TSTP Solution File: LCL182-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL182-3 : TPTP v8.1.0. Released v2.3.0.
% 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 : Sun Jul 17 14:35:11 EDT 2022

% Result   : Unsatisfiable 1.53s 1.68s
% Output   : Refutation 1.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   41 (  29 unt;   0 nHn;  41 RR)
%            Number of literals    :   55 (   0 equ;  15 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(implies__dfg(implies__dfg(p,q),implies__dfg(not__dfg(q),not__dfg(p)))),
    file('LCL182-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL182-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL182-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL182-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL182-3.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
    file('LCL182-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL182-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL182-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL182-3.p',unknown),
    [] ).

cnf(15,plain,
    axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(16,plain,
    axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(19,plain,
    ( ~ axiom(implies__dfg(u,v))
    | ~ theorem(u)
    | theorem(v) ),
    inference(res,[status(thm),theory(equality)],[8,9]),
    [iquote('0:Res:8.1,9.1')] ).

cnf(20,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[19,16]),
    [iquote('0:SoR:19.0,16.0')] ).

cnf(23,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[19,15]),
    [iquote('0:SoR:19.0,15.0')] ).

cnf(25,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[19,4]),
    [iquote('0:SoR:19.0,4.0')] ).

cnf(27,plain,
    ( ~ theorem(or__dfg(u,u))
    | theorem(u) ),
    inference(sor,[status(thm)],[19,2]),
    [iquote('0:SoR:19.0,2.0')] ).

cnf(36,plain,
    axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(spr,[status(thm),theory(equality)],[7,5]),
    [iquote('0:SpR:7.0,5.0')] ).

cnf(40,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,36]),
    [iquote('0:Rew:7.0,36.0')] ).

cnf(48,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[19,6]),
    [iquote('0:SoR:19.0,6.0')] ).

cnf(60,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[20,8]),
    [iquote('0:SoR:20.0,8.1')] ).

cnf(71,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
    inference(sor,[status(thm)],[60,4]),
    [iquote('0:SoR:60.0,4.0')] ).

cnf(72,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[60,3]),
    [iquote('0:SoR:60.0,3.0')] ).

cnf(76,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[19,40]),
    [iquote('0:SoR:19.0,40.0')] ).

cnf(77,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,implies__dfg(u,w)))),
    inference(spr,[status(thm),theory(equality)],[7,40]),
    [iquote('0:SpR:7.0,40.0')] ).

cnf(79,plain,
    axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,77]),
    [iquote('0:Rew:7.0,77.0')] ).

cnf(87,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[23,72]),
    [iquote('0:SoR:23.0,72.0')] ).

cnf(119,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    inference(sor,[status(thm)],[23,71]),
    [iquote('0:SoR:23.0,71.0')] ).

cnf(131,plain,
    ( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
    | theorem(implies__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[19,79]),
    [iquote('0:SoR:19.0,79.0')] ).

cnf(187,plain,
    theorem(or__dfg(u,implies__dfg(or__dfg(v,u),v))),
    inference(sor,[status(thm)],[76,119]),
    [iquote('0:SoR:76.0,119.0')] ).

cnf(190,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[76,87]),
    [iquote('0:SoR:76.0,87.0')] ).

cnf(192,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[27,190]),
    [iquote('0:SoR:27.0,190.0')] ).

cnf(196,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[20,192]),
    [iquote('0:SoR:20.0,192.0')] ).

cnf(201,plain,
    theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,196]),
    [iquote('0:SpR:7.0,196.0')] ).

cnf(203,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
    inference(sor,[status(thm)],[48,201]),
    [iquote('0:SoR:48.0,201.0')] ).

cnf(248,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),u),v)),
    inference(sor,[status(thm)],[25,187]),
    [iquote('0:SoR:25.0,187.0')] ).

cnf(1373,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
    inference(res,[status(thm),theory(equality)],[203,9]),
    [iquote('0:Res:203.0,9.1')] ).

cnf(3753,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
    inference(sor,[status(thm)],[1373,248]),
    [iquote('0:SoR:1373.0,248.0')] ).

cnf(4762,plain,
    theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
    inference(sor,[status(thm)],[23,3753]),
    [iquote('0:SoR:23.0,3753.0')] ).

cnf(4788,plain,
    theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
    inference(sor,[status(thm)],[131,4762]),
    [iquote('0:SoR:131.0,4762.0')] ).

cnf(4798,plain,
    theorem(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(v),not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,4788]),
    [iquote('0:SpR:7.0,4788.0')] ).

cnf(4800,plain,
    $false,
    inference(unc,[status(thm)],[4798,1]),
    [iquote('0:UnC:4798.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : LCL182-3 : TPTP v8.1.0. Released v2.3.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul  4 09:21:59 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 1.53/1.68  
% 1.53/1.68  SPASS V 3.9 
% 1.53/1.68  SPASS beiseite: Proof found.
% 1.53/1.68  % SZS status Theorem
% 1.53/1.68  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.53/1.68  SPASS derived 4508 clauses, backtracked 0 clauses, performed 0 splits and kept 2098 clauses.
% 1.53/1.68  SPASS allocated 81654 KBytes.
% 1.53/1.68  SPASS spent	0:00:01.28 on the problem.
% 1.53/1.68  		0:00:00.03 for the input.
% 1.53/1.68  		0:00:00.00 for the FLOTTER CNF translation.
% 1.53/1.68  		0:00:00.18 for inferences.
% 1.53/1.68  		0:00:00.00 for the backtracking.
% 1.53/1.68  		0:00:01.01 for the reduction.
% 1.53/1.68  
% 1.53/1.68  
% 1.53/1.68  Here is a proof with depth 15, length 41 :
% 1.53/1.68  % SZS output start Refutation
% See solution above
% 1.53/1.68  Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 1.53/1.68  
%------------------------------------------------------------------------------