TSTP Solution File: GRP710+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:49:07 EDT 2022
% Result : Theorem 1.13s 1.32s
% Output : Refutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of clauses : 47 ( 42 unt; 0 nHn; 47 RR)
% Number of literals : 52 ( 0 equ; 11 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,unit),u),
file('GRP710+1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(unit,u),u),
file('GRP710+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,i(u)),unit),
file('GRP710+1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(i(u),u),unit),
file('GRP710+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(mult(u,skc6),skc7)
| ~ equal(mult(skc5,v),skc4) ),
file('GRP710+1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(mult(mult(u,v),v),w),mult(u,mult(v,mult(v,w)))),
file('GRP710+1.p',unknown),
[] ).
cnf(21,plain,
equal(mult(u,mult(v,mult(v,unit))),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(22,plain,
equal(mult(u,mult(v,mult(v,i(mult(mult(u,v),v))))),unit),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(26,plain,
equal(mult(unit,mult(u,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(27,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(mult(unit,u),v)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(29,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(mult(unit,i(u)),v)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(32,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1,21]),
[iquote('0:Rew:1.0,21.0')] ).
cnf(33,plain,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[32,6]),
[iquote('0:Rew:32.0,6.0')] ).
cnf(34,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[2,26]),
[iquote('0:Rew:2.0,26.0')] ).
cnf(37,plain,
equal(mult(u,mult(v,mult(v,i(mult(u,mult(v,v)))))),unit),
inference(rew,[status(thm),theory(equality)],[32,22]),
[iquote('0:Rew:32.0,22.0')] ).
cnf(38,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[2,27]),
[iquote('0:Rew:2.0,27.0')] ).
cnf(39,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[2,29]),
[iquote('0:Rew:2.0,29.0')] ).
cnf(47,plain,
equal(mult(i(u),mult(u,u)),mult(unit,u)),
inference(spr,[status(thm),theory(equality)],[4,32]),
[iquote('0:SpR:4.0,32.0')] ).
cnf(49,plain,
equal(mult(u,mult(i(u),i(u))),mult(unit,i(u))),
inference(spr,[status(thm),theory(equality)],[3,32]),
[iquote('0:SpR:3.0,32.0')] ).
cnf(50,plain,
( ~ equal(mult(u,mult(skc6,skc6)),skc7)
| ~ equal(mult(skc5,v),skc4) ),
inference(spl,[status(thm),theory(equality)],[32,5]),
[iquote('0:SpL:32.0,5.0')] ).
cnf(53,plain,
equal(mult(i(u),mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[2,47]),
[iquote('0:Rew:2.0,47.0')] ).
cnf(54,plain,
equal(mult(u,mult(i(u),i(u))),i(u)),
inference(rew,[status(thm),theory(equality)],[2,49]),
[iquote('0:Rew:2.0,49.0')] ).
cnf(66,plain,
equal(mult(i(mult(u,u)),mult(u,mult(u,v))),mult(unit,v)),
inference(spr,[status(thm),theory(equality)],[4,33]),
[iquote('0:SpR:4.0,33.0')] ).
cnf(73,plain,
equal(mult(i(mult(u,u)),mult(u,mult(u,v))),v),
inference(rew,[status(thm),theory(equality)],[2,66]),
[iquote('0:Rew:2.0,66.0')] ).
cnf(161,plain,
equal(mult(i(i(u)),mult(i(u),u)),u),
inference(spr,[status(thm),theory(equality)],[53,38]),
[iquote('0:SpR:53.0,38.0')] ).
cnf(172,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[1,161,4]),
[iquote('0:Rew:1.0,161.0,4.0,161.0')] ).
cnf(214,plain,
equal(mult(i(i(mult(u,u))),mult(i(mult(u,u)),v)),v),
inference(spr,[status(thm),theory(equality)],[73,38]),
[iquote('0:SpR:73.0,38.0')] ).
cnf(221,plain,
equal(mult(i(mult(u,u)),mult(u,i(u))),mult(i(u),i(u))),
inference(spr,[status(thm),theory(equality)],[54,73]),
[iquote('0:SpR:54.0,73.0')] ).
cnf(241,plain,
equal(mult(u,mult(u,mult(i(mult(u,u)),v))),v),
inference(rew,[status(thm),theory(equality)],[34,214,172]),
[iquote('0:Rew:34.0,214.0,172.0,214.0')] ).
cnf(243,plain,
equal(mult(i(u),i(u)),i(mult(u,u))),
inference(rew,[status(thm),theory(equality)],[1,221,3]),
[iquote('0:Rew:1.0,221.0,3.0,221.0')] ).
cnf(285,plain,
equal(mult(i(u),mult(i(u),v)),mult(i(mult(u,u)),v)),
inference(spr,[status(thm),theory(equality)],[243,34]),
[iquote('0:SpR:243.0,34.0')] ).
