote('2:Res:1344.0,1368.0')] ).
cnf(1558,plain,
sum__dfg(additive_inverse(b),additive_identity,additive_identity),
inference(ssi,[status(thm)],[1544,2]),
[iquote('2:SSi:1544.0,2.0')] ).
cnf(1694,plain,
( ~ defined(u)
| ~ product(u,v,a)
| ~ product(additive_identity,v,additive_identity)
| ~ product(u,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[8,51]),
[iquote('0:Res:8.1,51.0')] ).
cnf(1700,plain,
( ~ defined(u)
| ~ product(u,v,a)
| ~ product(additive_identity,v,additive_identity)
| ~ product(additive_identity,v,additive_identity)
| defined(multiplicative_inverse(u)) ),
inference(res,[status(thm),theory(equality)],[23,51]),
[iquote('0:Res:23.2,51.0')] ).
cnf(1741,plain,
( ~ defined(u)
| ~ product(u,v,a)
| ~ product(additive_identity,v,additive_identity)
| defined(multiplicative_inverse(u)) ),
inference(obv,[status(thm),theory(equality)],[1700]),
[iquote('0:Obv:1700.2')] ).
cnf(1751,plain,
( ~ defined(additive_identity)
| sum__dfg(additive_identity,additive_inverse(additive_identity),b) ),
inference(res,[status(thm),theory(equality)],[9,1457]),
[iquote('2:Res:9.1,1457.0')] ).
cnf(1754,plain,
sum__dfg(additive_identity,additive_identity,b),
inference(res,[status(thm),theory(equality)],[1546,1457]),
[iquote('2:Res:1546.0,1457.0')] ).
cnf(1758,plain,
sum__dfg(additive_identity,additive_inverse(additive_identity),b),
inference(ssi,[status(thm)],[1751,19]),
[iquote('2:SSi:1751.0,19.0')] ).
cnf(1766,plain,
( ~ defined(additive_identity)
| ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,b,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1754,130]),
[iquote('2:Res:1754.0,130.1')] ).
cnf(1768,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,b,additive_identity) ),
inference(ssi,[status(thm)],[1766,19]),
[iquote('2:SSi:1766.0,19.0')] ).
cnf(1857,plain,
sum__dfg(additive_inverse(additive_identity),additive_identity,b),
inference(res,[status(thm),theory(equality)],[1758,10]),
[iquote('2:Res:1758.0,10.0')] ).
cnf(2135,plain,
( ~ defined(multiplicative_inverse(u))
| ~ defined(u)
| ~ product(multiplicative_identity,u,v)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),v,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[88,189]),
[iquote('0:Res:88.1,189.2')] ).
cnf(2138,plain,
( ~ defined(u)
| ~ product(multiplicative_identity,u,v)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),v,multiplicative_identity) ),
inference(mrr,[status(thm)],[2135,23]),
[iquote('0:MRR:2135.0,23.1')] ).
cnf(2181,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(b,u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1768,10]),
[iquote('2:Res:1768.1,10.0')] ).
cnf(3061,plain,
sum__dfg(b,additive_inverse(b),additive_identity),
inference(res,[status(thm),theory(equality)],[1558,2181]),
[iquote('2:Res:1558.0,2181.0')] ).
cnf(3081,plain,
sum__dfg(additive_inverse(b),b,additive_identity),
inference(res,[status(thm),theory(equality)],[3061,10]),
[iquote('2:Res:3061.0,10.0')] ).
cnf(3346,plain,
( ~ defined(additive_inverse(u))
| ~ defined(u)
| ~ product(v,multiplicative_identity,u)
| ~ sum__dfg(additive_inverse(u),v,w)
| product(w,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[88,305]),
[iquote('0:Res:88.1,305.2')] ).
