TSTP Solution File: BOO014-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Thu Jul 14 23:49:26 EDT 2022
% Result : Unsatisfiable 177.35s 177.60s
% Output : Refutation 178.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of clauses : 147 ( 67 unt; 0 nHn; 147 RR)
% Number of literals : 287 ( 0 equ; 146 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(inverse(u)),u),
file('BOO014-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(u,v,additive_identity)
| ~ product(u,w,additive_identity)
| ~ sum__dfg(u,v,multiplicative_identity)
| ~ sum__dfg(u,w,multiplicative_identity)
| equal(w,v) ),
file('BOO014-3.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(x__dfg,y__dfg,x_plus_y),
file('BOO014-3.p',unknown),
[] ).
cnf(4,axiom,
product(inverse(x__dfg),inverse(y__dfg),x_inverse_times_y_inverse),
file('BOO014-3.p',unknown),
[] ).
cnf(5,axiom,
~ equal(inverse(x_plus_y),x_inverse_times_y_inverse),
file('BOO014-3.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(u,v,add(u,v)),
file('BOO014-3.p',unknown),
[] ).
cnf(7,axiom,
product(u,v,multiply(u,v)),
file('BOO014-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(10,axiom,
sum__dfg(additive_identity,u,u),
file('BOO014-3.p',unknown),
[] ).
cnf(11,axiom,
sum__dfg(u,additive_identity,u),
file('BOO014-3.p',unknown),
[] ).
cnf(12,axiom,
product(multiplicative_identity,u,u),
file('BOO014-3.p',unknown),
[] ).
cnf(13,axiom,
product(u,multiplicative_identity,u),
file('BOO014-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,z)
| ~ product(y,x1,v)
| ~ product(x,x1,u)
| product(z,x1,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,v)
| ~ sum__dfg(u,y,z)
| ~ sum__dfg(u,x,x1)
| product(x1,z,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,y,z)
| ~ sum__dfg(x1,y,v)
| ~ sum__dfg(x1,x,u)
| sum__dfg(x1,z,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,u)
| ~ sum__dfg(y,v,z)
| ~ sum__dfg(x,v,x1)
| product(x1,z,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(u,v,w)
| ~ product(x,y,z)
| ~ sum__dfg(y,x1,v)
| ~ sum__dfg(x,x1,u)
| sum__dfg(z,x1,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(22,axiom,
sum__dfg(inverse(u),u,multiplicative_identity),
file('BOO014-3.p',unknown),
[] ).
cnf(23,axiom,
sum__dfg(u,inverse(u),multiplicative_identity),
file('BOO014-3.p',unknown),
[] ).
cnf(24,axiom,
product(inverse(u),u,additive_identity),
file('BOO014-3.p',unknown),
[] ).
cnf(25,axiom,
product(u,inverse(u),additive_identity),
file('BOO014-3.p',unknown),
[] ).
cnf(26,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('BOO014-3.p',unknown),
[] ).
cnf(33,plain,
( ~ product(u,x_inverse_times_y_inverse,additive_identity)
| ~ sum__dfg(u,x_inverse_times_y_inverse,multiplicative_identity)
| ~ product(u,inverse(x_plus_y),additive_identity)
| ~ sum__dfg(u,inverse(x_plus_y),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.4,5.0')] ).
cnf(44,plain,
product(inverse(y__dfg),inverse(x__dfg),x_inverse_times_y_inverse),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(45,plain,
product(u,v,multiply(v,u)),
inference(res,[status(thm),theory(equality)],[7,9]),
[iquote('0:Res:7.0,9.0')] ).
cnf(48,plain,
sum__dfg(y__dfg,x__dfg,x_plus_y),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.0')] ).
cnf(53,plain,
sum__dfg(u,v,add(v,u)),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.0')] ).
cnf(55,plain,
( ~ product(multiplicative_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[12,27]),
[iquote('0:Res:12.0,27.0')] ).
