TSTP Solution File: BOO035-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO035-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 23:49:30 EDT 2022
% Result : Unsatisfiable 1.65s 1.89s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 68 ( 58 unt; 0 nHn; 68 RR)
% Number of literals : 94 ( 0 equ; 37 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,y),z,multiply(w,x,x1))),multiply(x,multiply(x1,z,y),w)),v),
file('BOO035-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(multiply(a,b,inverse(b)),a)
| ~ equal(multiply(inverse(b),b,a),a)
| ~ equal(multiply(multiply(d,e,a),b,multiply(d,e,c)),multiply(d,e,multiply(a,b,c))) ),
file('BOO035-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,multiply(y,multiply(z,x1,x2),x3)),inverse(multiply(multiply(x3,y,x2),x1,multiply(x3,y,z))),multiply(w,x,multiply(x4,inverse(x4),x5)))),multiply(x,x5,w)),v),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,v,w),inverse(multiply(multiply(x,y,z),x1,multiply(x,y,x2))),multiply(y,multiply(x2,x1,z),x)),multiply(v,multiply(w,inverse(multiply(u,v,x3)),x3),u)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(13,plain,
equal(multiply(inverse(u),multiply(v,inverse(multiply(u,inverse(u),w)),w),u),v),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(14,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,u,x)),x),w),multiply(u,multiply(v,inverse(multiply(w,u,y)),y),w)),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(39,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,y),multiply(z,inverse(multiply(y,inverse(y),x1)),x1),multiply(w,x,inverse(y)))),multiply(x,z,w)),v),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(48,plain,
equal(multiply(multiply(u,v,w),inverse(multiply(multiply(x,y,z),multiply(x1,inverse(multiply(z,inverse(z),x2)),x2),multiply(x,y,inverse(z)))),multiply(y,x1,x)),multiply(v,multiply(w,inverse(multiply(u,v,x3)),x3),u)),
inference(spr,[status(thm),theory(equality)],[13,6]),
[iquote('0:SpR:13.0,6.0')] ).
cnf(94,plain,
equal(multiply(multiply(u,inverse(multiply(v,inverse(v),w)),w),multiply(x,inverse(multiply(inverse(v),multiply(u,inverse(multiply(v,inverse(v),w)),w),y)),y),inverse(v)),multiply(multiply(u,inverse(multiply(v,inverse(v),w)),w),multiply(x,inverse(u),v),inverse(v))),
inference(spr,[status(thm),theory(equality)],[13,14]),
[iquote('0:SpR:13.0,14.0')] ).
cnf(179,plain,
equal(multiply(multiply(inverse(u),inverse(multiply(u,inverse(u),v)),v),multiply(multiply(w,inverse(w),x),inverse(multiply(multiply(inverse(u),inverse(u),u),multiply(inverse(u),inverse(multiply(u,inverse(u),v)),v),y)),y),multiply(inverse(u),inverse(u),u)),multiply(multiply(inverse(u),inverse(multiply(u,inverse(u),v)),v),x,multiply(inverse(u),inverse(u),u))),
inference(spr,[status(thm),theory(equality)],[39,14]),
[iquote('0:SpR:39.0,14.0')] ).
cnf(213,plain,
equal(multiply(multiply(u,multiply(multiply(v,w,x),inverse(multiply(multiply(v,w,y),u,z)),z),multiply(v,w,y)),inverse(multiply(multiply(x1,x2,x3),multiply(x4,inverse(multiply(x3,inverse(x3),x5)),x5),multiply(x1,x2,inverse(x3)))),multiply(x2,x4,x1)),multiply(w,multiply(x,u,y),v)),
inference(spr,[status(thm),theory(equality)],[6,39]),
[iquote('0:SpR:6.0,39.0')] ).