cnf(3349,plain,
( ~ defined(u)
| ~ product(v,multiplicative_identity,u)
| ~ sum__dfg(additive_inverse(u),v,w)
| product(w,multiplicative_identity,additive_identity) ),
inference(ssi,[status(thm)],[3346,20]),
[iquote('0:SSi:3346.0,20.1')] ).
cnf(5319,plain,
( ~ defined(a)
| ~ defined(multiplicative_inverse(multiplicative_identity))
| product(multiplicative_identity,multiply(multiplicative_inverse(multiplicative_identity),a),b) ),
inference(res,[status(thm),theory(equality)],[108,1050]),
[iquote('1:Res:108.2,1050.0')] ).
cnf(5323,plain,
product(multiplicative_identity,multiply(multiplicative_inverse(multiplicative_identity),a),b),
inference(ssi,[status(thm)],[5319,1069,1]),
[iquote('1:SSi:5319.1,5319.0,1069.0,1.0')] ).
cnf(5878,plain,
( ~ defined(multiply(multiplicative_inverse(multiplicative_identity),a))
| product(b,multiplicative_identity,multiply(multiplicative_inverse(multiplicative_identity),a)) ),
inference(res,[status(thm),theory(equality)],[5323,1005]),
[iquote('1:Res:5323.0,1005.1')] ).
cnf(5900,plain,
product(b,multiplicative_identity,multiply(multiplicative_inverse(multiplicative_identity),a)),
inference(ssi,[status(thm)],[5878,21,1069,1]),
[iquote('1:SSi:5878.0,21.0,1069.0,1.2')] ).
cnf(6596,plain,
product(multiplicative_identity,b,multiply(multiplicative_inverse(multiplicative_identity),a)),
inference(res,[status(thm),theory(equality)],[5900,15]),
[iquote('1:Res:5900.0,15.0')] ).
cnf(11901,plain,
( ~ defined(b)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(b)) ),
inference(res,[status(thm),theory(equality)],[382,1741]),
[iquote('0:Res:382.0,1741.1')] ).
cnf(11940,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(b)) ),
inference(ssi,[status(thm)],[11901,2]),
[iquote('0:SSi:11901.0,2.0')] ).
cnf(12045,plain,
( ~ defined(additive_identity)
| defined(multiplicative_inverse(b)) ),
inference(res,[status(thm),theory(equality)],[88,11940]),
[iquote('0:Res:88.1,11940.0')] ).
cnf(12046,plain,
defined(multiplicative_inverse(b)),
inference(ssi,[status(thm)],[12045,19]),
[iquote('0:SSi:12045.0,19.0')] ).
cnf(12050,plain,
( ~ product(multiplicative_inverse(b),u,multiplicative_identity)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity) ),
inference(mrr,[status(thm)],[738,12046]),
[iquote('0:MRR:738.0,12046.0')] ).
cnf(13596,plain,
( ~ defined(b)
| ~ product(multiplicative_identity,b,u)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| sum__dfg(additive_identity,b,additive_identity) ),
inference(res,[status(thm),theory(equality)],[2138,12050]),
[iquote('0:Res:2138.3,12050.0')] ).
cnf(17712,plain,
( ~ defined(b)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(b,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[382,1694]),
[iquote('0:Res:382.0,1694.1')] ).
cnf(17763,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(b,multiplicative_identity,additive_identity) ),
inference(ssi,[status(thm)],[17712,2]),
[iquote('0:SSi:17712.0,2.0')] ).
cnf(17968,plain,
( ~ defined(b)
| ~ product(b,multiplicative_identity,b)
| product(additive_identity,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[3081,3349]),
[iquote('2:Res:3081.0,3349.2')] ).
cnf(17982,plain,
( ~ defined(additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(b,multiplicative_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[1857,3349]),
[iquote('2:Res:1857.0,3349.2')] ).
cnf(18012,plain,
( ~ product(b,multiplicative_identity,b)
| product(additive_identity,multiplicative_identity,additive_identity) ),
inference(ssi,[status(thm)],[17968,2]),
[iquote('2:SSi:17968.0,2.0')] ).