cnf(57,plain,
( ~ product(inverse(u),u,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[24,27]),
[iquote('0:Res:24.0,27.0')] ).
cnf(61,plain,
( ~ product(u,v,w)
| equal(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,27]),
[iquote('0:Res:7.0,27.0')] ).
cnf(83,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[10,26]),
[iquote('0:Res:10.0,26.0')] ).
cnf(84,plain,
( ~ sum__dfg(u,additive_identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[11,26]),
[iquote('0:Res:11.0,26.0')] ).
cnf(85,plain,
( ~ sum__dfg(inverse(u),u,v)
| equal(v,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[22,26]),
[iquote('0:Res:22.0,26.0')] ).
cnf(87,plain,
( ~ sum__dfg(u,v,w)
| equal(w,add(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,26]),
[iquote('0:Res:6.0,26.0')] ).
cnf(124,plain,
( ~ product(u,v,w)
| ~ sum__dfg(v,x,y)
| ~ sum__dfg(u,x,multiplicative_identity)
| sum__dfg(w,x,y) ),
inference(res,[status(thm),theory(equality)],[12,21]),
[iquote('0:Res:12.0,21.0')] ).
cnf(156,plain,
( ~ product(u,v,w)
| ~ sum__dfg(v,inverse(w),x)
| ~ sum__dfg(u,inverse(w),y)
| product(y,x,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[23,20]),
[iquote('0:Res:23.0,20.0')] ).
cnf(187,plain,
( ~ product(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(x,u,multiplicative_identity)
| sum__dfg(x,w,y) ),
inference(res,[status(thm),theory(equality)],[12,19]),
[iquote('0:Res:12.0,19.0')] ).
cnf(222,plain,
( ~ product(u,v,additive_identity)
| ~ sum__dfg(w,v,x)
| ~ sum__dfg(w,u,y)
| product(y,x,w) ),
inference(res,[status(thm),theory(equality)],[11,18]),
[iquote('0:Res:11.0,18.0')] ).
cnf(243,plain,
equal(multiply(u,v),multiply(v,u)),
inference(res,[status(thm),theory(equality)],[45,61]),
[iquote('0:Res:45.0,61.0')] ).
cnf(248,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,y)
| ~ product(u,x,additive_identity)
| product(w,x,y) ),
inference(res,[status(thm),theory(equality)],[10,17]),
[iquote('0:Res:10.0,17.0')] ).
cnf(283,plain,
equal(add(u,v),add(v,u)),
inference(res,[status(thm),theory(equality)],[53,87]),
[iquote('0:Res:53.0,87.0')] ).
cnf(298,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| ~ product(v,w,x)
| ~ product(u,w,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[12,16]),
[iquote('0:Res:12.0,16.0')] ).
cnf(301,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,inverse(w),x)
| ~ product(u,inverse(w),y)
| sum__dfg(y,x,additive_identity) ),
inference(res,[status(thm),theory(equality)],[25,16]),
[iquote('0:Res:25.0,16.0')] ).
cnf(333,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| ~ product(w,v,x)
| ~ product(w,u,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[13,14]),
[iquote('0:Res:13.0,14.0')] ).
cnf(646,plain,
( ~ sum__dfg(multiplicative_identity,u,v)
| ~ sum__dfg(w,u,multiplicative_identity)
| sum__dfg(w,u,v) ),
inference(res,[status(thm),theory(equality)],[13,124]),
[iquote('0:Res:13.0,124.0')] ).
cnf(648,plain,
( ~ sum__dfg(inverse(u),v,w)
| ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(additive_identity,v,w) ),
inference(res,[status(thm),theory(equality)],[25,124]),
[iquote('0:Res:25.0,124.0')] ).
cnf(832,plain,
( ~ sum__dfg(u,inverse(v),w)
| ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(u,additive_identity,w) ),
inference(res,[status(thm),theory(equality)],[25,187]),
[iquote('0:Res:25.0,187.0')] ).
