TSTP Solution File: GRP029-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP029-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 11:44:52 EDT 2022
% Result : Unsatisfiable 2.99s 3.17s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 7 unt; 0 nHn; 15 RR)
% Number of literals : 30 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP029-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP029-2.p',unknown),
[] ).
cnf(14,axiom,
product(identity,u,u),
file('GRP029-2.p',unknown),
[] ).
cnf(15,axiom,
product(inverse(u),u,identity),
file('GRP029-2.p',unknown),
[] ).
cnf(16,axiom,
~ product(not_right_identity(u),u,not_right_identity(u)),
file('GRP029-2.p',unknown),
[] ).
cnf(17,plain,
( ~ product(u,v,w)
| ~ product(x,v,not_right_identity(w))
| ~ product(not_right_identity(w),u,x) ),
inference(res,[status(thm),theory(equality)],[12,16]),
[iquote('0:Res:12.3,16.0')] ).
cnf(24,plain,
( ~ product(u,not_right_identity(v),v)
| ~ product(not_right_identity(v),u,identity) ),
inference(res,[status(thm),theory(equality)],[14,17]),
[iquote('0:Res:14.0,17.1')] ).
cnf(25,plain,
~ product(not_right_identity(identity),inverse(not_right_identity(identity)),identity),
inference(res,[status(thm),theory(equality)],[15,24]),
[iquote('0:Res:15.0,24.0')] ).
cnf(68,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[15,13]),
[iquote('0:Res:15.0,13.0')] ).
cnf(89,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[14,12]),
[iquote('0:Res:14.0,12.0')] ).
cnf(307,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[15,89]),
[iquote('0:Res:15.0,89.0')] ).
cnf(1196,plain,
product(inverse(inverse(u)),identity,u),
inference(res,[status(thm),theory(equality)],[15,307]),
[iquote('0:Res:15.0,307.0')] ).
cnf(1209,plain,
( ~ product(identity,u,inverse(v))
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[1196,68]),
[iquote('0:Res:1196.0,68.1')] ).
cnf(4809,plain,
product(u,inverse(u),identity),
inference(res,[status(thm),theory(equality)],[14,1209]),
[iquote('0:Res:14.0,1209.0')] ).
cnf(4823,plain,
$false,
inference(unc,[status(thm)],[4809,25]),
[iquote('0:UnC:4809.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP029-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 02:51:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.99/3.17
% 2.99/3.17 SPASS V 3.9
% 2.99/3.17 SPASS beiseite: Proof found.
% 2.99/3.17 % SZS status Theorem
% 2.99/3.17 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.99/3.17 SPASS derived 4805 clauses, backtracked 0 clauses, performed 0 splits and kept 3893 clauses.
% 2.99/3.17 SPASS allocated 66872 KBytes.
% 2.99/3.17 SPASS spent 0:00:02.79 on the problem.
% 2.99/3.17 0:00:00.04 for the input.
% 2.99/3.17 0:00:00.00 for the FLOTTER CNF translation.
% 2.99/3.17 0:00:00.05 for inferences.
% 2.99/3.17 0:00:00.00 for the backtracking.
% 2.99/3.17 0:00:02.67 for the reduction.
% 2.99/3.17
% 2.99/3.17
% 2.99/3.17 Here is a proof with depth 5, length 15 :
% 2.99/3.17 % SZS output start Refutation
% See solution above
% 2.99/3.17 Formulae used in the proof : associativity1 associativity2 left_identity left_inverse prove_there_is_a_right_identity
% 2.99/3.17
%------------------------------------------------------------------------------