TSTP Solution File: LCL320-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL320-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 14:36:16 EDT 2022

% Result   : Unsatisfiable 1.67s 1.88s
% Output   : Refutation 1.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   42 (  27 unt;   0 nHn;  42 RR)
%            Number of literals    :   59 (   0 equ;  18 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(or__dfg(implies__dfg(p,q),implies__dfg(not__dfg(p),q))),
    file('LCL320-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL320-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL320-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL320-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL320-3.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
    file('LCL320-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL320-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL320-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL320-3.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(20,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)],[20,16]),
    [iquote('0:SoR:20.0,16.0')] ).

cnf(24,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[20,15]),
    [iquote('0:SoR:20.0,15.0')] ).

cnf(27,plain,
    ( ~ theorem(u)
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[20,3]),
    [iquote('0:SoR:20.0,3.0')] ).

cnf(28,plain,
    ( ~ theorem(or__dfg(u,u))
    | theorem(u) ),
    inference(sor,[status(thm)],[20,2]),
    [iquote('0:SoR:20.0,2.0')] ).

cnf(29,plain,
    ( ~ theorem(or__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,or__dfg(u,w))) ),
    inference(sor,[status(thm)],[20,5]),
    [iquote('0:SoR:20.0,5.0')] ).

cnf(30,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(31,plain,
    axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
    inference(spr,[status(thm),theory(equality)],[7,5]),
    [iquote('0:SpR:7.0,5.0')] ).

cnf(34,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,30]),
    [iquote('0:Rew:7.0,30.0')] ).

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

cnf(44,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[20,6]),
    [iquote('0:SoR:20.0,6.0')] ).

cnf(51,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[20,34]),
    [iquote('0:SoR:20.0,34.0')] ).

cnf(64,plain,
    ( ~ theorem(or__dfg(u,implies__dfg(v,w)))
    | theorem(implies__dfg(v,or__dfg(u,w))) ),
    inference(sor,[status(thm)],[20,35]),
    [iquote('0:SoR:20.0,35.0')] ).

cnf(74,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(89,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[74,3]),
    [iquote('0:SoR:74.0,3.0')] ).

cnf(100,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[24,89]),
    [iquote('0:SoR:24.0,89.0')] ).

cnf(107,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,or__dfg(w,v))) ),
    inference(sor,[status(thm)],[29,27]),
    [iquote('0:SoR:29.0,27.1')] ).

cnf(131,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[44,8]),
    [iquote('0:SoR:44.0,8.1')] ).

cnf(151,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[51,100]),
    [iquote('0:SoR:51.0,100.0')] ).

cnf(153,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[28,151]),
    [iquote('0:SoR:28.0,151.0')] ).

cnf(157,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[21,153]),
    [iquote('0:SoR:21.0,153.0')] ).

cnf(263,plain,
    theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
    inference(sor,[status(thm)],[107,157]),
    [iquote('0:SoR:107.0,157.0')] ).

cnf(528,plain,
    theorem(implies__dfg(or__dfg(u,or__dfg(v,not__dfg(w))),or__dfg(u,implies__dfg(w,v)))),
    inference(sor,[status(thm)],[131,15]),
    [iquote('0:SoR:131.0,15.0')] ).

cnf(1534,plain,
    ( ~ theorem(or__dfg(u,or__dfg(v,not__dfg(w))))
    | theorem(or__dfg(u,implies__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[528,9]),
    [iquote('0:Res:528.0,9.1')] ).

cnf(4349,plain,
    theorem(or__dfg(u,implies__dfg(u,v))),
    inference(sor,[status(thm)],[1534,263]),
    [iquote('0:SoR:1534.0,263.0')] ).

cnf(4419,plain,
    theorem(implies__dfg(u,or__dfg(u,v))),
    inference(sor,[status(thm)],[64,4349]),
    [iquote('0:SoR:64.0,4349.0')] ).

cnf(4435,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(u))),
    inference(sor,[status(thm)],[21,4419]),
    [iquote('0:SoR:21.0,4419.0')] ).

cnf(4459,plain,
    theorem(or__dfg(or__dfg(u,v),or__dfg(w,not__dfg(u)))),
    inference(sor,[status(thm)],[107,4435]),
    [iquote('0:SoR:107.0,4435.0')] ).

cnf(5466,plain,
    theorem(or__dfg(or__dfg(u,v),implies__dfg(u,w))),
    inference(sor,[status(thm)],[1534,4459]),
    [iquote('0:SoR:1534.0,4459.0')] ).

cnf(5476,plain,
    theorem(or__dfg(implies__dfg(u,v),implies__dfg(not__dfg(u),w))),
    inference(spr,[status(thm),theory(equality)],[7,5466]),
    [iquote('0:SpR:7.0,5466.0')] ).

cnf(5477,plain,
    $false,
    inference(unc,[status(thm)],[5476,1]),
    [iquote('0:UnC:5476.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LCL320-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n008.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 : Sat Jul  2 11:28:08 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 1.67/1.88  
% 1.67/1.88  SPASS V 3.9 
% 1.67/1.88  SPASS beiseite: Proof found.
% 1.67/1.88  % SZS status Theorem
% 1.67/1.88  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.67/1.88  SPASS derived 5162 clauses, backtracked 0 clauses, performed 0 splits and kept 2412 clauses.
% 1.67/1.88  SPASS allocated 82266 KBytes.
% 1.67/1.88  SPASS spent	0:00:01.48 on the problem.
% 1.67/1.88  		0:00:00.03 for the input.
% 1.67/1.88  		0:00:00.00 for the FLOTTER CNF translation.
% 1.67/1.88  		0:00:00.19 for inferences.
% 1.67/1.88  		0:00:00.00 for the backtracking.
% 1.67/1.88  		0:00:01.20 for the reduction.
% 1.67/1.88  
% 1.67/1.88  
% 1.67/1.88  Here is a proof with depth 15, length 42 :
% 1.67/1.88  % SZS output start Refutation
% See solution above
% 1.67/1.88  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
% 1.67/1.88  
%------------------------------------------------------------------------------