TSTP Solution File: GRP022-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:44:48 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(inverse(inverse(a)),a),
file('GRP022-1.p',unknown),
[] ).
cnf(2,axiom,
product(identity,u,u),
file('GRP022-1.p',unknown),
[] ).
cnf(3,axiom,
product(u,identity,u),
file('GRP022-1.p',unknown),
[] ).
cnf(4,axiom,
product(inverse(u),u,identity),
file('GRP022-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP022-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP022-1.p',unknown),
[] ).
cnf(10,plain,
( ~ product(u,v,a)
| ~ product(u,v,inverse(inverse(a))) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.2,1.0')] ).
cnf(33,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(77,plain,
( ~ product(u,inverse(v),w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[4,33]),
[iquote('0:Res:4.0,33.0')] ).
cnf(93,plain,
product(identity,u,inverse(inverse(u))),
inference(res,[status(thm),theory(equality)],[4,77]),
[iquote('0:Res:4.0,77.0')] ).
cnf(98,plain,
~ product(identity,a,a),
inference(res,[status(thm),theory(equality)],[93,10]),
[iquote('0:Res:93.0,10.1')] ).
cnf(111,plain,
$false,
inference(mrr,[status(thm)],[98,2]),
[iquote('0:MRR:98.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n006.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 21:40:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 95 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.19/0.42 SPASS allocated 63161 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 4, length 12 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : prove_inverse_of_inverse_is_original left_identity right_identity left_inverse total_function2 associativity2
% 0.19/0.42
%------------------------------------------------------------------------------