cnf(422,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,multiply(inverse(x),multiply(inverse(w),inverse(multiply(x,inverse(x),y)),y),x),multiply(z,inverse(z),x1))),multiply(inverse(w),x1,w)),v),
inference(spr,[status(thm),theory(equality)],[39,3]),
[iquote('0:SpR:39.0,3.0')] ).
cnf(428,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,inverse(w),multiply(x,inverse(x),y))),multiply(inverse(w),y,w)),v),
inference(rew,[status(thm),theory(equality)],[13,422]),
[iquote('0:Rew:13.0,422.0')] ).
cnf(459,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,inverse(w),multiply(x,inverse(x),y))),multiply(inverse(w),y,w)),multiply(inverse(z),v,z)),
inference(spr,[status(thm),theory(equality)],[428]),
[iquote('0:SpR:428.0,428.0')] ).
cnf(467,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,inverse(w),inverse(inverse(x)))),multiply(inverse(multiply(x,inverse(x),multiply(w,inverse(w),inverse(inverse(x))))),x,multiply(x,inverse(x),multiply(w,inverse(w),inverse(inverse(x)))))),v),
inference(spr,[status(thm),theory(equality)],[428]),
[iquote('0:SpR:428.0,428.0')] ).
cnf(498,plain,
equal(multiply(inverse(u),v,u),v),
inference(rew,[status(thm),theory(equality)],[428,459]),
[iquote('0:Rew:428.0,459.0')] ).
cnf(500,plain,
equal(multiply(u,inverse(multiply(v,inverse(v),w)),w),u),
inference(rew,[status(thm),theory(equality)],[498,13]),
[iquote('0:Rew:498.0,13.0')] ).
cnf(519,plain,
equal(multiply(multiply(inverse(u),inverse(multiply(u,inverse(u),v)),v),multiply(multiply(w,inverse(w),x),inverse(multiply(inverse(u),multiply(inverse(u),inverse(multiply(u,inverse(u),v)),v),y)),y),inverse(u)),multiply(multiply(inverse(u),inverse(multiply(u,inverse(u),v)),v),x,inverse(u))),
inference(rew,[status(thm),theory(equality)],[498,179]),
[iquote('0:Rew:498.0,179.0')] ).
cnf(521,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,y),z,multiply(w,x,inverse(y)))),multiply(x,z,w)),v),
inference(rew,[status(thm),theory(equality)],[500,39]),
[iquote('0:Rew:500.0,39.0')] ).
cnf(549,plain,
equal(multiply(multiply(u,multiply(multiply(v,w,x),inverse(multiply(multiply(v,w,y),u,z)),z),multiply(v,w,y)),inverse(multiply(multiply(x1,x2,x3),x4,multiply(x1,x2,inverse(x3)))),multiply(x2,x4,x1)),multiply(w,multiply(x,u,y),v)),
inference(rew,[status(thm),theory(equality)],[500,213]),
[iquote('0:Rew:500.0,213.0')] ).
cnf(575,plain,
equal(multiply(u,multiply(v,inverse(multiply(inverse(w),u,x)),x),inverse(w)),multiply(u,multiply(v,inverse(u),w),inverse(w))),
inference(rew,[status(thm),theory(equality)],[500,94]),
[iquote('0:Rew:500.0,94.0')] ).
cnf(579,plain,
equal(multiply(multiply(u,v,w),inverse(multiply(multiply(x,y,z),x1,multiply(x,y,inverse(z)))),multiply(y,x1,x)),multiply(v,multiply(w,inverse(multiply(u,v,x2)),x2),u)),
inference(rew,[status(thm),theory(equality)],[500,48]),
[iquote('0:Rew:500.0,48.0')] ).
cnf(606,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,inverse(w),inverse(inverse(x)))),x),v),
inference(rew,[status(thm),theory(equality)],[498,467]),
[iquote('0:Rew:498.0,467.0')] ).
