TSTP Solution File: LCL499+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 14:37:23 EDT 2022

% Result   : Theorem 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   26 (  17 unt;   0 nHn;  26 RR)
%            Number of literals    :   38 (   0 equ;  14 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    9 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    op_implies_or,
    file('LCL499+1.p',unknown),
    [] ).

cnf(5,axiom,
    op_and,
    file('LCL499+1.p',unknown),
    [] ).

cnf(7,axiom,
    modus_ponens,
    file('LCL499+1.p',unknown),
    [] ).

cnf(8,axiom,
    r1,
    file('LCL499+1.p',unknown),
    [] ).

cnf(10,axiom,
    r3,
    file('LCL499+1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ kn1,
    file('LCL499+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
    | kn1 ),
    file('LCL499+1.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ r1
    | is_a_theorem(implies__dfg(or__dfg(u,u),u)) ),
    file('LCL499+1.p',unknown),
    [] ).

cnf(49,axiom,
    ( ~ r3
    | is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
    file('LCL499+1.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ op_implies_or
    | equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
    file('LCL499+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ is_a_theorem(u)
    | ~ modus_ponens
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    file('LCL499+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ op_and
    | equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
    file('LCL499+1.p',unknown),
    [] ).

cnf(76,plain,
    is_a_theorem(implies__dfg(or__dfg(u,u),u)),
    inference(mrr,[status(thm)],[34,8]),
    [iquote('0:MRR:34.0,8.0')] ).

cnf(77,plain,
    ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87))),
    inference(mrr,[status(thm)],[31,14]),
    [iquote('0:MRR:31.1,14.0')] ).

cnf(79,plain,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    inference(mrr,[status(thm)],[51,4]),
    [iquote('0:MRR:51.0,4.0')] ).

cnf(80,plain,
    is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    inference(mrr,[status(thm)],[49,10]),
    [iquote('0:MRR:49.0,10.0')] ).

cnf(83,plain,
    ( ~ op_and
    | equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[79,59]),
    [iquote('0:Rew:79.0,59.1')] ).

cnf(84,plain,
    equal(not__dfg(implies__dfg(u,not__dfg(v))),and__dfg(u,v)),
    inference(mrr,[status(thm)],[83,5]),
    [iquote('0:MRR:83.0,5.0')] ).

cnf(94,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    inference(mrr,[status(thm)],[53,7]),
    [iquote('0:MRR:53.1,7.0')] ).

cnf(113,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(u)),not__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[79,76]),
    [iquote('0:SpR:79.0,76.0')] ).

cnf(171,plain,
    equal(implies__dfg(implies__dfg(u,not__dfg(v)),w),or__dfg(and__dfg(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[84,79]),
    [iquote('0:SpR:84.0,79.0')] ).

cnf(185,plain,
    is_a_theorem(or__dfg(and__dfg(u,u),not__dfg(u))),
    inference(rew,[status(thm),theory(equality)],[171,113]),
    [iquote('0:Rew:171.0,113.0')] ).

cnf(252,plain,
    ( ~ is_a_theorem(or__dfg(u,v))
    | is_a_theorem(or__dfg(v,u)) ),
    inference(res,[status(thm),theory(equality)],[80,94]),
    [iquote('0:Res:80.0,94.1')] ).

cnf(345,plain,
    is_a_theorem(or__dfg(not__dfg(u),and__dfg(u,u))),
    inference(sor,[status(thm)],[252,185]),
    [iquote('0:SoR:252.0,185.0')] ).

cnf(354,plain,
    is_a_theorem(implies__dfg(u,and__dfg(u,u))),
    inference(rew,[status(thm),theory(equality)],[79,345]),
    [iquote('0:Rew:79.0,345.0')] ).

cnf(355,plain,
    $false,
    inference(unc,[status(thm)],[354,77]),
    [iquote('0:UnC:354.0,77.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL499+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 21:47:03 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.49  
% 0.18/0.49  SPASS V 3.9 
% 0.18/0.49  SPASS beiseite: Proof found.
% 0.18/0.49  % SZS status Theorem
% 0.18/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.49  SPASS derived 218 clauses, backtracked 0 clauses, performed 0 splits and kept 198 clauses.
% 0.18/0.49  SPASS allocated 98110 KBytes.
% 0.18/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.18/0.49  		0:00:00.04 for the input.
% 0.18/0.49  		0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.49  		0:00:00.00 for inferences.
% 0.18/0.49  		0:00:00.00 for the backtracking.
% 0.18/0.49  		0:00:00.02 for the reduction.
% 0.18/0.49  
% 0.18/0.49  
% 0.18/0.49  Here is a proof with depth 2, length 26 :
% 0.18/0.49  % SZS output start Refutation
% See solution above
% 0.18/0.49  Formulae used in the proof : principia_op_implies_or principia_op_and principia_modus_ponens principia_r1 principia_r3 rosser_kn1 kn1 r1 r3 op_implies_or modus_ponens principia_r2 r2 op_and
% 0.18/0.49  
%------------------------------------------------------------------------------