TSTP Solution File: LCL180-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL180-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 14:35:09 EDT 2022

% Result   : Unsatisfiable 1.06s 1.22s
% Output   : Refutation 1.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   31 (  21 unt;   0 nHn;  31 RR)
%            Number of literals    :   43 (   0 equ;  13 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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(implies__dfg(not__dfg(not__dfg(p)),p)),
    file('LCL180-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL180-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL180-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL180-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL180-3.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
    file('LCL180-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL180-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL180-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL180-3.p',unknown),
    [] ).

cnf(16,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(17,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(18,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(21,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[18,17]),
    [iquote('0:SoR:18.0,17.0')] ).

cnf(25,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[18,16]),
    [iquote('0:SoR:18.0,16.0')] ).

cnf(27,plain,
    ( ~ theorem(or__dfg(u,u))
    | theorem(u) ),
    inference(sor,[status(thm)],[18,2]),
    [iquote('0:SoR:18.0,2.0')] ).

cnf(31,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(35,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,31]),
    [iquote('0:Rew:7.0,31.0')] ).

cnf(43,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[18,6]),
    [iquote('0:SoR:18.0,6.0')] ).

cnf(52,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[18,35]),
    [iquote('0:SoR:18.0,35.0')] ).

cnf(68,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[21,8]),
    [iquote('0:SoR:21.0,8.1')] ).

cnf(78,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[68,3]),
    [iquote('0:SoR:68.0,3.0')] ).

cnf(93,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[25,78]),
    [iquote('0:SoR:25.0,78.0')] ).

cnf(166,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[52,93]),
    [iquote('0:SoR:52.0,93.0')] ).

cnf(168,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[27,166]),
    [iquote('0:SoR:27.0,166.0')] ).

cnf(172,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[21,168]),
    [iquote('0:SoR:21.0,168.0')] ).

cnf(177,plain,
    theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,172]),
    [iquote('0:SpR:7.0,172.0')] ).

cnf(179,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
    inference(sor,[status(thm)],[43,177]),
    [iquote('0:SoR:43.0,177.0')] ).

cnf(1365,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
    inference(res,[status(thm),theory(equality)],[179,9]),
    [iquote('0:Res:179.0,9.1')] ).

cnf(3804,plain,
    theorem(or__dfg(u,not__dfg(not__dfg(not__dfg(u))))),
    inference(sor,[status(thm)],[1365,172]),
    [iquote('0:SoR:1365.0,172.0')] ).

cnf(3894,plain,
    theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
    inference(sor,[status(thm)],[25,3804]),
    [iquote('0:SoR:25.0,3804.0')] ).

cnf(3896,plain,
    $false,
    inference(unc,[status(thm)],[3894,1]),
    [iquote('0:UnC:3894.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL180-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n026.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 Jul  4 00:38:21 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.06/1.22  
% 1.06/1.22  SPASS V 3.9 
% 1.06/1.22  SPASS beiseite: Proof found.
% 1.06/1.22  % SZS status Theorem
% 1.06/1.22  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.06/1.22  SPASS derived 3691 clauses, backtracked 0 clauses, performed 0 splits and kept 1688 clauses.
% 1.06/1.22  SPASS allocated 80377 KBytes.
% 1.06/1.22  SPASS spent	0:00:00.85 on the problem.
% 1.06/1.22  		0:00:00.03 for the input.
% 1.06/1.22  		0:00:00.00 for the FLOTTER CNF translation.
% 1.06/1.22  		0:00:00.13 for inferences.
% 1.06/1.22  		0:00:00.00 for the backtracking.
% 1.06/1.22  		0:00:00.64 for the reduction.
% 1.06/1.22  
% 1.06/1.22  
% 1.06/1.22  Here is a proof with depth 13, length 31 :
% 1.06/1.22  % SZS output start Refutation
% See solution above
% 1.06/1.22  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
% 1.06/1.22  
%------------------------------------------------------------------------------