TSTP Solution File: LCL525+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL525+1 : TPTP v8.1.0. Released v3.3.0.
% 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 14:37:30 EDT 2022

% Result   : Theorem 0.19s 0.56s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   26 (  16 unt;   0 nHn;  26 RR)
%            Number of literals    :   40 (   0 equ;  19 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    op_strict_implies,
    file('LCL525+1.p',unknown),
    [] ).

cnf(10,axiom,
    modus_ponens,
    file('LCL525+1.p',unknown),
    [] ).

cnf(26,axiom,
    necessitation,
    file('LCL525+1.p',unknown),
    [] ).

cnf(28,axiom,
    axiom_M,
    file('LCL525+1.p',unknown),
    [] ).

cnf(30,axiom,
    ~ modus_ponens_strict_implies,
    file('LCL525+1.p',unknown),
    [] ).

cnf(33,axiom,
    is_a_theorem(skc151),
    file('LCL525+1.p',unknown),
    [] ).

cnf(38,axiom,
    is_a_theorem(strict_implies(skc151,skc150)),
    file('LCL525+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ is_a_theorem(skc150)
    | modus_ponens_strict_implies ),
    file('LCL525+1.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ axiom_M
    | is_a_theorem(implies__dfg(necessarily(u),u)) ),
    file('LCL525+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ is_a_theorem(u)
    | ~ necessitation
    | is_a_theorem(necessarily(u)) ),
    file('LCL525+1.p',unknown),
    [] ).

cnf(106,axiom,
    ( ~ op_strict_implies
    | equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
    file('LCL525+1.p',unknown),
    [] ).

cnf(108,axiom,
    ( ~ is_a_theorem(u)
    | ~ modus_ponens
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    file('LCL525+1.p',unknown),
    [] ).

cnf(147,plain,
    ~ is_a_theorem(skc150),
    inference(mrr,[status(thm)],[39,30]),
    [iquote('0:MRR:39.1,30.0')] ).

cnf(148,plain,
    is_a_theorem(implies__dfg(necessarily(u),u)),
    inference(mrr,[status(thm)],[46,28]),
    [iquote('0:MRR:46.0,28.0')] ).

cnf(149,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(necessarily(u)) ),
    inference(mrr,[status(thm)],[68,26]),
    [iquote('0:MRR:68.1,26.0')] ).

cnf(159,plain,
    equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
    inference(mrr,[status(thm)],[106,4]),
    [iquote('0:MRR:106.0,4.0')] ).

cnf(175,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    inference(mrr,[status(thm)],[108,10]),
    [iquote('0:MRR:108.1,10.0')] ).

cnf(188,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,skc150)) ),
    inference(res,[status(thm),theory(equality)],[175,147]),
    [iquote('0:Res:175.2,147.0')] ).

cnf(197,plain,
    ~ is_a_theorem(necessarily(skc150)),
    inference(res,[status(thm),theory(equality)],[148,188]),
    [iquote('0:Res:148.0,188.1')] ).

cnf(201,plain,
    ~ is_a_theorem(skc150),
    inference(sor,[status(thm)],[197,149]),
    [iquote('0:SoR:197.0,149.1')] ).

cnf(218,plain,
    is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
    inference(spr,[status(thm),theory(equality)],[159,148]),
    [iquote('0:SpR:159.0,148.0')] ).

cnf(426,plain,
    ( ~ is_a_theorem(strict_implies(u,v))
    | is_a_theorem(implies__dfg(u,v)) ),
    inference(res,[status(thm),theory(equality)],[218,175]),
    [iquote('0:Res:218.0,175.1')] ).

cnf(727,plain,
    is_a_theorem(implies__dfg(skc151,skc150)),
    inference(sor,[status(thm)],[426,38]),
    [iquote('0:SoR:426.0,38.0')] ).

cnf(732,plain,
    ( ~ is_a_theorem(skc151)
    | is_a_theorem(skc150) ),
    inference(res,[status(thm),theory(equality)],[727,175]),
    [iquote('0:Res:727.0,175.1')] ).

cnf(734,plain,
    is_a_theorem(skc150),
    inference(ssi,[status(thm)],[732,33]),
    [iquote('0:SSi:732.0,33.0')] ).

cnf(735,plain,
    $false,
    inference(mrr,[status(thm)],[734,201]),
    [iquote('0:MRR:734.0,201.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : LCL525+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul  4 20:58:44 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.19/0.56  
% 0.19/0.56  SPASS V 3.9 
% 0.19/0.56  SPASS beiseite: Proof found.
% 0.19/0.56  % SZS status Theorem
% 0.19/0.56  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.56  SPASS derived 465 clauses, backtracked 0 clauses, performed 1 splits and kept 399 clauses.
% 0.19/0.56  SPASS allocated 98658 KBytes.
% 0.19/0.56  SPASS spent	0:00:00.19 on the problem.
% 0.19/0.56  		0:00:00.04 for the input.
% 0.19/0.56  		0:00:00.06 for the FLOTTER CNF translation.
% 0.19/0.56  		0:00:00.01 for inferences.
% 0.19/0.56  		0:00:00.00 for the backtracking.
% 0.19/0.56  		0:00:00.05 for the reduction.
% 0.19/0.56  
% 0.19/0.56  
% 0.19/0.56  Here is a proof with depth 4, length 26 :
% 0.19/0.56  % SZS output start Refutation
% See solution above
% 0.19/0.56  Formulae used in the proof : s1_0_op_strict_implies hilbert_modus_ponens km5_necessitation km5_axiom_M s1_0_modus_ponens_strict_implies modus_ponens_strict_implies axiom_M necessitation op_strict_implies modus_ponens hilbert_and_3 and_3
% 0.19/0.56  
%------------------------------------------------------------------------------