cnf(618,plain,
equal(multiply(inverse(u),multiply(multiply(v,inverse(v),w),inverse(inverse(u)),u),inverse(u)),multiply(inverse(u),w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[575,519,500]),
[iquote('0:Rew:575.0,519.0,500.0,519.0')] ).
cnf(646,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,inverse(w),x),y,multiply(w,inverse(w),z))),multiply(z,y,x)),v),
inference(spr,[status(thm),theory(equality)],[498,1]),
[iquote('0:SpR:498.0,1.0')] ).
cnf(658,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(multiply(v,w,x),y,multiply(v,w,z))),multiply(w,multiply(z,y,x),v)),u),
inference(spr,[status(thm),theory(equality)],[498,1]),
[iquote('0:SpR:498.0,1.0')] ).
cnf(687,plain,
equal(multiply(inverse(multiply(u,inverse(u),v)),multiply(w,inverse(multiply(x,inverse(multiply(u,inverse(u),v)),y)),y),x),multiply(inverse(multiply(u,inverse(u),v)),multiply(w,inverse(x),v),x)),
inference(spr,[status(thm),theory(equality)],[500,14]),
[iquote('0:SpR:500.0,14.0')] ).
cnf(699,plain,
equal(inverse(multiply(u,inverse(u),v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[500,498]),
[iquote('0:SpR:500.0,498.0')] ).
cnf(711,plain,
equal(multiply(u,inverse(inverse(inverse(v))),v),u),
inference(spr,[status(thm),theory(equality)],[498,500]),
[iquote('0:SpR:498.0,500.0')] ).
cnf(712,plain,
equal(multiply(u,inverse(v),v),u),
inference(rew,[status(thm),theory(equality)],[699,500]),
[iquote('0:Rew:699.0,500.0')] ).
cnf(761,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(inverse(inverse(w))),w),v),
inference(rew,[status(thm),theory(equality)],[699,606]),
[iquote('0:Rew:699.0,606.0')] ).
cnf(794,plain,
equal(multiply(u,inverse(u),v),v),
inference(rew,[status(thm),theory(equality)],[711,761]),
[iquote('0:Rew:711.0,761.0')] ).
cnf(796,plain,
equal(multiply(u,inverse(multiply(multiply(v,w,x),y,multiply(v,w,z))),multiply(w,multiply(z,y,x),v)),u),
inference(rew,[status(thm),theory(equality)],[794,1]),
[iquote('0:Rew:794.0,1.0')] ).
cnf(819,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,inverse(w),x),y,z)),multiply(z,y,x)),v),
inference(rew,[status(thm),theory(equality)],[794,646]),
[iquote('0:Rew:794.0,646.0')] ).
cnf(870,plain,
equal(multiply(inverse(u),multiply(v,inverse(inverse(u)),u),inverse(u)),multiply(inverse(u),v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[794,618]),
[iquote('0:Rew:794.0,618.0')] ).
cnf(891,plain,
equal(multiply(u,inverse(multiply(multiply(v,w,x),y,multiply(v,w,inverse(x)))),multiply(w,y,v)),u),
inference(rew,[status(thm),theory(equality)],[794,521]),
[iquote('0:Rew:794.0,521.0')] ).
cnf(917,plain,
equal(multiply(u,multiply(multiply(v,w,x),inverse(multiply(multiply(v,w,y),u,z)),z),multiply(v,w,y)),multiply(w,multiply(x,u,y),v)),
inference(rew,[status(thm),theory(equality)],[891,549]),
[iquote('0:Rew:891.0,549.0')] ).
cnf(918,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,u,x)),x),w),multiply(w,u,v)),
inference(rew,[status(thm),theory(equality)],[891,579]),
[iquote('0:Rew:891.0,579.0')] ).
cnf(921,plain,
equal(multiply(u,multiply(v,inverse(u),w),inverse(w)),multiply(inverse(w),u,v)),
inference(rew,[status(thm),theory(equality)],[918,575]),
[iquote('0:Rew:918.0,575.0')] ).
