TSTP Solution File: GRP008-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% 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 11:44:43 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 13 unt; 2 nHn; 20 RR)
% Number of literals : 30 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( q(u)
| product(u,j(u),h(u))
| product(j(u),u,h(u)) ),
file('GRP008-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(u,j(u),h(u))
| ~ product(j(u),u,h(u))
| q(u) ),
file('GRP008-1.p',unknown),
[] ).
cnf(4,axiom,
~ q(identity),
file('GRP008-1.p',unknown),
[] ).
cnf(5,axiom,
product(identity,u,u),
file('GRP008-1.p',unknown),
[] ).
cnf(6,axiom,
product(u,identity,u),
file('GRP008-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP008-1.p',unknown),
[] ).
cnf(13,plain,
( ~ product(identity,j(identity),h(identity))
| ~ product(j(identity),identity,h(identity)) ),
inference(res,[status(thm),theory(equality)],[3,4]),
[iquote('0:Res:3.2,4.0')] ).
cnf(14,plain,
( product(identity,j(identity),h(identity))
| product(j(identity),identity,h(identity)) ),
inference(res,[status(thm),theory(equality)],[2,4]),
[iquote('0:Res:2.2,4.0')] ).
cnf(15,plain,
product(identity,j(identity),h(identity)),
inference(spt,[spt(split,[position(s1)])],[14]),
[iquote('1:Spt:14.0')] ).
cnf(16,plain,
~ product(j(identity),identity,h(identity)),
inference(mrr,[status(thm)],[13,15]),
[iquote('1:MRR:13.0,15.0')] ).
cnf(24,plain,
( ~ product(identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[5,10]),
[iquote('0:Res:5.0,10.0')] ).
cnf(25,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.0,10.0')] ).
cnf(34,plain,
equal(h(identity),j(identity)),
inference(res,[status(thm),theory(equality)],[15,24]),
[iquote('1:Res:15.0,24.0')] ).
cnf(36,plain,
~ product(j(identity),identity,j(identity)),
inference(rew,[status(thm),theory(equality)],[34,16]),
[iquote('1:Rew:34.0,16.0')] ).
cnf(38,plain,
$false,
inference(mrr,[status(thm)],[36,6]),
[iquote('1:MRR:36.0,6.0')] ).
cnf(39,plain,
~ product(identity,j(identity),h(identity)),
inference(spt,[spt(split,[position(sa)])],[38,15]),
[iquote('1:Spt:38.0,14.0,15.0')] ).
cnf(40,plain,
product(j(identity),identity,h(identity)),
inference(spt,[spt(split,[position(s2)])],[14]),
[iquote('1:Spt:38.0,14.1')] ).
cnf(53,plain,
equal(h(identity),j(identity)),
inference(res,[status(thm),theory(equality)],[40,25]),
[iquote('1:Res:40.0,25.0')] ).
cnf(55,plain,
~ product(identity,j(identity),j(identity)),
inference(rew,[status(thm),theory(equality)],[53,39]),
[iquote('1:Rew:53.0,39.0')] ).
cnf(57,plain,
$false,
inference(mrr,[status(thm)],[55,5]),
[iquote('1:MRR:55.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 13 17:56:39 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.40
% 0.14/0.40 SPASS V 3.9
% 0.14/0.40 SPASS beiseite: Proof found.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 SPASS derived 39 clauses, backtracked 3 clauses, performed 1 splits and kept 35 clauses.
% 0.14/0.40 SPASS allocated 75621 KBytes.
% 0.14/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.14/0.40 0:00:00.03 for the input.
% 0.14/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.40 0:00:00.00 for inferences.
% 0.14/0.40 0:00:00.00 for the backtracking.
% 0.14/0.40 0:00:00.00 for the reduction.
% 0.14/0.40
% 0.14/0.40
% 0.14/0.40 Here is a proof with depth 3, length 20 :
% 0.14/0.40 % SZS output start Refutation
% See solution above
% 0.14/0.40 Formulae used in the proof : unknown_meaning3 unknown_meaning4 prove_identity_is_q left_identity right_identity total_function2
% 0.14/0.40
%------------------------------------------------------------------------------