TSTP Solution File: GRP077-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:45:11 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of clauses : 75 ( 69 unt; 0 nHn; 75 RR)
% Number of literals : 85 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(u,double_divide(double_divide(double_divide(identity,double_divide(double_divide(u,identity),double_divide(v,w))),v),identity)),w),
file('GRP077-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP077-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP077-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP077-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(multiply(inverse(a1),a1),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
file('GRP077-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),double_divide(v,w))))),w),
inference(rew,[status(thm),theory(equality)],[6,1,3]),
[iquote('0:Rew:6.0,1.0,3.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
( ~ equal(multiply(identity,a2),a2)
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.1')] ).
cnf(15,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(inverse(identity),identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(17,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(21,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),identity)))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(24,plain,
equal(double_divide(u,multiply(v,double_divide(identity,inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[3,21]),
[iquote('0:Rew:3.0,21.0')] ).
cnf(26,plain,
equal(double_divide(u,inverse(inverse(double_divide(identity,double_divide(inverse(u),double_divide(identity,v)))))),v),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(27,plain,
equal(double_divide(u,inverse(multiply(double_divide(inverse(u),double_divide(identity,v)),identity))),v),
inference(rew,[status(thm),theory(equality)],[6,26]),
[iquote('0:Rew:6.0,26.0')] ).
cnf(62,plain,
equal(multiply(multiply(u,double_divide(identity,inverse(inverse(v)))),v),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[24,6]),
[iquote('0:SpR:24.0,6.0')] ).
cnf(69,plain,
equal(double_divide(u,inverse(inverse(double_divide(identity,inverse(inverse(u)))))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[13,24]),
[iquote('0:SpR:13.0,24.0')] ).
cnf(70,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),double_divide(u,inverse(identity))),
inference(spr,[status(thm),theory(equality)],[17,24]),
[iquote('0:SpR:17.0,24.0')] ).
cnf(72,plain,
equal(double_divide(u,inverse(multiply(inverse(inverse(u)),identity))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[6,69]),
[iquote('0:Rew:6.0,69.0')] ).
cnf(73,plain,
equal(double_divide(u,double_divide(u,inverse(identity))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[70,72]),
[iquote('0:Rew:70.0,72.0')] ).
cnf(81,plain,
equal(double_divide(u,multiply(inverse(u),double_divide(identity,inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[73,7]),
[iquote('0:SpR:73.0,7.0')] ).
cnf(86,plain,
equal(double_divide(u,multiply(inverse(u),identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[4,81]),
[iquote('0:Rew:4.0,81.0')] ).
cnf(102,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),inverse(identity))))),multiply(inverse(v),identity)),
inference(spr,[status(thm),theory(equality)],[86,7]),
[iquote('0:SpR:86.0,7.0')] ).
cnf(105,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,86]),
[iquote('0:SpR:12.0,86.0')] ).
cnf(106,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,105]),
[iquote('0:Rew:4.0,105.0')] ).
cnf(109,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(identity,identity)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[106,15]),
[iquote('0:Rew:106.0,15.1')] ).
cnf(112,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),double_divide(u,identity)),
inference(rew,[status(thm),theory(equality)],[106,70]),
[iquote('0:Rew:106.0,70.0')] ).
cnf(118,plain,
equal(inverse(multiply(inverse(inverse(u)),identity)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[3,112]),
[iquote('0:Rew:3.0,112.0')] ).
cnf(125,plain,
equal(double_divide(u,multiply(v,double_divide(identity,double_divide(inverse(u),identity)))),multiply(inverse(v),identity)),
inference(rew,[status(thm),theory(equality)],[106,102]),
[iquote('0:Rew:106.0,102.0')] ).
cnf(126,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[24,125,3]),
[iquote('0:Rew:24.0,125.0,3.0,125.0')] ).
cnf(127,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[126,118]),
[iquote('0:Rew:126.0,118.0')] ).
cnf(130,plain,
( ~ equal(inverse(inverse(a2)),a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[109]),
[iquote('0:Obv:109.1')] ).
cnf(132,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,double_divide(identity,double_divide(u,v))))),v),
inference(spr,[status(thm),theory(equality)],[106,7]),
[iquote('0:SpR:106.0,7.0')] ).
cnf(133,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,inverse(identity)))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[106,24]),
[iquote('0:SpR:106.0,24.0')] ).
cnf(138,plain,
equal(double_divide(identity,multiply(u,identity)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[106,133,3]),
[iquote('0:Rew:106.0,133.0,3.0,133.0,106.0,133.0')] ).
cnf(151,plain,
equal(multiply(multiply(u,v),identity),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,126]),
[iquote('0:SpR:6.0,126.0')] ).
cnf(166,plain,
equal(inverse(inverse(multiply(u,v))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[6,127]),
[iquote('0:SpR:6.0,127.0')] ).
cnf(169,plain,
equal(multiply(multiply(u,identity),identity),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[138,6]),
[iquote('0:SpR:138.0,6.0')] ).
cnf(175,plain,
equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[126,138]),
[iquote('0:SpR:126.0,138.0')] ).
cnf(178,plain,
equal(double_divide(u,multiply(v,inverse(inverse(inverse(u))))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[175,24]),
[iquote('0:Rew:175.0,24.0')] ).
cnf(185,plain,
equal(multiply(multiply(u,inverse(inverse(inverse(v)))),v),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[175,62]),
[iquote('0:Rew:175.0,62.0')] ).
