TSTP Solution File: GRP682+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:48:57 EDT 2022
% Result : Theorem 0.52s 0.73s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of clauses : 47 ( 45 unt; 0 nHn; 47 RR)
% Number of literals : 49 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ld(u,mult(u,u)),u),
file('GRP682+1.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP682+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP682+1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP682+1.p',unknown),
[] ).
cnf(5,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP682+1.p',unknown),
[] ).
cnf(6,axiom,
equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
file('GRP682+1.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP682+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(ld(ld(skc6,skc7),mult(ld(skc6,skc7),skc8)),ld(skc6,mult(skc6,skc8)))
| ~ equal(ld(rd(skc9,skc10),mult(rd(skc9,skc10),skc11)),ld(skc9,mult(skc9,skc11))) ),
file('GRP682+1.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)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(19,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
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)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(65,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),mult(ld(u,u),rd(mult(u,w),w))),
inference(spr,[status(thm),theory(equality)],[27,7]),
[iquote('0:SpR:27.0,7.0')] ).
cnf(72,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(mult(ld(u,u),u),w),w)),
inference(rew,[status(thm),theory(equality)],[53,65]),
[iquote('0:Rew:53.0,65.0')] ).
cnf(73,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[27,72]),
[iquote('0:Rew:27.0,72.0')] ).
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(130,plain,
equal(rd(mult(rd(u,v),v),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[73,2]),
[iquote('0:SpR:73.0,2.0')] ).
cnf(135,plain,
equal(rd(mult(mult(u,rd(v,w)),rd(v,w)),rd(v,w)),mult(rd(mult(u,w),w),rd(v,w))),
inference(spr,[status(thm),theory(equality)],[73,4]),
[iquote('0:SpR:73.0,4.0')] ).
cnf(145,plain,
equal(rd(rd(mult(mult(u,v),w),w),rd(mult(v,w),w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[53,73]),
[iquote('0:SpR:53.0,73.0')] ).
cnf(148,plain,
equal(rd(rd(mult(u,v),v),v),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[4,130]),
[iquote('0:Rew:4.0,130.0')] ).
cnf(165,plain,
equal(mult(rd(mult(u,v),v),rd(w,v)),mult(u,rd(w,v))),
inference(rew,[status(thm),theory(equality)],[102,135]),
[iquote('0:Rew:102.0,135.0')] ).
cnf(176,plain,
equal(rd(rd(mult(u,v),v),rd(w,v)),rd(u,rd(w,v))),
inference(spr,[status(thm),theory(equality)],[73,148]),
[iquote('0:SpR:73.0,148.0')] ).
cnf(183,plain,
equal(rd(mult(u,v),rd(mult(v,w),w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[176,145]),
[iquote('0:Rew:176.0,145.0')] ).
cnf(194,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)],[27,6]),
[iquote('0:SpR:27.0,6.0')] ).
cnf(195,plain,
equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(208,plain,
equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[195,106]),
[iquote('0:Rew:195.0,106.0')] ).
cnf(209,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[27,208]),
[iquote('0:Rew:27.0,208.0')] ).
cnf(215,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)],[209,194,195]),
[iquote('0:Rew:209.0,194.0,195.0,194.0')] ).
cnf(216,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1,215]),
[iquote('0:Rew:1.0,215.0')] ).
cnf(217,plain,
( ~ equal(ld(skc6,mult(skc6,skc8)),ld(skc6,mult(skc6,skc8)))
| ~ equal(ld(rd(skc9,skc10),mult(rd(skc9,skc10),skc11)),ld(skc9,mult(skc9,skc11))) ),
inference(rew,[status(thm),theory(equality)],[216,8]),
[iquote('0:Rew:216.0,8.0')] ).
cnf(237,plain,
~ equal(ld(rd(skc9,skc10),mult(rd(skc9,skc10),skc11)),ld(skc9,mult(skc9,skc11))),
inference(obv,[status(thm),theory(equality)],[217]),
[iquote('0:Obv:217.0')] ).
