%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% 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 11:49:07 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of clauses : 50 ( 43 unt; 1 nHn; 50 RR)
% Number of literals : 57 ( 0 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,unit),u),
file('GRP711+1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(unit,u),u),
file('GRP711+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,i(u)),unit),
file('GRP711+1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(i(u),u),unit),
file('GRP711+1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(skc10,skc11),mult(skc9,skc11)),
file('GRP711+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(u,v)
| skP0(v,u,w) ),
file('GRP711+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(skc10,skc9)
| ~ skP0(skc6,skc7,skc8) ),
file('GRP711+1.p',unknown),
[] ).
cnf(8,axiom,
( equal(mult(u,v),mult(u,w))
| skP0(w,v,u) ),
file('GRP711+1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(mult(u,v),v),w),mult(u,mult(v,mult(v,w)))),
file('GRP711+1.p',unknown),
[] ).
cnf(49,plain,
( ~ equal(skc7,skc6)
| ~ equal(skc10,skc9) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.1,7.1')] ).
cnf(50,plain,
( ~ equal(skc10,skc9)
| equal(mult(skc8,skc7),mult(skc8,skc6)) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.1,7.1')] ).
cnf(52,plain,
equal(mult(u,mult(v,mult(v,unit))),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[9,1]),
[iquote('0:SpR:9.0,1.0')] ).
cnf(53,plain,
equal(mult(u,mult(v,mult(v,i(mult(mult(u,v),v))))),unit),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(57,plain,
equal(mult(unit,mult(u,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(58,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(mult(unit,u),v)),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(60,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(mult(unit,i(u)),v)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(64,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1,52]),
[iquote('0:Rew:1.0,52.0')] ).
cnf(65,plain,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[64,9]),
[iquote('0:Rew:64.0,9.0')] ).
cnf(66,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[2,57]),
[iquote('0:Rew:2.0,57.0')] ).
cnf(69,plain,
equal(mult(u,mult(v,mult(v,i(mult(u,mult(v,v)))))),unit),
inference(rew,[status(thm),theory(equality)],[64,53]),
[iquote('0:Rew:64.0,53.0')] ).
cnf(70,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[2,58]),
[iquote('0:Rew:2.0,58.0')] ).
cnf(73,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[2,60]),
[iquote('0:Rew:2.0,60.0')] ).
cnf(79,plain,
equal(mult(i(u),mult(u,u)),mult(unit,u)),
inference(spr,[status(thm),theory(equality)],[4,64]),
[iquote('0:SpR:4.0,64.0')] ).
cnf(81,plain,
equal(mult(u,mult(i(u),i(u))),mult(unit,i(u))),
inference(spr,[status(thm),theory(equality)],[3,64]),
[iquote('0:SpR:3.0,64.0')] ).
cnf(82,plain,
equal(mult(mult(skc9,skc11),skc11),mult(skc10,mult(skc11,skc11))),
inference(spr,[status(thm),theory(equality)],[5,64]),
[iquote('0:SpR:5.0,64.0')] ).
cnf(86,plain,
equal(mult(i(u),mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[2,79]),
[iquote('0:Rew:2.0,79.0')] ).
cnf(87,plain,
equal(mult(skc10,mult(skc11,skc11)),mult(skc9,mult(skc11,skc11))),
inference(rew,[status(thm),theory(equality)],[64,82]),
[iquote('0:Rew:64.0,82.0')] ).
cnf(88,plain,
equal(mult(u,mult(i(u),i(u))),i(u)),
inference(rew,[status(thm),theory(equality)],[2,81]),
[iquote('0:Rew:2.0,81.0')] ).
cnf(101,plain,
equal(mult(i(mult(u,u)),mult(u,mult(u,v))),mult(unit,v)),
inference(spr,[status(thm),theory(equality)],[4,65]),
[iquote('0:SpR:4.0,65.0')] ).
cnf(107,plain,
equal(mult(i(mult(u,u)),mult(u,mult(u,v))),v),
inference(rew,[status(thm),theory(equality)],[2,101]),
[iquote('0:Rew:2.0,101.0')] ).
cnf(175,plain,
equal(mult(i(i(u)),mult(i(u),u)),u),
inference(spr,[status(thm),theory(equality)],[86,70]),
[iquote('0:SpR:86.0,70.0')] ).
cnf(185,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[1,175,4]),
[iquote('0:Rew:1.0,175.0,4.0,175.0')] ).