cnf(18013,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(mrr,[status(thm)],[18012,94]),
[iquote('2:MRR:18012.0,94.0')] ).
cnf(18020,plain,
~ product(b,multiplicative_identity,additive_identity),
inference(mrr,[status(thm)],[17763,18013]),
[iquote('2:MRR:17763.0,18013.0')] ).
cnf(18031,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(b,multiplicative_identity,additive_identity) ),
inference(ssi,[status(thm)],[17982,19]),
[iquote('2:SSi:17982.0,19.0')] ).
cnf(18032,plain,
$false,
inference(mrr,[status(thm)],[18031,18013,18020]),
[iquote('2:MRR:18031.0,18031.1,18013.0,18020.0')] ).
cnf(18078,plain,
~ sum__dfg(additive_identity,b,additive_identity),
inference(spt,[spt(split,[position(s2sa)])],[18032,1344]),
[iquote('2:Spt:18032.0,1343.0,1344.0')] ).
cnf(18079,plain,
product(a,multiplicative_inverse(b),multiplicative_identity),
inference(spt,[spt(split,[position(s2s2)])],[1343]),
[iquote('2:Spt:18032.0,1343.1')] ).
cnf(18157,plain,
( ~ product(multiplicative_identity,b,u)
| ~ product(u,multiplicative_inverse(a),multiplicative_identity)
| sum__dfg(additive_identity,b,additive_identity) ),
inference(ssi,[status(thm)],[13596,2]),
[iquote('0:SSi:13596.0,2.0')] ).
cnf(18158,plain,
( ~ product(multiplicative_identity,b,u)
| sum__dfg(additive_identity,b,additive_identity) ),
inference(mrr,[status(thm)],[18157,991]),
[iquote('0:MRR:18157.1,991.1')] ).
cnf(18159,plain,
~ product(multiplicative_identity,b,u),
inference(mrr,[status(thm)],[18158,18078]),
[iquote('2:MRR:18158.1,18078.0')] ).
cnf(18160,plain,
$false,
inference(unc,[status(thm)],[18159,6596]),
[iquote('2:UnC:18159.0,6596.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : FLD026-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.10 % Command : run_spass %d %s
% 0.09/0.30 % Computer : n022.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Tue Jun 7 03:20:05 EDT 2022
% 0.09/0.30 % CPUTime :
% 15.43/15.71
% 15.43/15.71 SPASS V 3.9
% 15.43/15.71 SPASS beiseite: Proof found.
% 15.43/15.71 % SZS status Theorem
% 15.43/15.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.43/15.71 SPASS derived 13162 clauses, backtracked 517 clauses, performed 2 splits and kept 8944 clauses.
% 15.43/15.71 SPASS allocated 88992 KBytes.
% 15.43/15.71 SPASS spent 0:0:15.39 on the problem.
% 15.43/15.71 0:00:00.03 for the input.
% 15.43/15.71 0:00:00.00 for the FLOTTER CNF translation.
% 15.43/15.71 0:00:00.13 for inferences.
% 15.43/15.71 0:00:00.77 for the backtracking.
% 15.43/15.71 0:0:14.32 for the reduction.
% 15.43/15.71
% 15.43/15.71
% 15.43/15.71 Here is a proof with depth 16, length 133 :
% 15.43/15.71 % SZS output start Refutation
% See solution above
% 15.83/16.08 Formulae used in the proof : a_is_defined b_is_defined not_sum_3 product_4 not_product_5 associativity_addition_1 existence_of_identity_addition existence_of_inverse_addition commutativity_addition associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_1 distributivity_2 well_definedness_of_additive_identity well_definedness_of_additive_inverse well_definedness_of_multiplication well_definedness_of_multiplicative_identity well_definedness_of_multiplicative_inverse totality_of_multiplication different_identities
% 15.83/16.08
%------------------------------------------------------------------------------