TSTP Solution File: GRP092-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP092-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:45:16 EDT 2022
% Result : Unsatisfiable 0.36s 0.53s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 63 ( 55 unt; 0 nHn; 63 RR)
% Number of literals : 79 ( 0 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,v),divide(divide(u,w),v)),w),
file('GRP092-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP092-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP092-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP092-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP092-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(9,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(15,plain,
equal(divide(u,identity),multiply(u,identity)),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(16,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(identity,a2),a2) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.3')] ).
cnf(17,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[13,16,12]),
[iquote('0:Rew:13.0,16.3,12.0,16.1,12.0,16.1')] ).
cnf(18,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(obv,[status(thm),theory(equality)],[17]),
[iquote('0:Obv:17.1')] ).
cnf(23,plain,
equal(divide(divide(u,v),divide(identity,v)),u),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(26,plain,
equal(divide(divide(u,divide(u,v)),identity),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(27,plain,
equal(divide(divide(u,inverse(v)),multiply(divide(u,w),v)),w),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(28,plain,
equal(divide(identity,divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(31,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[7,23,6]),
[iquote('0:Rew:7.0,23.0,6.0,23.0')] ).
cnf(32,plain,
equal(multiply(divide(u,divide(u,v)),identity),v),
inference(rew,[status(thm),theory(equality)],[15,26]),
[iquote('0:Rew:15.0,26.0')] ).
cnf(33,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(rew,[status(thm),theory(equality)],[6,28]),
[iquote('0:Rew:6.0,28.0')] ).
cnf(36,plain,
equal(divide(multiply(u,v),multiply(divide(u,w),v)),w),
inference(rew,[status(thm),theory(equality)],[7,27]),
[iquote('0:Rew:7.0,27.0')] ).
cnf(55,plain,
equal(multiply(identity,u),u),
inference(spr,[status(thm),theory(equality)],[4,31]),
[iquote('0:SpR:4.0,31.0')] ).
cnf(57,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[7,31]),
[iquote('0:SpR:7.0,31.0')] ).
cnf(60,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,55]),
[iquote('0:Rew:13.0,55.0')] ).
cnf(62,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[60,18]),
[iquote('0:Rew:60.0,18.2')] ).
cnf(63,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[62]),
[iquote('0:Obv:62.2')] ).
cnf(66,plain,
equal(multiply(u,inverse(v)),divide(u,v)),
inference(spr,[status(thm),theory(equality)],[60,7]),
[iquote('0:SpR:60.0,7.0')] ).
cnf(69,plain,
equal(divide(multiply(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[66,57]),
[iquote('0:Rew:66.0,57.0')] ).
cnf(90,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[33,60]),
[iquote('0:SpR:33.0,60.0')] ).
cnf(94,plain,
equal(inverse(divide(inverse(u),identity)),u),
inference(spr,[status(thm),theory(equality)],[6,33]),
[iquote('0:SpR:6.0,33.0')] ).
cnf(102,plain,
equal(inverse(multiply(inverse(u),identity)),u),
inference(rew,[status(thm),theory(equality)],[15,94]),
[iquote('0:Rew:15.0,94.0')] ).
cnf(109,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(spr,[status(thm),theory(equality)],[102,60]),
[iquote('0:SpR:102.0,60.0')] ).
cnf(126,plain,
equal(multiply(u,identity),u),
inference(spr,[status(thm),theory(equality)],[60,109]),
[iquote('0:SpR:60.0,109.0')] ).
cnf(129,plain,
equal(divide(u,divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[126,32]),
[iquote('0:Rew:126.0,32.0')] ).
cnf(149,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[129,31]),
[iquote('0:SpR:129.0,31.0')] ).
cnf(156,plain,
equal(divide(u,multiply(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[7,129]),
[iquote('0:SpR:7.0,129.0')] ).
cnf(179,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[69,149]),
[iquote('0:SpR:69.0,149.0')] ).
cnf(181,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[179,63]),
[iquote('0:Rew:179.0,63.1')] ).
cnf(186,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[179,181]),
[iquote('0:Rew:179.0,181.0')] ).
cnf(187,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[186]),
[iquote('0:Obv:186.0')] ).
cnf(212,plain,
equal(multiply(inverse(u),v),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[66,179]),
[iquote('0:SpR:66.0,179.0')] ).
