TSTP Solution File: GRP029-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP029-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 7 unt; 0 nHn; 13 RR)
% Number of literals : 25 ( 0 equ; 13 neg)
% Maximal clause size : 4 ( 1 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(1,axiom,
product(identity,u,u),
file('GRP029-1.p',unknown),
[] ).
cnf(2,axiom,
product(inverse(u),u,identity),
file('GRP029-1.p',unknown),
[] ).
cnf(3,axiom,
~ product(not_right_identity(u),u,not_right_identity(u)),
file('GRP029-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP029-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP029-1.p',unknown),
[] ).
cnf(22,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.0')] ).
cnf(36,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(60,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[2,36]),
[iquote('0:Res:2.0,36.0')] ).
cnf(126,plain,
product(inverse(inverse(u)),identity,u),
inference(res,[status(thm),theory(equality)],[2,60]),
[iquote('0:Res:2.0,60.0')] ).
cnf(130,plain,
( ~ product(identity,u,inverse(v))
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[126,22]),
[iquote('0:Res:126.0,22.1')] ).
cnf(160,plain,
product(u,inverse(u),identity),
inference(res,[status(thm),theory(equality)],[1,130]),
[iquote('0:Res:1.0,130.0')] ).
cnf(173,plain,
product(u,identity,u),
inference(res,[status(thm),theory(equality)],[160,60]),
[iquote('0:Res:160.0,60.0')] ).
cnf(176,plain,
$false,
inference(unc,[status(thm)],[173,3]),
[iquote('0:UnC:173.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP029-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n025.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 : Tue Jun 14 13:16:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 148 clauses, backtracked 0 clauses, performed 0 splits and kept 74 clauses.
% 0.20/0.43 SPASS allocated 63218 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 6, length 13 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : left_identity left_inverse prove_there_is_a_right_identity associativity1 associativity2
% 0.20/0.43
%------------------------------------------------------------------------------