cnf(951,plain,
equal(multiply(inverse(u),inverse(u),v),multiply(inverse(u),v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[921,870]),
[iquote('0:Rew:921.0,870.0')] ).
cnf(956,plain,
equal(multiply(u,inverse(multiply(v,w,x)),multiply(x,w,v)),u),
inference(rew,[status(thm),theory(equality)],[794,819]),
[iquote('0:Rew:794.0,819.0,794.0,819.0')] ).
cnf(959,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[796,658]),
[iquote('0:Rew:796.0,658.0')] ).
cnf(973,plain,
equal(multiply(multiply(u,v,w),x,multiply(u,v,y)),multiply(v,multiply(y,x,w),u)),
inference(rew,[status(thm),theory(equality)],[918,917]),
[iquote('0:Rew:918.0,917.0')] ).
cnf(974,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(multiply(a,b,inverse(b)),a)
| ~ equal(multiply(inverse(b),b,a),a)
| ~ equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))) ),
inference(rew,[status(thm),theory(equality)],[973,2]),
[iquote('0:Rew:973.0,2.4')] ).
cnf(1009,plain,
equal(multiply(inverse(u),multiply(v,inverse(w),u),w),multiply(w,inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[918,687,794]),
[iquote('0:Rew:918.0,687.0,794.0,687.0')] ).
cnf(1252,plain,
equal(multiply(u,v,inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[959,498]),
[iquote('0:SpR:959.0,498.0')] ).
cnf(1258,plain,
equal(multiply(u,v,inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[959,712]),
[iquote('0:SpR:959.0,712.0')] ).
cnf(1259,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(a,a)
| ~ equal(multiply(inverse(b),b,a),a)
| ~ equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))) ),
inference(rew,[status(thm),theory(equality)],[1258,974]),
[iquote('0:Rew:1258.0,974.2')] ).
cnf(1261,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(multiply(inverse(b),b,a),a)
| ~ equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))) ),
inference(obv,[status(thm),theory(equality)],[1259]),
[iquote('0:Obv:1259.2')] ).
cnf(1265,plain,
equal(multiply(inverse(u),u,v),v),
inference(spr,[status(thm),theory(equality)],[959,794]),
[iquote('0:SpR:959.0,794.0')] ).
cnf(1266,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(a,a)
| ~ equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))) ),
inference(rew,[status(thm),theory(equality)],[1265,1261]),
[iquote('0:Rew:1265.0,1261.2')] ).
cnf(1268,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(multiply(e,multiply(c,b,a),d),multiply(d,e,multiply(a,b,c))) ),
inference(obv,[status(thm),theory(equality)],[1266]),
[iquote('0:Obv:1266.2')] ).
cnf(1292,plain,
equal(multiply(u,u,v),multiply(u,v,u)),
inference(spr,[status(thm),theory(equality)],[959,951]),
[iquote('0:SpR:959.0,951.0')] ).
cnf(1307,plain,
equal(multiply(u,v,w),multiply(w,v,u)),
inference(spr,[status(thm),theory(equality)],[956,794]),
[iquote('0:SpR:956.0,794.0')] ).
cnf(1329,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(b,a,a),a)
| ~ equal(multiply(d,multiply(c,b,a),e),multiply(d,e,multiply(a,b,c))) ),
inference(rew,[status(thm),theory(equality)],[1307,1268]),
[iquote('0:Rew:1307.0,1268.2')] ).
cnf(1359,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(d,multiply(a,b,c),e),multiply(d,e,multiply(a,b,c))) ),
inference(rew,[status(thm),theory(equality)],[1307,1329]),
[iquote('0:Rew:1307.0,1329.2,1307.0,1329.1')] ).
