TSTP Solution File: LCL239-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 14:35:48 EDT 2022

% Result   : Unsatisfiable 1.07s 1.25s
% Output   : Refutation 1.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   31 (  21 unt;   0 nHn;  31 RR)
%            Number of literals    :   44 (   0 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(not__dfg(and__dfg(p,not__dfg(p)))),
    file('LCL239-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL239-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL239-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL239-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL239-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL239-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL239-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL239-3.p',unknown),
    [] ).

cnf(10,axiom,
    equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
    file('LCL239-3.p',unknown),
    [] ).

cnf(11,plain,
    equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
    inference(rew,[status(thm),theory(equality)],[7,10]),
    [iquote('0:Rew:7.0,10.0')] ).

cnf(18,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(19,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,
    equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[11,7]),
    [iquote('0:SpR:11.0,7.0')] ).

cnf(38,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(39,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[38,19]),
    [iquote('0:SoR:38.0,19.0')] ).

cnf(42,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[38,18]),
    [iquote('0:SoR:38.0,18.0')] ).

cnf(44,plain,
    ( ~ theorem(or__dfg(u,u))
    | theorem(u) ),
    inference(sor,[status(thm)],[38,2]),
    [iquote('0:SoR:38.0,2.0')] ).

cnf(50,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(54,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,50]),
    [iquote('0:Rew:7.0,50.0')] ).

cnf(88,plain,
    ( ~ theorem(implies__dfg(u,not__dfg(v)))
    | ~ theorem(or__dfg(and__dfg(u,v),w))
    | theorem(w) ),
    inference(spl,[status(thm),theory(equality)],[20,9]),
    [iquote('0:SpL:20.0,9.1')] ).

cnf(108,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[39,8]),
    [iquote('0:SoR:39.0,8.1')] ).

cnf(114,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[38,54]),
    [iquote('0:SoR:38.0,54.0')] ).

cnf(131,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[108,3]),
    [iquote('0:SoR:108.0,3.0')] ).

cnf(156,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[42,131]),
    [iquote('0:SoR:42.0,131.0')] ).

cnf(367,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[114,156]),
    [iquote('0:SoR:114.0,156.0')] ).

cnf(369,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[44,367]),
    [iquote('0:SoR:44.0,367.0')] ).

cnf(374,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[39,369]),
    [iquote('0:SoR:39.0,369.0')] ).

cnf(381,plain,
    theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,374]),
    [iquote('0:SpR:7.0,374.0')] ).

cnf(609,plain,
    ( ~ theorem(or__dfg(and__dfg(u,not__dfg(u)),v))
    | theorem(v) ),
    inference(sor,[status(thm)],[88,381]),
    [iquote('0:SoR:88.0,381.0')] ).

cnf(3733,plain,
    theorem(not__dfg(and__dfg(u,not__dfg(u)))),
    inference(res,[status(thm),theory(equality)],[374,609]),
    [iquote('0:Res:374.0,609.0')] ).

cnf(3743,plain,
    $false,
    inference(unc,[status(thm)],[3733,1]),
    [iquote('0:UnC:3733.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n005.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 20:31:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.07/1.25  
% 1.07/1.25  SPASS V 3.9 
% 1.07/1.25  SPASS beiseite: Proof found.
% 1.07/1.25  % SZS status Theorem
% 1.07/1.25  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.07/1.25  SPASS derived 3160 clauses, backtracked 0 clauses, performed 0 splits and kept 1480 clauses.
% 1.07/1.25  SPASS allocated 82423 KBytes.
% 1.07/1.25  SPASS spent	0:00:00.87 on the problem.
% 1.07/1.25  		0:00:00.04 for the input.
% 1.07/1.25  		0:00:00.00 for the FLOTTER CNF translation.
% 1.07/1.25  		0:00:00.06 for inferences.
% 1.07/1.25  		0:00:00.00 for the backtracking.
% 1.07/1.25  		0:00:00.74 for the reduction.
% 1.07/1.25  
% 1.07/1.25  
% 1.07/1.25  Here is a proof with depth 11, length 31 :
% 1.07/1.25  % SZS output start Refutation
% See solution above
% 1.07/1.25  Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 implies_definition rule_1 rule_2 and_defn
% 1.07/1.25  
%------------------------------------------------------------------------------