TSTP Solution File: GRP665-12 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP665-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:48:50 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 8 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP665-12.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(rd(mult(u,v),u),mult(u,w)),mult(u,mult(v,w))),
file('GRP665-12.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(op_c,u),mult(u,op_c)),
file('GRP665-12.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(mult(x0__dfg,x1__dfg),op_c),mult(x0__dfg,mult(x1__dfg,op_c))),
file('GRP665-12.p',unknown),
[] ).
cnf(11,plain,
~ equal(mult(x0__dfg,mult(op_c,x1__dfg)),mult(op_c,mult(x0__dfg,x1__dfg))),
inference(rew,[status(thm),theory(equality)],[9,10]),
[iquote('0:Rew:9.0,10.0,9.0,10.0')] ).
cnf(22,plain,
equal(rd(mult(u,op_c),u),op_c),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(146,plain,
equal(mult(op_c,mult(u,v)),mult(u,mult(op_c,v))),
inference(spr,[status(thm),theory(equality)],[22,7]),
[iquote('0:SpR:22.0,7.0')] ).
cnf(147,plain,
$false,
inference(unc,[status(thm)],[146,11]),
[iquote('0:UnC:146.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP665-12 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 19:59:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 134 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.18/0.41 SPASS allocated 63244 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.03 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 2, length 8 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : f04 f07 f09 goal
% 0.18/0.41
%------------------------------------------------------------------------------