TSTP Solution File: BOO075-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0.
% 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 : Thu Jul 14 23:49:34 EDT 2022
% Result : Unsatisfiable 0.69s 0.86s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,nand__dfg(w,u))),v),
file('BOO075-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(nand__dfg(nand__dfg(a,a),nand__dfg(b,a)),a),
file('BOO075-1.p',unknown),
[] ).
cnf(4,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,v),nand__dfg(nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(w,v),v)),nand__dfg(u,v)),nand__dfg(u,v))),w),nand__dfg(v,nand__dfg(nand__dfg(w,v),v))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,nand__dfg(v,w)),nand__dfg(nand__dfg(x,nand__dfg(u,nand__dfg(v,w))),nand__dfg(u,nand__dfg(v,w)))),nand__dfg(x,u)),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(11,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,v),nand__dfg(nand__dfg(w,nand__dfg(u,v)),nand__dfg(u,v))),nand__dfg(w,u)),w),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(17,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,nand__dfg(w,nand__dfg(nand__dfg(u,w),w)))),v),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(20,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,nand__dfg(v,w)),nand__dfg(u,nand__dfg(u,nand__dfg(v,w)))),nand__dfg(nand__dfg(w,nand__dfg(nand__dfg(u,w),w)),u)),nand__dfg(w,nand__dfg(nand__dfg(u,w),w))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(67,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(v,v),v)),u),u)),v),nand__dfg(v,nand__dfg(nand__dfg(v,v),v))),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(88,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(v,v),v)),nand__dfg(v,nand__dfg(v,nand__dfg(nand__dfg(v,v),v)))),u),u)),nand__dfg(v,nand__dfg(nand__dfg(v,v),v))),nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(v,v),v)),nand__dfg(v,nand__dfg(v,nand__dfg(nand__dfg(v,v),v))))),
inference(spr,[status(thm),theory(equality)],[1,67]),
[iquote('0:SpR:1.0,67.0')] ).
cnf(92,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,nand__dfg(nand__dfg(v,v),v))),v),
inference(rew,[status(thm),theory(equality)],[17,88]),
[iquote('0:Rew:17.0,88.0')] ).
cnf(99,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(u,u),u)),nand__dfg(u,nand__dfg(u,nand__dfg(nand__dfg(u,u),u)))),nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(u,v),v)),u)),nand__dfg(v,nand__dfg(nand__dfg(u,v),v))),
inference(spr,[status(thm),theory(equality)],[92,11]),
[iquote('0:SpR:92.0,11.0')] ).
cnf(120,plain,
equal(nand__dfg(u,nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(u,v),v)),u)),nand__dfg(v,nand__dfg(nand__dfg(u,v),v))),
inference(rew,[status(thm),theory(equality)],[17,99]),
[iquote('0:Rew:17.0,99.0')] ).
cnf(144,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(u,u),u)),nand__dfg(v,nand__dfg(nand__dfg(u,v),v))),u),
inference(spr,[status(thm),theory(equality)],[120,1]),
[iquote('0:SpR:120.0,1.0')] ).
cnf(160,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(v,v),v)),nand__dfg(v,nand__dfg(v,nand__dfg(nand__dfg(v,v),v)))),nand__dfg(u,nand__dfg(nand__dfg(v,u),u)))),nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(v,v),v)),nand__dfg(v,nand__dfg(v,nand__dfg(nand__dfg(v,v),v))))),
inference(spr,[status(thm),theory(equality)],[92,120]),
[iquote('0:SpR:92.0,120.0')] ).
cnf(165,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,nand__dfg(u,nand__dfg(nand__dfg(v,u),u)))),v),
inference(rew,[status(thm),theory(equality)],[17,160]),
[iquote('0:Rew:17.0,160.0')] ).
cnf(279,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,nand__dfg(u,nand__dfg(nand__dfg(v,u),u)))),nand__dfg(nand__dfg(v,nand__dfg(nand__dfg(v,v),v)),u)),nand__dfg(v,nand__dfg(nand__dfg(v,v),v))),
inference(spr,[status(thm),theory(equality)],[144,11]),
[iquote('0:SpR:144.0,11.0')] ).
cnf(289,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,nand__dfg(u,nand__dfg(nand__dfg(v,u),u)))),v),nand__dfg(v,nand__dfg(nand__dfg(v,v),v))),
inference(spr,[status(thm),theory(equality)],[144,67]),
[iquote('0:SpR:144.0,67.0')] ).
cnf(312,plain,
equal(nand__dfg(u,nand__dfg(nand__dfg(u,u),u)),nand__dfg(u,u)),
inference(rew,[status(thm),theory(equality)],[165,289]),
[iquote('0:Rew:165.0,289.0')] ).
cnf(314,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(v,v)),v),
inference(rew,[status(thm),theory(equality)],[312,92]),
[iquote('0:Rew:312.0,92.0')] ).
cnf(315,plain,
equal(nand__dfg(nand__dfg(u,u),nand__dfg(v,nand__dfg(nand__dfg(u,v),v))),u),
inference(rew,[status(thm),theory(equality)],[312,144]),
[iquote('0:Rew:312.0,144.0')] ).
cnf(345,plain,
equal(nand__dfg(u,nand__dfg(nand__dfg(u,u),v)),nand__dfg(u,u)),
inference(rew,[status(thm),theory(equality)],[165,279,312]),
[iquote('0:Rew:165.0,279.0,312.0,279.0')] ).
cnf(412,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(u,u),u)),nand__dfg(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1,345]),
[iquote('0:SpR:1.0,345.0')] ).
