TSTP Solution File: GRP710-11 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:49:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 0 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(1,axiom,
equal(mult(u,unit),u),
file('GRP710-11.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(unit,u),u),
file('GRP710-11.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(mult(mult(u,v),v),w),mult(u,mult(v,mult(v,w)))),
file('GRP710-11.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(u,i(u)),unit),
file('GRP710-11.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(i(u),u),unit),
file('GRP710-11.p',unknown),
[] ).
cnf(6,axiom,
~ equal(mult(u,x4__dfg),x3__dfg),
file('GRP710-11.p',unknown),
[] ).
cnf(19,plain,
equal(mult(u,mult(v,mult(v,unit))),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(24,plain,
equal(mult(unit,mult(u,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(25,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(mult(unit,u),v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(27,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(mult(unit,i(u)),v)),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(30,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1,19]),
[iquote('0:Rew:1.0,19.0')] ).
cnf(31,plain,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[30,3]),
[iquote('0:Rew:30.0,3.0')] ).
cnf(32,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[2,24]),
[iquote('0:Rew:2.0,24.0')] ).
cnf(36,plain,
equal(mult(i(u),mult(u,mult(u,v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[2,25]),
[iquote('0:Rew:2.0,25.0')] ).
cnf(37,plain,
equal(mult(u,mult(i(u),mult(i(u),v))),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[2,27]),
[iquote('0:Rew:2.0,27.0')] ).
cnf(47,plain,
equal(mult(i(mult(u,u)),mult(u,mult(u,v))),mult(unit,v)),
inference(spr,[status(thm),theory(equality)],[5,31]),
[iquote('0:SpR:5.0,31.0')] ).
cnf(53,plain,
equal(mult(i(mult(u,u)),mult(u,mult(u,v))),v),
inference(rew,[status(thm),theory(equality)],[2,47]),
[iquote('0:Rew:2.0,47.0')] ).
cnf(87,plain,
equal(mult(i(u),mult(u,u)),mult(unit,u)),
inference(spr,[status(thm),theory(equality)],[5,30]),
[iquote('0:SpR:5.0,30.0')] ).
cnf(89,plain,
equal(mult(u,mult(i(u),i(u))),mult(unit,i(u))),
inference(spr,[status(thm),theory(equality)],[4,30]),
[iquote('0:SpR:4.0,30.0')] ).
cnf(91,plain,
~ equal(mult(u,mult(x4__dfg,x4__dfg)),x3__dfg),
inference(spl,[status(thm),theory(equality)],[30,6]),
[iquote('0:SpL:30.0,6.0')] ).
cnf(98,plain,
equal(mult(i(u),mult(u,u)),u),
inference(rew,[status(thm),theory(equality)],[2,87]),
[iquote('0:Rew:2.0,87.0')] ).
cnf(99,plain,
equal(mult(u,mult(i(u),i(u))),i(u)),
inference(rew,[status(thm),theory(equality)],[2,89]),
[iquote('0:Rew:2.0,89.0')] ).
cnf(108,plain,
~ equal(mult(u,mult(v,mult(v,mult(x4__dfg,x4__dfg)))),x3__dfg),
inference(spl,[status(thm),theory(equality)],[31,91]),
[iquote('0:SpL:31.0,91.0')] ).
cnf(211,plain,
equal(mult(i(i(u)),mult(i(u),u)),u),
inference(spr,[status(thm),theory(equality)],[98,36]),
[iquote('0:SpR:98.0,36.0')] ).
cnf(221,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[1,211,5]),
[iquote('0:Rew:1.0,211.0,5.0,211.0')] ).
cnf(310,plain,
equal(mult(i(i(mult(u,u))),mult(i(mult(u,u)),v)),v),
inference(spr,[status(thm),theory(equality)],[53,36]),
[iquote('0:SpR:53.0,36.0')] ).
cnf(317,plain,
equal(mult(i(mult(u,u)),mult(u,i(u))),mult(i(u),i(u))),
inference(spr,[status(thm),theory(equality)],[99,53]),
[iquote('0:SpR:99.0,53.0')] ).
cnf(339,plain,
equal(mult(u,mult(u,mult(i(mult(u,u)),v))),v),
inference(rew,[status(thm),theory(equality)],[32,310,221]),
[iquote('0:Rew:32.0,310.0,221.0,310.0')] ).
cnf(341,plain,
equal(mult(i(u),i(u)),i(mult(u,u))),
inference(rew,[status(thm),theory(equality)],[1,317,4]),
[iquote('0:Rew:1.0,317.0,4.0,317.0')] ).
cnf(511,plain,
equal(mult(i(u),mult(i(u),v)),mult(i(mult(u,u)),v)),
inference(spr,[status(thm),theory(equality)],[341,32]),
[iquote('0:SpR:341.0,32.0')] ).
cnf(534,plain,
equal(mult(u,mult(i(mult(u,u)),v)),mult(i(u),v)),
inference(rew,[status(thm),theory(equality)],[511,37]),
[iquote('0:Rew:511.0,37.0')] ).
cnf(535,plain,
equal(mult(u,mult(i(u),v)),v),
inference(rew,[status(thm),theory(equality)],[534,339]),
[iquote('0:Rew:534.0,339.0')] ).
cnf(547,plain,
equal(mult(i(u),mult(u,v)),v),
inference(spr,[status(thm),theory(equality)],[535,36]),
[iquote('0:SpR:535.0,36.0')] ).
cnf(826,plain,
~ equal(mult(u,mult(i(x4__dfg),x4__dfg)),x3__dfg),
inference(spl,[status(thm),theory(equality)],[547,108]),
[iquote('0:SpL:547.0,108.0')] ).
cnf(841,plain,
~ equal(u,x3__dfg),
inference(rew,[status(thm),theory(equality)],[1,826,5]),
[iquote('0:Rew:1.0,826.0,5.0,826.0')] ).
cnf(842,plain,
$false,
inference(obv,[status(thm),theory(equality)],[841]),
[iquote('0:Obv:841.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP710-11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:20:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 531 clauses, backtracked 0 clauses, performed 0 splits and kept 165 clauses.
% 0.19/0.51 SPASS allocated 64395 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.51 0:00:00.03 for the input.
% 0.19/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.08 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 4, length 36 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : f01 f02 f03 f04 f05 goal
% 0.19/0.51
%------------------------------------------------------------------------------