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  
%------------------------------------------------------------------------------