cnf(833,plain,
( ~ sum__dfg(u,inverse(y__dfg),v)
| ~ sum__dfg(u,inverse(x__dfg),multiplicative_identity)
| sum__dfg(u,x_inverse_times_y_inverse,v) ),
inference(res,[status(thm),theory(equality)],[4,187]),
[iquote('0:Res:4.0,187.0')] ).
cnf(935,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,inverse(v),x)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[24,222]),
[iquote('0:Res:24.0,222.0')] ).
cnf(955,plain,
( ~ product(x__dfg,u,v)
| ~ product(y__dfg,u,additive_identity)
| product(x_plus_y,u,v) ),
inference(res,[status(thm),theory(equality)],[48,248]),
[iquote('0:Res:48.0,248.0')] ).
cnf(965,plain,
( ~ product(additive_identity,u,v)
| ~ product(w,u,additive_identity)
| product(w,u,v) ),
inference(res,[status(thm),theory(equality)],[11,248]),
[iquote('0:Res:11.0,248.0')] ).
cnf(1049,plain,
( ~ product(x__dfg,u,v)
| ~ product(y__dfg,u,additive_identity)
| product(u,x_plus_y,v) ),
inference(res,[status(thm),theory(equality)],[955,9]),
[iquote('0:Res:955.2,9.0')] ).
cnf(1087,plain,
( ~ product(u,v,w)
| ~ product(inverse(u),v,x)
| sum__dfg(x,w,v) ),
inference(res,[status(thm),theory(equality)],[22,298]),
[iquote('0:Res:22.0,298.0')] ).
cnf(1327,plain,
( ~ product(u,v,w)
| ~ product(u,inverse(v),x)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[22,333]),
[iquote('0:Res:22.0,333.0')] ).
cnf(1350,plain,
( ~ product(y__dfg,u,additive_identity)
| product(u,x_plus_y,multiply(x__dfg,u)) ),
inference(res,[status(thm),theory(equality)],[7,1049]),
[iquote('0:Res:7.0,1049.0')] ).
cnf(1351,plain,
( ~ product(y__dfg,u,additive_identity)
| product(u,x_plus_y,multiply(u,x__dfg)) ),
inference(res,[status(thm),theory(equality)],[45,1049]),
[iquote('0:Res:45.0,1049.0')] ).
cnf(1427,plain,
( ~ product(y__dfg,inverse(x_plus_y),additive_identity)
| equal(multiply(x__dfg,inverse(x_plus_y)),additive_identity) ),
inference(res,[status(thm),theory(equality)],[1350,57]),
[iquote('0:Res:1350.1,57.0')] ).
cnf(1452,plain,
( ~ product(y__dfg,u,additive_identity)
| equal(multiply(u,x_plus_y),multiply(u,x__dfg)) ),
inference(res,[status(thm),theory(equality)],[1351,61]),
[iquote('0:Res:1351.1,61.0')] ).
cnf(2305,plain,
( ~ product(u,v,w)
| ~ sum__dfg(u,inverse(w),x)
| product(x,add(v,inverse(w)),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[6,156]),
[iquote('0:Res:6.0,156.1')] ).
cnf(2306,plain,
( ~ product(u,v,w)
| ~ sum__dfg(u,inverse(w),x)
| product(x,add(inverse(w),v),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[53,156]),
[iquote('0:Res:53.0,156.1')] ).
cnf(2336,plain,
( ~ sum__dfg(u,v,v)
| ~ product(u,inverse(v),w)
| sum__dfg(w,additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[25,301]),
[iquote('0:Res:25.0,301.1')] ).
cnf(2341,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,inverse(w),x)
| sum__dfg(x,multiply(v,inverse(w)),additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,301]),
[iquote('0:Res:7.0,301.1')] ).
cnf(2342,plain,
( ~ sum__dfg(u,v,w)
| ~ product(u,inverse(w),x)
| sum__dfg(x,multiply(inverse(w),v),additive_identity) ),
inference(res,[status(thm),theory(equality)],[45,301]),
[iquote('0:Res:45.0,301.1')] ).