cnf(305,plain,
equal(mult(u,mult(i(mult(u,u)),v)),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[285,39]),
[iquote('0:Rew:285.0,39.0')] ).
cnf(306,plain,
equal(mult(u,mult(i(u),v)),v),
inference(rew,[status(thm),theory(equality)],[305,241]),
[iquote('0:Rew:305.0,241.0')] ).
cnf(317,plain,
equal(mult(i(mult(u,u)),mult(u,v)),mult(i(u),v)),
inference(spr,[status(thm),theory(equality)],[306,73]),
[iquote('0:SpR:306.0,73.0')] ).
cnf(318,plain,
equal(mult(i(u),mult(u,v)),v),
inference(spr,[status(thm),theory(equality)],[306,38]),
[iquote('0:SpR:306.0,38.0')] ).
cnf(422,plain,
equal(mult(u,mult(u,i(mult(v,mult(u,u))))),mult(i(v),unit)),
inference(spr,[status(thm),theory(equality)],[37,318]),
[iquote('0:SpR:37.0,318.0')] ).
cnf(459,plain,
equal(mult(u,mult(u,i(mult(v,mult(u,u))))),i(v)),
inference(rew,[status(thm),theory(equality)],[1,422]),
[iquote('0:Rew:1.0,422.0')] ).
cnf(612,plain,
equal(mult(i(u),mult(u,i(mult(v,mult(u,u))))),mult(i(mult(u,u)),i(v))),
inference(spr,[status(thm),theory(equality)],[459,317]),
[iquote('0:SpR:459.0,317.0')] ).
cnf(651,plain,
equal(mult(i(mult(u,u)),i(v)),i(mult(v,mult(u,u)))),
inference(rew,[status(thm),theory(equality)],[318,612]),
[iquote('0:Rew:318.0,612.0')] ).
cnf(1071,plain,
equal(i(mult(i(u),mult(v,v))),mult(i(mult(v,v)),u)),
inference(spr,[status(thm),theory(equality)],[172,651]),
[iquote('0:SpR:172.0,651.0')] ).
cnf(1396,plain,
equal(i(mult(i(mult(u,u)),v)),mult(i(v),mult(u,u))),
inference(spr,[status(thm),theory(equality)],[1071,172]),
[iquote('0:SpR:1071.0,172.0')] ).
cnf(1588,plain,
equal(mult(i(mult(u,v)),mult(u,u)),i(mult(i(u),v))),
inference(spr,[status(thm),theory(equality)],[317,1396]),
[iquote('0:SpR:317.0,1396.0')] ).
cnf(2944,plain,
( ~ equal(i(mult(i(skc6),u)),skc7)
| ~ equal(mult(skc5,v),skc4) ),
inference(spl,[status(thm),theory(equality)],[1588,50]),
[iquote('0:SpL:1588.0,50.0')] ).
cnf(3088,plain,
( ~ equal(i(u),skc7)
| ~ equal(mult(skc5,v),skc4) ),
inference(spl,[status(thm),theory(equality)],[306,2944]),
[iquote('0:SpL:306.0,2944.0')] ).
cnf(3106,plain,
( ~ equal(i(u),skc7)
| ~ equal(v,skc4) ),
inference(spl,[status(thm),theory(equality)],[306,3088]),
[iquote('0:SpL:306.0,3088.1')] ).
cnf(3108,plain,
~ equal(i(u),skc7),
inference(aed,[status(thm),theory(equality)],[3106]),
[iquote('0:AED:3106.1')] ).
cnf(3109,plain,
$false,
inference(unc,[status(thm)],[3108,172]),
[iquote('0:UnC:3108.0,172.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 20:34:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.13/1.32
% 1.13/1.32 SPASS V 3.9
% 1.13/1.32 SPASS beiseite: Proof found.
% 1.13/1.32 % SZS status Theorem
% 1.13/1.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.13/1.32 SPASS derived 1662 clauses, backtracked 0 clauses, performed 0 splits and kept 543 clauses.
% 1.13/1.32 SPASS allocated 92067 KBytes.
% 1.13/1.32 SPASS spent 0:00:00.92 on the problem.
% 1.13/1.32 0:00:00.03 for the input.
% 1.13/1.32 0:00:00.02 for the FLOTTER CNF translation.
% 1.13/1.32 0:00:00.02 for inferences.
% 1.13/1.32 0:00:00.00 for the backtracking.
% 1.13/1.32 0:00:00.82 for the reduction.
% 1.13/1.32
% 1.13/1.32
% 1.13/1.32 Here is a proof with depth 11, length 47 :
% 1.13/1.32 % SZS output start Refutation
% See solution above
% 1.13/1.32 Formulae used in the proof : f01 f02 f04 f05 goals f03
% 1.13/1.32
%------------------------------------------------------------------------------