TSTP Solution File: GRP683+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP683+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 0.78s 0.96s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of clauses : 55 ( 53 unt; 0 nHn; 55 RR)
% Number of literals : 57 ( 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('GRP683+1.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP683+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP683+1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP683+1.p',unknown),
[] ).
cnf(5,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP683+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('GRP683+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('GRP683+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(mult(skc6,ld(skc7,mult(skc7,skc8))),mult(skc6,skc8))
| ~ equal(mult(rd(mult(skc9,skc10),skc10),skc11),mult(skc9,skc11)) ),
file('GRP683+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(21,plain,
equal(rd(mult(ld(u,u),v),v),ld(u,mult(u,ld(v,v)))),
inference(rew,[status(thm),theory(equality)],[20,5]),
[iquote('0:Rew:20.0,5.0')] ).
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(139,plain,
equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[102,73]),
[iquote('0:SpR:102.0,73.0')] ).
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(211,plain,
equal(rd(ld(u,mult(u,v)),v),ld(u,mult(u,ld(v,v)))),
inference(rew,[status(thm),theory(equality)],[209,21]),
[iquote('0:Rew:209.0,21.0')] ).
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(407,plain,
equal(rd(ld(u,mult(u,mult(v,w))),mult(v,w)),rd(mult(ld(u,u),w),w)),
inference(spr,[status(thm),theory(equality)],[209,139]),
[iquote('0:SpR:209.0,139.0')] ).
cnf(409,plain,
equal(ld(u,mult(u,ld(mult(v,w),mult(v,w)))),ld(u,mult(u,ld(w,w)))),
inference(rew,[status(thm),theory(equality)],[211,407,209]),
[iquote('0:Rew:211.0,407.0,211.0,407.0,209.0,407.0')] ).
cnf(655,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(716,plain,
equal(ld(u,mult(u,ld(mult(u,v),mult(u,v)))),rd(mult(u,v),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[655,211]),
[iquote('0:SpR:655.0,211.0')] ).
cnf(730,plain,
equal(ld(u,mult(u,ld(mult(u,v),mult(u,v)))),ld(mult(u,v),mult(u,v))),
inference(rew,[status(thm),theory(equality)],[20,716]),
[iquote('0:Rew:20.0,716.0')] ).
cnf(731,plain,
equal(ld(mult(u,v),mult(u,v)),ld(u,mult(u,ld(v,v)))),
inference(rew,[status(thm),theory(equality)],[409,730]),
[iquote('0:Rew:409.0,730.0')] ).
cnf(967,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(979,plain,
equal(rd(mult(rd(mult(u,v),v),w),w),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[183,967]),
[iquote('0:Rew:183.0,967.0')] ).
cnf(1009,plain,
equal(ld(mult(u,v),mult(mult(u,v),w)),ld(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[655,216]),
[iquote('0:SpR:655.0,216.0')] ).
cnf(1512,plain,
equal(mult(ld(u,mult(u,ld(v,v))),w),ld(mult(u,v),mult(mult(u,v),w))),
inference(spr,[status(thm),theory(equality)],[731,209]),
[iquote('0:SpR:731.0,209.0')] ).
cnf(1536,plain,
equal(ld(mult(u,v),mult(mult(u,v),w)),ld(u,mult(u,ld(v,mult(v,w))))),
inference(rew,[status(thm),theory(equality)],[209,1512,195]),
[iquote('0:Rew:209.0,1512.0,195.0,1512.0')] ).
cnf(1537,plain,
equal(ld(u,mult(u,ld(v,mult(v,w)))),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1009,1536]),
[iquote('0:Rew:1009.0,1536.0')] ).
cnf(1675,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)],[979,4]),
[iquote('0:SpR:979.0,4.0')] ).
cnf(1747,plain,
equal(mult(rd(mult(u,v),v),w),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[102,1675,4]),
[iquote('0:Rew:102.0,1675.0,102.0,1675.0,4.0,1675.0')] ).
cnf(1748,plain,
( ~ equal(mult(skc6,ld(skc7,mult(skc7,skc8))),mult(skc6,skc8))
| ~ equal(mult(skc9,skc11),mult(skc9,skc11)) ),
inference(rew,[status(thm),theory(equality)],[1747,8]),
[iquote('0:Rew:1747.0,8.1')] ).
cnf(1773,plain,
~ equal(mult(skc6,ld(skc7,mult(skc7,skc8))),mult(skc6,skc8)),
inference(obv,[status(thm),theory(equality)],[1748]),
[iquote('0:Obv:1748.1')] ).
cnf(3558,plain,
equal(ld(u,mult(u,mult(u,ld(v,mult(v,w))))),mult(u,ld(u,mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[1537,3]),
[iquote('0:SpR:1537.0,3.0')] ).
cnf(3609,plain,
equal(mult(u,ld(v,mult(v,w))),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[655,3558,3]),
[iquote('0:Rew:655.0,3558.0,655.0,3558.0,3.0,3558.0')] ).
cnf(3610,plain,
$false,
inference(unc,[status(thm)],[3609,1773]),
[iquote('0:UnC:3609.0,1773.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP683+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 07:37:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.78/0.96
% 0.78/0.96 SPASS V 3.9
% 0.78/0.96 SPASS beiseite: Proof found.
% 0.78/0.96 % SZS status Theorem
% 0.78/0.96 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.96 SPASS derived 2078 clauses, backtracked 0 clauses, performed 0 splits and kept 683 clauses.
% 0.78/0.96 SPASS allocated 90315 KBytes.
% 0.78/0.96 SPASS spent 0:00:00.59 on the problem.
% 0.78/0.96 0:00:00.03 for the input.
% 0.78/0.96 0:00:00.02 for the FLOTTER CNF translation.
% 0.78/0.96 0:00:00.02 for inferences.
% 0.78/0.96 0:00:00.00 for the backtracking.
% 0.78/0.96 0:00:00.49 for the reduction.
% 0.78/0.96
% 0.78/0.96
% 0.78/0.96 Here is a proof with depth 6, length 55 :
% 0.78/0.96 % SZS output start Refutation
% See solution above
% 0.78/0.96 Formulae used in the proof : f01 f02 f03 f04 f07 f05 f06 goals
% 0.78/0.96
%------------------------------------------------------------------------------