cnf(3285,plain,
( ~ product(x_plus_y,x_inverse_times_y_inverse,additive_identity)
| ~ sum__dfg(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity)
| ~ sum__dfg(x_plus_y,inverse(x_plus_y),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[25,33]),
[iquote('0:Res:25.0,33.2')] ).
cnf(3291,plain,
( ~ product(x_plus_y,x_inverse_times_y_inverse,additive_identity)
| ~ sum__dfg(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity) ),
inference(mrr,[status(thm)],[3285,23]),
[iquote('0:MRR:3285.2,23.0')] ).
cnf(3983,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(u,v,add(multiplicative_identity,v)) ),
inference(res,[status(thm),theory(equality)],[6,646]),
[iquote('0:Res:6.0,646.0')] ).
cnf(4021,plain,
( ~ sum__dfg(inverse(u),u,multiplicative_identity)
| equal(add(multiplicative_identity,u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[3983,85]),
[iquote('0:Res:3983.1,85.0')] ).
cnf(4033,plain,
equal(add(multiplicative_identity,u),multiplicative_identity),
inference(mrr,[status(thm)],[4021,22]),
[iquote('0:MRR:4021.0,22.0')] ).
cnf(4077,plain,
sum__dfg(u,multiplicative_identity,multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[4033,53]),
[iquote('0:SpR:4033.0,53.0')] ).
cnf(4651,plain,
( ~ sum__dfg(u,multiplicative_identity,v)
| equal(v,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[4077,26]),
[iquote('0:Res:4077.0,26.0')] ).
cnf(5632,plain,
( ~ product(u,v,additive_identity)
| product(u,v,multiply(additive_identity,v)) ),
inference(res,[status(thm),theory(equality)],[7,965]),
[iquote('0:Res:7.0,965.0')] ).
cnf(6133,plain,
( ~ product(inverse(u),u,additive_identity)
| equal(multiply(additive_identity,u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[5632,57]),
[iquote('0:Res:5632.1,57.0')] ).
cnf(6156,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(mrr,[status(thm)],[6133,24]),
[iquote('0:MRR:6133.0,24.0')] ).
cnf(6232,plain,
product(u,additive_identity,additive_identity),
inference(spr,[status(thm),theory(equality)],[6156,45]),
[iquote('0:SpR:6156.0,45.0')] ).
cnf(6365,plain,
( ~ product(u,additive_identity,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[6232,27]),
[iquote('0:Res:6232.0,27.0')] ).
cnf(7024,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(additive_identity,v,add(inverse(u),v)) ),
inference(res,[status(thm),theory(equality)],[6,648]),
[iquote('0:Res:6.0,648.0')] ).
cnf(7152,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(u,additive_identity,add(u,inverse(v))) ),
inference(res,[status(thm),theory(equality)],[6,832]),
[iquote('0:Res:6.0,832.0')] ).
cnf(8946,plain,
( ~ sum__dfg(u,v,v)
| sum__dfg(multiply(inverse(v),u),additive_identity,additive_identity) ),
inference(res,[status(thm),theory(equality)],[45,2336]),
[iquote('0:Res:45.0,2336.1')] ).
cnf(9350,plain,
( ~ sum__dfg(u,v,w)
| product(add(u,inverse(v)),w,u) ),
inference(res,[status(thm),theory(equality)],[6,935]),
[iquote('0:Res:6.0,935.1')] ).
cnf(9518,plain,
( ~ product(u,v,w)
| sum__dfg(multiply(v,inverse(u)),w,v) ),
inference(res,[status(thm),theory(equality)],[45,1087]),
[iquote('0:Res:45.0,1087.1')] ).
cnf(9817,plain,
( ~ product(u,v,w)
| sum__dfg(multiply(u,inverse(v)),w,u) ),
inference(res,[status(thm),theory(equality)],[7,1327]),
[iquote('0:Res:7.0,1327.1')] ).
