TSTP Solution File: LCL203-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL203-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 14:35:24 EDT 2022

% Result   : Unsatisfiable 2.22s 2.40s
% Output   : Refutation 2.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   55 (  37 unt;   0 nHn;  55 RR)
%            Number of literals    :   76 (   0 equ;  23 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(not__dfg(or__dfg(p,q)),or__dfg(not__dfg(p),not__dfg(q)))),
    file('LCL203-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL203-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL203-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL203-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL203-3.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
    file('LCL203-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL203-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL203-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL203-3.p',unknown),
    [] ).

cnf(10,plain,
    ~ theorem(implies__dfg(not__dfg(or__dfg(p,q)),implies__dfg(p,not__dfg(q)))),
    inference(rew,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Rew:7.0,1.0')] ).

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(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)],[20,17]),
    [iquote('0:SoR:20.0,17.0')] ).

cnf(24,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[20,16]),
    [iquote('0:SoR:20.0,16.0')] ).

cnf(26,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[20,4]),
    [iquote('0:SoR:20.0,4.0')] ).

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(36,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(37,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(41,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,37]),
    [iquote('0:Rew:7.0,37.0')] ).

cnf(49,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(61,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(72,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
    inference(sor,[status(thm)],[61,4]),
    [iquote('0:SoR:61.0,4.0')] ).

cnf(73,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[61,3]),
    [iquote('0:SoR:61.0,3.0')] ).

cnf(77,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[20,41]),
    [iquote('0:SoR:20.0,41.0')] ).

cnf(78,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)],[7,41]),
    [iquote('0:SpR:7.0,41.0')] ).

cnf(80,plain,
    axiom(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,78]),
    [iquote('0:Rew:7.0,78.0')] ).

cnf(88,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[24,73]),
    [iquote('0:SoR:24.0,73.0')] ).

cnf(120,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    inference(sor,[status(thm)],[24,72]),
    [iquote('0:SoR:24.0,72.0')] ).

cnf(132,plain,
    ( ~ theorem(implies__dfg(u,implies__dfg(v,w)))
    | theorem(implies__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[20,80]),
    [iquote('0:SoR:20.0,80.0')] ).

cnf(145,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,or__dfg(w,v))) ),
    inference(sor,[status(thm)],[36,27]),
    [iquote('0:SoR:36.0,27.1')] ).

cnf(188,plain,
    theorem(or__dfg(u,implies__dfg(or__dfg(v,u),v))),
    inference(sor,[status(thm)],[77,120]),
    [iquote('0:SoR:77.0,120.0')] ).

cnf(191,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[77,88]),
    [iquote('0:SoR:77.0,88.0')] ).

cnf(193,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[28,191]),
    [iquote('0:SoR:28.0,191.0')] ).

cnf(197,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[21,193]),
    [iquote('0:SoR:21.0,193.0')] ).

cnf(198,plain,
    theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
    inference(sor,[status(thm)],[77,193]),
    [iquote('0:SoR:77.0,193.0')] ).

cnf(202,plain,
    theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,197]),
    [iquote('0:SpR:7.0,197.0')] ).

cnf(204,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
    inference(sor,[status(thm)],[49,202]),
    [iquote('0:SoR:49.0,202.0')] ).

cnf(263,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),u),v)),
    inference(sor,[status(thm)],[26,188]),
    [iquote('0:SoR:26.0,188.0')] ).

cnf(269,plain,
    theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
    inference(spr,[status(thm),theory(equality)],[7,198]),
    [iquote('0:SpR:7.0,198.0')] ).

cnf(271,plain,
    theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
    inference(rew,[status(thm),theory(equality)],[7,269]),
    [iquote('0:Rew:7.0,269.0')] ).

cnf(282,plain,
    theorem(or__dfg(u,or__dfg(v,not__dfg(u)))),
    inference(sor,[status(thm)],[145,197]),
    [iquote('0:SoR:145.0,197.0')] ).

cnf(290,plain,
    theorem(or__dfg(or__dfg(u,not__dfg(v)),v)),
    inference(sor,[status(thm)],[26,282]),
    [iquote('0:SoR:26.0,282.0')] ).

cnf(299,plain,
    theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
    inference(spr,[status(thm),theory(equality)],[7,290]),
    [iquote('0:SpR:7.0,290.0')] ).

cnf(319,plain,
    theorem(or__dfg(implies__dfg(u,not__dfg(v)),or__dfg(w,v))),
    inference(sor,[status(thm)],[145,299]),
    [iquote('0:SoR:145.0,299.0')] ).

cnf(444,plain,
    ( ~ theorem(u)
    | theorem(implies__dfg(implies__dfg(u,v),v)) ),
    inference(res,[status(thm),theory(equality)],[271,9]),
    [iquote('0:Res:271.0,9.1')] ).

cnf(843,plain,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    inference(res,[status(thm),theory(equality)],[444,9]),
    [iquote('0:Res:444.1,9.1')] ).

cnf(1386,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
    inference(res,[status(thm),theory(equality)],[204,9]),
    [iquote('0:Res:204.0,9.1')] ).

cnf(3768,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),u),not__dfg(not__dfg(v)))),
    inference(sor,[status(thm)],[1386,263]),
    [iquote('0:SoR:1386.0,263.0')] ).

cnf(4783,plain,
    theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(v,u),v))),
    inference(sor,[status(thm)],[24,3768]),
    [iquote('0:SoR:24.0,3768.0')] ).

cnf(4800,plain,
    theorem(implies__dfg(or__dfg(u,v),implies__dfg(not__dfg(v),u))),
    inference(sor,[status(thm)],[132,4783]),
    [iquote('0:SoR:132.0,4783.0')] ).

cnf(4803,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(implies__dfg(not__dfg(v),u)) ),
    inference(sor,[status(thm)],[843,4800]),
    [iquote('0:SoR:843.1,4800.0')] ).

cnf(6183,plain,
    theorem(implies__dfg(not__dfg(or__dfg(u,v)),implies__dfg(w,not__dfg(v)))),
    inference(sor,[status(thm)],[4803,319]),
    [iquote('0:SoR:4803.0,319.0')] ).

cnf(6396,plain,
    $false,
    inference(unc,[status(thm)],[6183,10]),
    [iquote('0:UnC:6183.0,10.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL203-3 : TPTP v8.1.0. Released v2.3.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul  4 02:18:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.22/2.40  
% 2.22/2.40  SPASS V 3.9 
% 2.22/2.40  SPASS beiseite: Proof found.
% 2.22/2.40  % SZS status Theorem
% 2.22/2.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.22/2.40  SPASS derived 6055 clauses, backtracked 0 clauses, performed 0 splits and kept 2813 clauses.
% 2.22/2.40  SPASS allocated 83838 KBytes.
% 2.22/2.40  SPASS spent	0:00:02.01 on the problem.
% 2.22/2.40  		0:00:00.04 for the input.
% 2.22/2.40  		0:00:00.00 for the FLOTTER CNF translation.
% 2.22/2.40  		0:00:00.24 for inferences.
% 2.22/2.40  		0:00:00.00 for the backtracking.
% 2.22/2.40  		0:00:01.67 for the reduction.
% 2.22/2.40  
% 2.22/2.40  
% 2.22/2.40  Here is a proof with depth 16, length 55 :
% 2.22/2.40  % SZS output start Refutation
% See solution above
% 2.22/2.40  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
% 2.22/2.40  
%------------------------------------------------------------------------------