cnf(188,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[151,169]),
[iquote('0:Rew:151.0,169.0')] ).
cnf(192,plain,
equal(double_divide(u,inverse(inverse(inverse(double_divide(inverse(u),double_divide(identity,v)))))),v),
inference(rew,[status(thm),theory(equality)],[188,27]),
[iquote('0:Rew:188.0,27.0')] ).
cnf(196,plain,
equal(double_divide(u,multiply(v,inverse(u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[127,178]),
[iquote('0:Rew:127.0,178.0')] ).
cnf(198,plain,
equal(multiply(multiply(u,inverse(v)),v),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[127,185]),
[iquote('0:Rew:127.0,185.0')] ).
cnf(199,plain,
equal(double_divide(u,inverse(inverse(multiply(double_divide(identity,v),inverse(u))))),v),
inference(rew,[status(thm),theory(equality)],[6,192]),
[iquote('0:Rew:6.0,192.0')] ).
cnf(200,plain,
equal(inverse(double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[196,199,166]),
[iquote('0:Rew:196.0,199.0,166.0,199.0')] ).
cnf(201,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,200]),
[iquote('0:Rew:6.0,200.0')] ).
cnf(202,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[188,201]),
[iquote('0:Rew:188.0,201.0')] ).
cnf(203,plain,
( ~ equal(a2,a2)
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[202,130]),
[iquote('0:Rew:202.0,130.0')] ).
cnf(208,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[202,188]),
[iquote('0:Rew:202.0,188.0')] ).
cnf(209,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[202,198]),
[iquote('0:Rew:202.0,198.0')] ).
cnf(212,plain,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
inference(obv,[status(thm),theory(equality)],[203]),
[iquote('0:Obv:203.0')] ).
cnf(219,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,202]),
[iquote('0:SpR:6.0,202.0')] ).
cnf(241,plain,
equal(double_divide(identity,multiply(u,identity)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[106,196]),
[iquote('0:SpR:106.0,196.0')] ).
cnf(247,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[208,241]),
[iquote('0:Rew:208.0,241.0')] ).
cnf(248,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(inverse(u),double_divide(v,w))))),w),
inference(rew,[status(thm),theory(equality)],[247,7]),
[iquote('0:Rew:247.0,7.0')] ).
cnf(252,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,inverse(double_divide(u,v))))),v),
inference(rew,[status(thm),theory(equality)],[247,132]),
[iquote('0:Rew:247.0,132.0')] ).
cnf(265,plain,
equal(double_divide(identity,multiply(u,double_divide(identity,multiply(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[6,252]),
[iquote('0:Rew:6.0,252.0')] ).
cnf(266,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[219,265,247]),
[iquote('0:Rew:219.0,265.0,247.0,265.0,219.0,265.0,247.0,265.0')] ).
cnf(267,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(v,w),inverse(u)))),w),
inference(rew,[status(thm),theory(equality)],[6,248]),
[iquote('0:Rew:6.0,248.0')] ).
cnf(297,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[266,6]),
[iquote('0:SpR:266.0,6.0')] ).
cnf(303,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[196,266]),
[iquote('0:SpR:196.0,266.0')] ).
cnf(336,plain,
equal(multiply(u,multiply(double_divide(u,v),inverse(w))),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[267,266]),
[iquote('0:SpR:267.0,266.0')] ).
cnf(381,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[202,209]),
[iquote('0:SpR:202.0,209.0')] ).
cnf(397,plain,
equal(multiply(multiply(u,double_divide(v,w)),multiply(w,v)),u),
inference(spr,[status(thm),theory(equality)],[219,209]),
[iquote('0:SpR:219.0,209.0')] ).
cnf(549,plain,
equal(multiply(inverse(u),inverse(double_divide(v,u))),v),
inference(spr,[status(thm),theory(equality)],[297,381]),
[iquote('0:SpR:297.0,381.0')] ).
cnf(558,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[6,549]),
[iquote('0:Rew:6.0,549.0')] ).
cnf(575,plain,
equal(multiply(multiply(u,v),multiply(double_divide(v,u),w)),w),
inference(spr,[status(thm),theory(equality)],[6,558]),
[iquote('0:SpR:6.0,558.0')] ).
cnf(790,plain,
equal(multiply(double_divide(u,v),inverse(w)),double_divide(multiply(v,u),w)),
inference(spr,[status(thm),theory(equality)],[6,303]),
[iquote('0:SpR:6.0,303.0')] ).
cnf(802,plain,
equal(multiply(u,double_divide(multiply(v,u),w)),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[790,336]),
[iquote('0:Rew:790.0,336.0')] ).
cnf(1703,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(u,w))),w),
inference(spr,[status(thm),theory(equality)],[802,397]),
[iquote('0:SpR:802.0,397.0')] ).
cnf(1820,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1703,575]),
[iquote('0:SpR:1703.0,575.0')] ).
cnf(1876,plain,
$false,
inference(unc,[status(thm)],[1820,212]),
[iquote('0:UnC:1820.0,212.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.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 : Tue Jun 14 02:38:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 1055 clauses, backtracked 0 clauses, performed 0 splits and kept 147 clauses.
% 0.19/0.52 SPASS allocated 64837 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 9, length 75 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms
% 0.19/0.53
%------------------------------------------------------------------------------