cnf(24644,plain,
( ~ product(u,v,w)
| product(add(u,inverse(w)),add(v,inverse(w)),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[6,2305]),
[iquote('0:Res:6.0,2305.1')] ).
cnf(24695,plain,
( ~ product(u,v,w)
| product(add(u,inverse(w)),add(inverse(w),v),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[6,2306]),
[iquote('0:Res:6.0,2306.1')] ).
cnf(25390,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(multiply(u,inverse(w)),multiply(v,inverse(w)),additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,2341]),
[iquote('0:Res:7.0,2341.1')] ).
cnf(25724,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(multiply(u,inverse(w)),multiply(inverse(w),v),additive_identity) ),
inference(res,[status(thm),theory(equality)],[7,2342]),
[iquote('0:Res:7.0,2342.1')] ).
cnf(34680,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| equal(add(inverse(u),v),v) ),
inference(res,[status(thm),theory(equality)],[7024,83]),
[iquote('0:Res:7024.1,83.0')] ).
cnf(35349,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| equal(add(u,inverse(v)),u) ),
inference(res,[status(thm),theory(equality)],[7152,84]),
[iquote('0:Res:7152.1,84.0')] ).
cnf(39622,plain,
( ~ sum__dfg(u,v,additive_identity)
| equal(u,additive_identity) ),
inference(res,[status(thm),theory(equality)],[9350,6365]),
[iquote('0:Res:9350.1,6365.0')] ).
cnf(43206,plain,
( ~ product(u,v,multiplicative_identity)
| equal(u,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[9817,4651]),
[iquote('0:Res:9817.1,4651.0')] ).
cnf(83521,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(v,inverse(u),v) ),
inference(spr,[status(thm),theory(equality)],[34680,53]),
[iquote('0:SpR:34680.1,53.0')] ).
cnf(84383,plain,
( ~ sum__dfg(inverse(u),v,multiplicative_identity)
| sum__dfg(v,u,v) ),
inference(spr,[status(thm),theory(equality)],[1,83521]),
[iquote('0:SpR:1.0,83521.1')] ).
cnf(88454,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(inverse(v),u,u) ),
inference(spr,[status(thm),theory(equality)],[35349,53]),
[iquote('0:SpR:35349.1,53.0')] ).
cnf(89007,plain,
( ~ sum__dfg(u,inverse(v),multiplicative_identity)
| sum__dfg(v,u,u) ),
inference(spr,[status(thm),theory(equality)],[1,88454]),
[iquote('0:SpR:1.0,88454.1')] ).
cnf(91648,plain,
( ~ product(u,v,w)
| equal(add(u,inverse(w)),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[24644,43206]),
[iquote('0:Res:24644.1,43206.0')] ).
cnf(91662,plain,
( ~ product(u,v,w)
| product(multiplicative_identity,add(inverse(w),v),multiplicative_identity) ),
inference(rew,[status(thm),theory(equality)],[91648,24695]),
[iquote('0:Rew:91648.1,24695.1')] ).
cnf(93143,plain,
product(multiplicative_identity,add(inverse(x_inverse_times_y_inverse),inverse(y__dfg)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[4,91662]),
[iquote('0:Res:4.0,91662.0')] ).
cnf(93144,plain,
product(multiplicative_identity,add(inverse(x_inverse_times_y_inverse),inverse(x__dfg)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[44,91662]),
[iquote('0:Res:44.0,91662.0')] ).
cnf(93145,plain,
product(multiplicative_identity,add(inverse(multiply(u,v)),v),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[7,91662]),
[iquote('0:Res:7.0,91662.0')] ).
cnf(93341,plain,
product(multiplicative_identity,add(inverse(y__dfg),inverse(x_inverse_times_y_inverse)),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[283,93143]),
[iquote('0:Rew:283.0,93143.0')] ).