cnf(1360,plain,
( ~ equal(multiply(a,a,b),a)
| ~ equal(multiply(d,multiply(a,b,c),e),multiply(d,e,multiply(a,b,c))) ),
inference(obv,[status(thm),theory(equality)],[1359]),
[iquote('0:Obv:1359.0')] ).
cnf(1924,plain,
equal(multiply(inverse(u),multiply(v,inverse(w),u),w),multiply(inverse(u),w,v)),
inference(spr,[status(thm),theory(equality)],[921,1307]),
[iquote('0:SpR:921.0,1307.0')] ).
cnf(1953,plain,
equal(multiply(u,inverse(u),inverse(inverse(v))),multiply(inverse(inverse(v)),u,v)),
inference(spr,[status(thm),theory(equality)],[1252,921]),
[iquote('0:SpR:1252.0,921.0')] ).
cnf(1967,plain,
equal(multiply(u,v,u),u),
inference(rew,[status(thm),theory(equality)],[794,1953,959]),
[iquote('0:Rew:794.0,1953.0,959.0,1953.0')] ).
cnf(1971,plain,
equal(multiply(u,u,v),u),
inference(rew,[status(thm),theory(equality)],[1967,1292]),
[iquote('0:Rew:1967.0,1292.0')] ).
cnf(2004,plain,
( ~ equal(a,a)
| ~ equal(multiply(d,multiply(a,b,c),e),multiply(d,e,multiply(a,b,c))) ),
inference(rew,[status(thm),theory(equality)],[1971,1360]),
[iquote('0:Rew:1971.0,1360.0')] ).
cnf(2039,plain,
equal(multiply(u,inverse(v),w),multiply(inverse(v),u,w)),
inference(rew,[status(thm),theory(equality)],[1009,1924]),
[iquote('0:Rew:1009.0,1924.0')] ).
cnf(2063,plain,
~ equal(multiply(d,multiply(a,b,c),e),multiply(d,e,multiply(a,b,c))),
inference(obv,[status(thm),theory(equality)],[2004]),
[iquote('0:Obv:2004.0')] ).
cnf(2176,plain,
equal(multiply(u,v,w),multiply(v,u,w)),
inference(spr,[status(thm),theory(equality)],[959,2039]),
[iquote('0:SpR:959.0,2039.0')] ).
cnf(2202,plain,
equal(multiply(u,v,w),multiply(w,u,v)),
inference(spr,[status(thm),theory(equality)],[2176,1307]),
[iquote('0:SpR:2176.0,1307.0')] ).
cnf(2239,plain,
equal(multiply(u,v,w),multiply(u,w,v)),
inference(spr,[status(thm),theory(equality)],[2202,1307]),
[iquote('0:SpR:2202.0,1307.0')] ).
cnf(2274,plain,
$false,
inference(unc,[status(thm)],[2239,2063]),
[iquote('0:UnC:2239.0,2063.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO035-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 17:30:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.65/1.89
% 1.65/1.89 SPASS V 3.9
% 1.65/1.89 SPASS beiseite: Proof found.
% 1.65/1.89 % SZS status Theorem
% 1.65/1.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.89 SPASS derived 1580 clauses, backtracked 0 clauses, performed 0 splits and kept 582 clauses.
% 1.65/1.89 SPASS allocated 72080 KBytes.
% 1.65/1.89 SPASS spent 0:00:01.53 on the problem.
% 1.65/1.89 0:00:00.04 for the input.
% 1.65/1.89 0:00:00.00 for the FLOTTER CNF translation.
% 1.65/1.89 0:00:00.02 for inferences.
% 1.65/1.89 0:00:00.00 for the backtracking.
% 1.65/1.89 0:00:01.45 for the reduction.
% 1.65/1.89
% 1.65/1.89
% 1.65/1.89 Here is a proof with depth 11, length 68 :
% 1.65/1.89 % SZS output start Refutation
% See solution above
% 1.73/1.92 Formulae used in the proof : single_axiom prove_tba_axioms
% 1.73/1.92
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