cnf(657,plain,
equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[1,195]),
[iquote('0:SpR:1.0,195.0')] ).
cnf(969,plain,
equal(rd(mult(u,rd(v,w)),rd(mult(rd(v,w),x),x)),rd(mult(rd(mult(u,w),w),x),x)),
inference(spr,[status(thm),theory(equality)],[165,183]),
[iquote('0:SpR:165.0,183.0')] ).
cnf(981,plain,
equal(rd(mult(rd(mult(u,v),v),w),w),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[183,969]),
[iquote('0:Rew:183.0,969.0')] ).
cnf(1011,plain,
equal(ld(mult(u,v),mult(mult(u,v),w)),ld(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[657,216]),
[iquote('0:SpR:657.0,216.0')] ).
cnf(1677,plain,
equal(rd(mult(mult(rd(mult(u,v),v),w),w),w),mult(rd(mult(u,w),w),w)),
inference(spr,[status(thm),theory(equality)],[981,4]),
[iquote('0:SpR:981.0,4.0')] ).
cnf(1749,plain,
equal(mult(rd(mult(u,v),v),w),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[102,1677,4]),
[iquote('0:Rew:102.0,1677.0,102.0,1677.0,4.0,1677.0')] ).
cnf(2078,plain,
equal(ld(rd(mult(u,v),v),mult(rd(mult(u,v),v),w)),ld(rd(u,v),mult(rd(u,v),w))),
inference(spr,[status(thm),theory(equality)],[4,1011]),
[iquote('0:SpR:4.0,1011.0')] ).
cnf(2081,plain,
equal(ld(mult(u,v),mult(mult(u,v),w)),ld(rd(mult(u,x),x),mult(rd(mult(u,x),x),w))),
inference(spr,[status(thm),theory(equality)],[1749,1011]),
[iquote('0:SpR:1749.0,1011.0')] ).
cnf(2085,plain,
equal(ld(rd(mult(u,v),v),mult(u,w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1011,2081,1749]),
[iquote('0:Rew:1011.0,2081.0,1749.0,2081.0')] ).
cnf(2097,plain,
equal(ld(rd(mult(u,v),v),mult(u,w)),ld(rd(u,v),mult(rd(u,v),w))),
inference(rew,[status(thm),theory(equality)],[1749,2078]),
[iquote('0:Rew:1749.0,2078.0')] ).
cnf(2098,plain,
equal(ld(rd(u,v),mult(rd(u,v),w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[2085,2097]),
[iquote('0:Rew:2085.0,2097.0')] ).
cnf(2099,plain,
$false,
inference(unc,[status(thm)],[2098,237]),
[iquote('0:UnC:2098.0,237.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.11 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 14 04:20:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.52/0.73
% 0.52/0.73 SPASS V 3.9
% 0.52/0.73 SPASS beiseite: Proof found.
% 0.52/0.73 % SZS status Theorem
% 0.52/0.73 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.73 SPASS derived 1242 clauses, backtracked 0 clauses, performed 0 splits and kept 412 clauses.
% 0.52/0.73 SPASS allocated 88311 KBytes.
% 0.52/0.73 SPASS spent 0:00:00.38 on the problem.
% 0.52/0.73 0:00:00.04 for the input.
% 0.52/0.73 0:00:00.03 for the FLOTTER CNF translation.
% 0.52/0.73 0:00:00.01 for inferences.
% 0.52/0.73 0:00:00.00 for the backtracking.
% 0.52/0.73 0:00:00.27 for the reduction.
% 0.52/0.73
% 0.52/0.73
% 0.52/0.73 Here is a proof with depth 7, length 47 :
% 0.52/0.73 % SZS output start Refutation
% See solution above
% 0.52/0.73 Formulae used in the proof : f01 f02 f03 f04 f07 f05 f06 goals
% 0.52/0.73
%------------------------------------------------------------------------------