cnf(415,plain,
equal(nand__dfg(nand__dfg(u,u),nand__dfg(u,v)),u),
inference(rew,[status(thm),theory(equality)],[345,412]),
[iquote('0:Rew:345.0,412.0')] ).
cnf(484,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,v),nand__dfg(u,nand__dfg(u,v))),nand__dfg(nand__dfg(u,u),nand__dfg(u,u))),nand__dfg(u,u)),
inference(spr,[status(thm),theory(equality)],[415,314]),
[iquote('0:SpR:415.0,314.0')] ).
cnf(489,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,v),nand__dfg(u,nand__dfg(u,v))),u),nand__dfg(u,u)),
inference(rew,[status(thm),theory(equality)],[415,484]),
[iquote('0:Rew:415.0,484.0')] ).
cnf(503,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(nand__dfg(nand__dfg(u,nand__dfg(v,w)),nand__dfg(u,nand__dfg(u,nand__dfg(v,w)))),u),u)),nand__dfg(w,nand__dfg(nand__dfg(u,w),w))),nand__dfg(nand__dfg(u,nand__dfg(v,w)),nand__dfg(u,nand__dfg(u,nand__dfg(v,w))))),
inference(spr,[status(thm),theory(equality)],[20,1]),
[iquote('0:SpR:20.0,1.0')] ).
cnf(580,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(nand__dfg(u,u),u)),nand__dfg(v,nand__dfg(nand__dfg(u,v),v))),nand__dfg(nand__dfg(u,nand__dfg(w,v)),nand__dfg(u,nand__dfg(u,nand__dfg(w,v))))),
inference(rew,[status(thm),theory(equality)],[489,503]),
[iquote('0:Rew:489.0,503.0')] ).
cnf(581,plain,
equal(nand__dfg(nand__dfg(u,u),nand__dfg(v,nand__dfg(nand__dfg(u,v),v))),nand__dfg(nand__dfg(u,nand__dfg(w,v)),nand__dfg(u,nand__dfg(u,nand__dfg(w,v))))),
inference(rew,[status(thm),theory(equality)],[345,580]),
[iquote('0:Rew:345.0,580.0')] ).
cnf(582,plain,
equal(nand__dfg(nand__dfg(u,nand__dfg(v,w)),nand__dfg(u,nand__dfg(u,nand__dfg(v,w)))),u),
inference(rew,[status(thm),theory(equality)],[315,581]),
[iquote('0:Rew:315.0,581.0')] ).
cnf(1005,plain,
equal(nand__dfg(nand__dfg(u,v),nand__dfg(u,nand__dfg(u,v))),u),
inference(spr,[status(thm),theory(equality)],[582]),
[iquote('0:SpR:582.0,582.0')] ).
cnf(1147,plain,
equal(nand__dfg(u,nand__dfg(nand__dfg(u,v),u)),nand__dfg(u,v)),
inference(spr,[status(thm),theory(equality)],[1005]),
[iquote('0:SpR:1005.0,1005.0')] ).
cnf(1215,plain,
equal(nand__dfg(nand__dfg(nand__dfg(nand__dfg(u,v),u),nand__dfg(nand__dfg(u,v),nand__dfg(nand__dfg(u,v),u))),nand__dfg(u,u)),u),
inference(spr,[status(thm),theory(equality)],[1147,314]),
[iquote('0:SpR:1147.0,314.0')] ).
cnf(1255,plain,
equal(nand__dfg(nand__dfg(u,v),nand__dfg(u,u)),u),
inference(rew,[status(thm),theory(equality)],[1005,1215]),
[iquote('0:Rew:1005.0,1215.0')] ).
cnf(1270,plain,
equal(nand__dfg(nand__dfg(nand__dfg(u,u),nand__dfg(u,nand__dfg(u,u))),v),nand__dfg(u,nand__dfg(nand__dfg(v,u),u))),
inference(spr,[status(thm),theory(equality)],[1255,4]),
[iquote('0:SpR:1255.0,4.0')] ).
cnf(1340,plain,
equal(nand__dfg(u,nand__dfg(nand__dfg(v,u),u)),nand__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[1005,1270]),
[iquote('0:Rew:1005.0,1270.0')] ).
cnf(1344,plain,
equal(nand__dfg(nand__dfg(u,u),nand__dfg(v,u)),u),
inference(rew,[status(thm),theory(equality)],[1340,315]),
[iquote('0:Rew:1340.0,315.0')] ).
cnf(1421,plain,
$false,
inference(unc,[status(thm)],[1344,2]),
[iquote('0:UnC:1344.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO075-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n029.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 1 20:31:46 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.69/0.86
% 0.69/0.86 SPASS V 3.9
% 0.69/0.86 SPASS beiseite: Proof found.
% 0.69/0.86 % SZS status Theorem
% 0.69/0.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.86 SPASS derived 1104 clauses, backtracked 0 clauses, performed 0 splits and kept 338 clauses.
% 0.69/0.86 SPASS allocated 67253 KBytes.
% 0.69/0.86 SPASS spent 0:00:00.50 on the problem.
% 0.69/0.86 0:00:00.04 for the input.
% 0.69/0.86 0:00:00.00 for the FLOTTER CNF translation.
% 0.69/0.86 0:00:00.02 for inferences.
% 0.69/0.86 0:00:00.00 for the backtracking.
% 0.69/0.86 0:00:00.43 for the reduction.
% 0.69/0.86
% 0.69/0.86
% 0.69/0.86 Here is a proof with depth 9, length 37 :
% 0.69/0.86 % SZS output start Refutation
% See solution above
% 0.69/0.86 Formulae used in the proof : sh_1 prove_meredith_2_basis_1
% 0.69/0.86
%------------------------------------------------------------------------------