%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 11:48:44 EDT 2022
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 15 unt; 0 nHn; 17 RR)
% Number of literals : 19 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP656+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP656+1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP656+1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,mult(v,w)),u),mult(mult(u,v),mult(w,u))),
file('GRP656+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(mult(u,skf3(u)),skf3(u))
| ~ equal(mult(skf2(u),u),skf2(u)) ),
file('GRP656+1.p',unknown),
[] ).
cnf(17,plain,
equal(rd(mult(mult(u,v),mult(w,u)),u),mult(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(18,plain,
equal(ld(mult(u,mult(v,w)),mult(mult(u,v),mult(w,u))),u),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(37,plain,
equal(rd(mult(mult(u,v),w),u),mult(u,mult(v,rd(w,u)))),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(125,plain,
equal(mult(u,mult(v,rd(u,u))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[37,4]),
[iquote('0:SpR:37.0,4.0')] ).
cnf(147,plain,
equal(mult(u,rd(v,v)),ld(v,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[125,2]),
[iquote('0:SpR:125.0,2.0')] ).
cnf(162,plain,
equal(mult(u,rd(v,v)),u),
inference(rew,[status(thm),theory(equality)],[2,147]),
[iquote('0:Rew:2.0,147.0')] ).
cnf(243,plain,
equal(ld(mult(u,v),mult(mult(u,v),mult(rd(w,w),u))),u),
inference(spr,[status(thm),theory(equality)],[162,18]),
[iquote('0:SpR:162.0,18.0')] ).
cnf(247,plain,
( ~ equal(mult(rd(u,u),skf3(rd(u,u))),skf3(rd(u,u)))
| ~ equal(skf2(rd(u,u)),skf2(rd(u,u))) ),
inference(spl,[status(thm),theory(equality)],[162,6]),
[iquote('0:SpL:162.0,6.1')] ).
cnf(278,plain,
equal(mult(rd(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,243]),
[iquote('0:Rew:2.0,243.0')] ).
cnf(323,plain,
~ equal(mult(rd(u,u),skf3(rd(u,u))),skf3(rd(u,u))),
inference(obv,[status(thm),theory(equality)],[247]),
[iquote('0:Obv:247.1')] ).
cnf(324,plain,
~ equal(skf3(rd(u,u)),skf3(rd(u,u))),
inference(rew,[status(thm),theory(equality)],[278,323]),
[iquote('0:Rew:278.0,323.0')] ).
cnf(325,plain,
$false,
inference(obv,[status(thm),theory(equality)],[324]),
[iquote('0:Obv:324.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP656+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 08:51:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.49
% 0.18/0.49 SPASS V 3.9
% 0.18/0.49 SPASS beiseite: Proof found.
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.49 SPASS derived 226 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.18/0.49 SPASS allocated 85790 KBytes.
% 0.18/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.49 0:00:00.03 for the input.
% 0.18/0.49 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.49 0:00:00.00 for inferences.
% 0.18/0.49 0:00:00.00 for the backtracking.
% 0.18/0.49 0:00:00.05 for the reduction.
% 0.18/0.49
% 0.18/0.49
% 0.18/0.49 Here is a proof with depth 5, length 17 :
% 0.18/0.49 % SZS output start Refutation
% See solution above
% 0.18/0.49 Formulae used in the proof : f02 f03 f04 f05 goals
% 0.18/0.49
%------------------------------------------------------------------------------