cnf(254,plain,
equal(mult(i(i(mult(u,u))),mult(i(mult(u,u)),v)),v),
inference(spr,[status(thm),theory(equality)],[107,70]),
[iquote('0:SpR:107.0,70.0')] ).
cnf(261,plain,
equal(mult(i(mult(u,u)),mult(u,i(u))),mult(i(u),i(u))),
inference(spr,[status(thm),theory(equality)],[88,107]),
[iquote('0:SpR:88.0,107.0')] ).
cnf(263,plain,
( ~ equal(skc10,skc9)
| equal(mult(i(mult(skc8,skc8)),mult(skc8,mult(skc8,skc6))),skc7) ),
inference(spr,[status(thm),theory(equality)],[50,107]),
[iquote('0:SpR:50.1,107.0')] ).
cnf(285,plain,
equal(mult(u,mult(u,mult(i(mult(u,u)),v))),v),
inference(rew,[status(thm),theory(equality)],[66,254,185]),
[iquote('0:Rew:66.0,254.0,185.0,254.0')] ).
cnf(287,plain,
equal(mult(i(u),i(u)),i(mult(u,u))),
inference(rew,[status(thm),theory(equality)],[1,261,3]),
[iquote('0:Rew:1.0,261.0,3.0,261.0')] ).
cnf(293,plain,
( ~ equal(skc10,skc9)
| equal(skc7,skc6) ),
inference(rew,[status(thm),theory(equality)],[107,263]),
[iquote('0:Rew:107.0,263.1')] ).
cnf(294,plain,
~ equal(skc10,skc9),
inference(mrr,[status(thm)],[293,49]),
[iquote('0:MRR:293.1,49.0')] ).
cnf(336,plain,
equal(mult(i(u),mult(i(u),v)),mult(i(mult(u,u)),v)),
inference(spr,[status(thm),theory(equality)],[287,66]),
[iquote('0:SpR:287.0,66.0')] ).
cnf(353,plain,
equal(mult(u,mult(i(mult(u,u)),v)),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[336,73]),
[iquote('0:Rew:336.0,73.0')] ).
cnf(354,plain,
equal(mult(u,mult(i(u),v)),v),
inference(rew,[status(thm),theory(equality)],[353,285]),
[iquote('0:Rew:353.0,285.0')] ).
cnf(364,plain,
equal(mult(i(u),mult(u,v)),v),
inference(spr,[status(thm),theory(equality)],[354,70]),
[iquote('0:SpR:354.0,70.0')] ).
cnf(549,plain,
equal(mult(u,mult(u,i(mult(v,mult(u,u))))),mult(i(v),unit)),
inference(spr,[status(thm),theory(equality)],[69,364]),
[iquote('0:SpR:69.0,364.0')] ).
cnf(593,plain,
equal(mult(u,mult(u,i(mult(v,mult(u,u))))),i(v)),
inference(rew,[status(thm),theory(equality)],[1,549]),
[iquote('0:Rew:1.0,549.0')] ).
cnf(721,plain,
equal(mult(skc11,mult(skc11,i(mult(skc9,mult(skc11,skc11))))),i(skc10)),
inference(spr,[status(thm),theory(equality)],[87,593]),
[iquote('0:SpR:87.0,593.0')] ).
cnf(738,plain,
equal(i(skc10),i(skc9)),
inference(rew,[status(thm),theory(equality)],[593,721]),
[iquote('0:Rew:593.0,721.0')] ).
cnf(785,plain,
equal(i(i(skc9)),skc10),
inference(spr,[status(thm),theory(equality)],[738,185]),
[iquote('0:SpR:738.0,185.0')] ).
cnf(790,plain,
equal(skc10,skc9),
inference(rew,[status(thm),theory(equality)],[185,785]),
[iquote('0:Rew:185.0,785.0')] ).
cnf(791,plain,
$false,
inference(mrr,[status(thm)],[790,294]),
[iquote('0:MRR:790.0,294.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % 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 : Mon Jun 13 08:58:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 459 clauses, backtracked 0 clauses, performed 0 splits and kept 129 clauses.
% 0.20/0.50 SPASS allocated 86164 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.15 on the problem.
% 0.20/0.50 0:00:00.03 for the input.
% 0.20/0.50 0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.01 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.06 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 6, length 50 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : f01 f02 f04 f05 goals f03
% 0.20/0.50
%------------------------------------------------------------------------------