TSTP Solution File: GRP682-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP682-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:48:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ld(u,mult(u,u)),u),
file('GRP682-10.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP682-10.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP682-10.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP682-10.p',unknown),
[] ).
cnf(5,axiom,
equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
file('GRP682-10.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP682-10.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP682-10.p',unknown),
[] ).
cnf(8,axiom,
~ equal(ld(ld(x0__dfg,x1__dfg),mult(ld(x0__dfg,x1__dfg),x2__dfg)),ld(x0__dfg,mult(x0__dfg,x2__dfg))),
file('GRP682-10.p',unknown),
[] ).
cnf(17,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(rd(u,u),v),v),v)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(19,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(20,plain,
equal(rd(u,u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2,19,1,3]),
[iquote('0:Rew:2.0,19.0,1.0,19.0,3.0,19.0')] ).
cnf(23,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(ld(u,u),v),v),v)),
inference(rew,[status(thm),theory(equality)],[20,17]),
[iquote('0:Rew:20.0,17.0')] ).
cnf(25,plain,
equal(mult(ld(u,u),u),rd(mult(u,u),u)),
inference(spr,[status(thm),theory(equality)],[20,4]),
[iquote('0:SpR:20.0,4.0')] ).
cnf(27,plain,
equal(mult(ld(u,u),u),u),
inference(rew,[status(thm),theory(equality)],[2,25]),
[iquote('0:Rew:2.0,25.0')] ).
cnf(53,plain,
equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(102,plain,
equal(rd(mult(mult(u,v),v),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[2,53]),
[iquote('0:SpR:2.0,53.0')] ).
cnf(106,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[102,23]),
[iquote('0:Rew:102.0,23.0')] ).
cnf(177,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),mult(ld(u,mult(u,ld(w,w))),w)),
inference(spr,[status(thm),theory(equality)],[27,5]),
[iquote('0:SpR:27.0,5.0')] ).
cnf(178,plain,
equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(191,plain,
equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[178,106]),
[iquote('0:Rew:178.0,106.0')] ).
cnf(192,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[27,191]),
[iquote('0:Rew:27.0,191.0')] ).
cnf(198,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,ld(w,mult(w,w))))),
inference(rew,[status(thm),theory(equality)],[192,177,178]),
[iquote('0:Rew:192.0,177.0,178.0,177.0')] ).
cnf(199,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1,198]),
[iquote('0:Rew:1.0,198.0')] ).
cnf(200,plain,
$false,
inference(unc,[status(thm)],[199,8]),
[iquote('0:UnC:199.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP682-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.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 : Mon Jun 13 14:32:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 138 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.20/0.45 SPASS allocated 63591 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.03 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 3, length 24 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 0.20/0.45
%------------------------------------------------------------------------------