TSTP Solution File: GRP028-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP028-4 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:44:51 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 8 RR)
% Number of literals : 14 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP028-4.p',unknown),
[] ).
cnf(3,axiom,
product(left_solution(u,v),u,v),
file('GRP028-4.p',unknown),
[] ).
cnf(4,axiom,
product(u,right_solution(u,v),v),
file('GRP028-4.p',unknown),
[] ).
cnf(5,axiom,
~ product(not_identity(u),u,not_identity(u)),
file('GRP028-4.p',unknown),
[] ).
cnf(14,plain,
( ~ product(u,v,w)
| ~ product(left_solution(w,x),u,y)
| product(y,v,x) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.0')] ).
cnf(26,plain,
( ~ product(u,v,u)
| product(w,v,w) ),
inference(res,[status(thm),theory(equality)],[3,14]),
[iquote('0:Res:3.0,14.1')] ).
cnf(38,plain,
product(u,right_solution(v,v),u),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.0,26.0')] ).
cnf(40,plain,
$false,
inference(unc,[status(thm)],[38,5]),
[iquote('0:UnC:38.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP028-4 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Mon Jun 13 13:22:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 34 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.19/0.41 SPASS allocated 63136 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 3, length 8 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : associativity1 left_soln right_soln prove_there_is_a_right_identity
% 0.19/0.41
%------------------------------------------------------------------------------