cnf(93342,plain,
product(multiplicative_identity,add(inverse(x__dfg),inverse(x_inverse_times_y_inverse)),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[283,93144]),
[iquote('0:Rew:283.0,93144.0')] ).
cnf(93343,plain,
product(multiplicative_identity,add(u,inverse(multiply(v,u))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[283,93145]),
[iquote('0:Rew:283.0,93145.0')] ).
cnf(93541,plain,
equal(add(inverse(y__dfg),inverse(x_inverse_times_y_inverse)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[93341,55]),
[iquote('0:Res:93341.0,55.0')] ).
cnf(93635,plain,
sum__dfg(inverse(y__dfg),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[93541,6]),
[iquote('0:SpR:93541.0,6.0')] ).
cnf(93772,plain,
sum__dfg(x_inverse_times_y_inverse,inverse(y__dfg),inverse(y__dfg)),
inference(res,[status(thm),theory(equality)],[93635,89007]),
[iquote('0:Res:93635.0,89007.0')] ).
cnf(94293,plain,
sum__dfg(multiply(inverse(inverse(y__dfg)),x_inverse_times_y_inverse),additive_identity,additive_identity),
inference(res,[status(thm),theory(equality)],[93772,8946]),
[iquote('0:Res:93772.0,8946.0')] ).
cnf(94306,plain,
sum__dfg(multiply(y__dfg,x_inverse_times_y_inverse),additive_identity,additive_identity),
inference(rew,[status(thm),theory(equality)],[1,94293]),
[iquote('0:Rew:1.0,94293.0')] ).
cnf(94553,plain,
equal(multiply(y__dfg,x_inverse_times_y_inverse),additive_identity),
inference(res,[status(thm),theory(equality)],[94306,84]),
[iquote('0:Res:94306.0,84.0')] ).
cnf(94652,plain,
product(y__dfg,x_inverse_times_y_inverse,additive_identity),
inference(spr,[status(thm),theory(equality)],[94553,7]),
[iquote('0:SpR:94553.0,7.0')] ).
cnf(94774,plain,
equal(multiply(x_inverse_times_y_inverse,x_plus_y),multiply(x_inverse_times_y_inverse,x__dfg)),
inference(res,[status(thm),theory(equality)],[94652,1452]),
[iquote('0:Res:94652.0,1452.0')] ).
cnf(94779,plain,
equal(multiply(x_plus_y,x_inverse_times_y_inverse),multiply(x__dfg,x_inverse_times_y_inverse)),
inference(rew,[status(thm),theory(equality)],[243,94774]),
[iquote('0:Rew:243.0,94774.0,243.0,94774.0')] ).
cnf(95735,plain,
( ~ sum__dfg(u,v,w)
| equal(multiply(u,inverse(w)),additive_identity) ),
inference(res,[status(thm),theory(equality)],[25390,39622]),
[iquote('0:Res:25390.1,39622.0')] ).
cnf(95743,plain,
( ~ sum__dfg(u,v,w)
| sum__dfg(additive_identity,multiply(inverse(w),v),additive_identity) ),
inference(rew,[status(thm),theory(equality)],[95735,25724]),
[iquote('0:Rew:95735.1,25724.1')] ).
cnf(96010,plain,
product(x_plus_y,x_inverse_times_y_inverse,multiply(x__dfg,x_inverse_times_y_inverse)),
inference(spr,[status(thm),theory(equality)],[94779,7]),
[iquote('0:SpR:94779.0,7.0')] ).
cnf(96300,plain,
equal(add(inverse(x__dfg),inverse(x_inverse_times_y_inverse)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[93342,55]),
[iquote('0:Res:93342.0,55.0')] ).
cnf(96393,plain,
sum__dfg(inverse(x__dfg),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[96300,6]),
[iquote('0:SpR:96300.0,6.0')] ).
cnf(96535,plain,
sum__dfg(inverse(x_inverse_times_y_inverse),x__dfg,inverse(x_inverse_times_y_inverse)),
inference(res,[status(thm),theory(equality)],[96393,84383]),
[iquote('0:Res:96393.0,84383.0')] ).