cnf(233,plain,
equal(inverse(divide(u,v)),divide(v,u)),
inference(spr,[status(thm),theory(equality)],[129,90]),
[iquote('0:SpR:129.0,90.0')] ).
cnf(245,plain,
equal(divide(inverse(u),v),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[156,90]),
[iquote('0:SpR:156.0,90.0')] ).
cnf(268,plain,
equal(divide(inverse(u),v),divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[212,66]),
[iquote('0:SpR:212.0,66.0')] ).
cnf(279,plain,
equal(inverse(multiply(u,v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[245,268]),
[iquote('0:Rew:245.0,268.0,245.0,268.0')] ).
cnf(301,plain,
equal(multiply(multiply(divide(u,v),w),v),multiply(u,w)),
inference(spr,[status(thm),theory(equality)],[36,149]),
[iquote('0:SpR:36.0,149.0')] ).
cnf(302,plain,
equal(divide(multiply(u,v),w),multiply(divide(u,w),v)),
inference(spr,[status(thm),theory(equality)],[36,129]),
[iquote('0:SpR:36.0,129.0')] ).
cnf(333,plain,
equal(multiply(u,multiply(divide(v,u),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[179,301]),
[iquote('0:Rew:179.0,301.0')] ).
cnf(381,plain,
equal(divide(u,divide(v,w)),multiply(divide(w,v),u)),
inference(spr,[status(thm),theory(equality)],[233,212]),
[iquote('0:SpR:233.0,212.0')] ).
cnf(444,plain,
equal(divide(u,inverse(multiply(v,w))),multiply(u,multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[279,7]),
[iquote('0:SpR:279.0,7.0')] ).
cnf(478,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[7,444]),
[iquote('0:Rew:7.0,444.0')] ).
cnf(653,plain,
equal(multiply(u,multiply(divide(v,divide(u,w)),x)),multiply(w,multiply(v,x))),
inference(spr,[status(thm),theory(equality)],[333]),
[iquote('0:SpR:333.0,333.0')] ).
cnf(685,plain,
equal(multiply(u,multiply(multiply(divide(v,u),w),x)),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[381,653]),
[iquote('0:Rew:381.0,653.0')] ).
cnf(690,plain,
equal(multiply(u,multiply(multiply(divide(v,u),w),x)),multiply(multiply(v,w),x)),
inference(spr,[status(thm),theory(equality)],[302,333]),
[iquote('0:SpR:302.0,333.0')] ).
cnf(721,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[685,690]),
[iquote('0:Rew:685.0,690.0')] ).
cnf(1013,plain,
equal(multiply(u,multiply(v,w)),multiply(multiply(w,v),u)),
inference(spr,[status(thm),theory(equality)],[478,179]),
[iquote('0:SpR:478.0,179.0')] ).
cnf(1069,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[721,1013]),
[iquote('0:Rew:721.0,1013.0')] ).
cnf(1070,plain,
~ equal(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[1069,187]),
[iquote('0:Rew:1069.0,187.0')] ).
cnf(1437,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[721,179]),
[iquote('0:SpR:721.0,179.0')] ).
cnf(1474,plain,
~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[1437,1070]),
[iquote('0:Rew:1437.0,1070.0')] ).
cnf(1486,plain,
~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[179,1474]),
[iquote('0:Rew:179.0,1474.0')] ).
cnf(1487,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1486]),
[iquote('0:Obv:1486.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP092-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 05:21:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.36/0.53
% 0.36/0.53 SPASS V 3.9
% 0.36/0.53 SPASS beiseite: Proof found.
% 0.36/0.53 % SZS status Theorem
% 0.36/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.53 SPASS derived 796 clauses, backtracked 0 clauses, performed 0 splits and kept 160 clauses.
% 0.36/0.53 SPASS allocated 64300 KBytes.
% 0.36/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.36/0.53 0:00:00.04 for the input.
% 0.36/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.53 0:00:00.01 for inferences.
% 0.36/0.53 0:00:00.00 for the backtracking.
% 0.36/0.53 0:00:00.10 for the reduction.
% 0.36/0.53
% 0.36/0.53
% 0.36/0.53 Here is a proof with depth 7, length 63 :
% 0.36/0.53 % SZS output start Refutation
% See solution above
% 0.36/0.53 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.36/0.53
%------------------------------------------------------------------------------