cnf(96926,plain,
sum__dfg(additive_identity,multiply(inverse(x_plus_y),y__dfg),additive_identity),
inference(res,[status(thm),theory(equality)],[3,95743]),
[iquote('0:Res:3.0,95743.0')] ).
cnf(97034,plain,
sum__dfg(additive_identity,multiply(inverse(inverse(x_inverse_times_y_inverse)),x__dfg),additive_identity),
inference(res,[status(thm),theory(equality)],[96535,95743]),
[iquote('0:Res:96535.0,95743.0')] ).
cnf(97098,plain,
sum__dfg(additive_identity,multiply(y__dfg,inverse(x_plus_y)),additive_identity),
inference(rew,[status(thm),theory(equality)],[243,96926]),
[iquote('0:Rew:243.0,96926.0')] ).
cnf(97108,plain,
sum__dfg(additive_identity,multiply(x__dfg,x_inverse_times_y_inverse),additive_identity),
inference(rew,[status(thm),theory(equality)],[243,97034,1]),
[iquote('0:Rew:243.0,97034.0,1.0,97034.0')] ).
cnf(97256,plain,
equal(multiply(x__dfg,x_inverse_times_y_inverse),additive_identity),
inference(res,[status(thm),theory(equality)],[97108,83]),
[iquote('0:Res:97108.0,83.0')] ).
cnf(97285,plain,
product(x_plus_y,x_inverse_times_y_inverse,additive_identity),
inference(rew,[status(thm),theory(equality)],[97256,96010]),
[iquote('0:Rew:97256.0,96010.0')] ).
cnf(97368,plain,
~ sum__dfg(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(mrr,[status(thm)],[3291,97285]),
[iquote('0:MRR:3291.0,97285.0')] ).
cnf(98823,plain,
equal(multiply(y__dfg,inverse(x_plus_y)),additive_identity),
inference(res,[status(thm),theory(equality)],[97098,83]),
[iquote('0:Res:97098.0,83.0')] ).
cnf(98960,plain,
product(y__dfg,inverse(x_plus_y),additive_identity),
inference(spr,[status(thm),theory(equality)],[98823,7]),
[iquote('0:SpR:98823.0,7.0')] ).
cnf(99011,plain,
( ~ product(x_plus_y,y__dfg,u)
| sum__dfg(additive_identity,u,y__dfg) ),
inference(spr,[status(thm),theory(equality)],[98823,9518]),
[iquote('0:SpR:98823.0,9518.1')] ).
cnf(99035,plain,
equal(multiply(x__dfg,inverse(x_plus_y)),additive_identity),
inference(mrr,[status(thm)],[1427,98960]),
[iquote('0:MRR:1427.0,98960.0')] ).
cnf(99315,plain,
( ~ product(x_plus_y,x__dfg,u)
| sum__dfg(additive_identity,u,x__dfg) ),
inference(spr,[status(thm),theory(equality)],[99035,9518]),
[iquote('0:SpR:99035.0,9518.1')] ).
cnf(102501,plain,
sum__dfg(additive_identity,multiply(x_plus_y,y__dfg),y__dfg),
inference(res,[status(thm),theory(equality)],[7,99011]),
[iquote('0:Res:7.0,99011.0')] ).
cnf(102562,plain,
sum__dfg(additive_identity,multiply(y__dfg,x_plus_y),y__dfg),
inference(rew,[status(thm),theory(equality)],[243,102501]),
[iquote('0:Rew:243.0,102501.0')] ).
cnf(102612,plain,
equal(multiply(y__dfg,x_plus_y),y__dfg),
inference(res,[status(thm),theory(equality)],[102562,83]),
[iquote('0:Res:102562.0,83.0')] ).
cnf(105227,plain,
sum__dfg(additive_identity,multiply(x_plus_y,x__dfg),x__dfg),
inference(res,[status(thm),theory(equality)],[7,99315]),
[iquote('0:Res:7.0,99315.0')] ).
cnf(105283,plain,
sum__dfg(additive_identity,multiply(x__dfg,x_plus_y),x__dfg),
inference(rew,[status(thm),theory(equality)],[243,105227]),
[iquote('0:Rew:243.0,105227.0')] ).
cnf(105336,plain,
equal(multiply(x__dfg,x_plus_y),x__dfg),
inference(res,[status(thm),theory(equality)],[105283,83]),
[iquote('0:Res:105283.0,83.0')] ).
cnf(108803,plain,
product(multiplicative_identity,add(x_plus_y,inverse(y__dfg)),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[102612,93343]),
[iquote('0:SpR:102612.0,93343.0')] ).
cnf(108804,plain,
product(multiplicative_identity,add(x_plus_y,inverse(x__dfg)),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[105336,93343]),
[iquote('0:SpR:105336.0,93343.0')] ).
cnf(109028,plain,
equal(add(x_plus_y,inverse(y__dfg)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[108803,55]),
[iquote('0:Res:108803.0,55.0')] ).
cnf(109122,plain,
sum__dfg(x_plus_y,inverse(y__dfg),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[109028,6]),
[iquote('0:SpR:109028.0,6.0')] ).
cnf(109336,plain,
( ~ sum__dfg(x_plus_y,inverse(x__dfg),multiplicative_identity)
| sum__dfg(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[109122,833]),
[iquote('0:Res:109122.0,833.0')] ).
cnf(109365,plain,
~ sum__dfg(x_plus_y,inverse(x__dfg),multiplicative_identity),
inference(mrr,[status(thm)],[109336,97368]),
[iquote('0:MRR:109336.1,97368.0')] ).
cnf(110481,plain,
equal(add(x_plus_y,inverse(x__dfg)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[108804,55]),
[iquote('0:Res:108804.0,55.0')] ).
cnf(110575,plain,
sum__dfg(x_plus_y,inverse(x__dfg),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[110481,6]),
[iquote('0:SpR:110481.0,6.0')] ).
cnf(110654,plain,
$false,
inference(mrr,[status(thm)],[110575,109365]),
[iquote('0:MRR:110575.0,109365.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 1 23:03:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 177.35/177.60
% 177.35/177.60 SPASS V 3.9
% 177.35/177.60 SPASS beiseite: Proof found.
% 177.35/177.60 % SZS status Theorem
% 177.35/177.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 177.35/177.60 SPASS derived 83030 clauses, backtracked 0 clauses, performed 0 splits and kept 27185 clauses.
% 177.35/177.60 SPASS allocated 126955 KBytes.
% 177.35/177.60 SPASS spent 0:2:57.16 on the problem.
% 177.35/177.60 0:00:00.03 for the input.
% 177.35/177.60 0:00:00.00 for the FLOTTER CNF translation.
% 177.35/177.60 0:00:01.00 for inferences.
% 177.35/177.60 0:00:00.00 for the backtracking.
% 177.35/177.60 0:2:55.30 for the reduction.
% 177.35/177.60
% 177.35/177.60
% 177.35/177.60 Here is a proof with depth 12, length 147 :
% 177.35/177.60 % SZS output start Refutation
% See solution above
% 178.53/178.73 Formulae used in the proof : inverse_is_self_cancelling inverse_is_unique x_plus_y x_inverse_times_y_inverse prove_equation closure_of_addition closure_of_multiplication commutativity_of_addition commutativity_of_multiplication additive_identity1 additive_identity2 multiplicative_identity1 multiplicative_identity2 distributivity1 distributivity3 distributivity4 distributivity5 distributivity6 distributivity7 distributivity8 additive_inverse1 additive_inverse2 multiplicative_inverse1 multiplicative_inverse2 addition_is_well_defined multiplication_is_well_defined
% 178.53/178.73
%------------------------------------------------------------------------------