TSTP Solution File: LCL488+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 14:37:19 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   33 (  21 unt;   0 nHn;  33 RR)
%            Number of literals    :   48 (   0 equ;  17 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   11 (  10 usr;   9 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    op_or,
    file('LCL488+1.p',unknown),
    [] ).

cnf(2,axiom,
    op_implies_and,
    file('LCL488+1.p',unknown),
    [] ).

cnf(4,axiom,
    op_implies_or,
    file('LCL488+1.p',unknown),
    [] ).

cnf(5,axiom,
    op_and,
    file('LCL488+1.p',unknown),
    [] ).

cnf(7,axiom,
    modus_ponens,
    file('LCL488+1.p',unknown),
    [] ).

cnf(9,axiom,
    r2,
    file('LCL488+1.p',unknown),
    [] ).

cnf(10,axiom,
    r3,
    file('LCL488+1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ and_2,
    file('LCL488+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ is_a_theorem(implies__dfg(and__dfg(skc71,skc70),skc70))
    | and_2 ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ r2
    | is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(49,axiom,
    ( ~ r3
    | is_a_theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ op_implies_or
    | equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(52,axiom,
    ( ~ op_implies_and
    | equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ is_a_theorem(u)
    | ~ modus_ponens
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ op_or
    | equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ op_and
    | equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)) ),
    file('LCL488+1.p',unknown),
    [] ).

cnf(75,plain,
    is_a_theorem(implies__dfg(u,or__dfg(v,u))),
    inference(mrr,[status(thm)],[36,9]),
    [iquote('0:MRR:36.0,9.0')] ).

cnf(78,plain,
    ~ is_a_theorem(implies__dfg(and__dfg(skc71,skc70),skc70)),
    inference(mrr,[status(thm)],[25,14]),
    [iquote('0:MRR:25.1,14.0')] ).

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(82,plain,
    equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
    inference(mrr,[status(thm)],[52,2]),
    [iquote('0:MRR:52.0,2.0')] ).

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(85,plain,
    ( ~ op_or
    | equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[82,58]),
    [iquote('0:Rew:82.0,58.1')] ).

cnf(86,plain,
    equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
    inference(mrr,[status(thm)],[85,1]),
    [iquote('0:MRR:85.0,1.0')] ).

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(114,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
    inference(spr,[status(thm),theory(equality)],[79,75]),
    [iquote('0:SpR:79.0,75.0')] ).

cnf(126,plain,
    is_a_theorem(or__dfg(u,implies__dfg(v,not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[86,114]),
    [iquote('0:SpR:86.0,114.0')] ).

cnf(173,plain,
    equal(or__dfg(implies__dfg(u,not__dfg(v)),w),implies__dfg(and__dfg(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[84,86]),
    [iquote('0:SpR:84.0,86.0')] ).

cnf(262,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(365,plain,
    is_a_theorem(or__dfg(implies__dfg(u,not__dfg(v)),v)),
    inference(sor,[status(thm)],[262,126]),
    [iquote('0:SoR:262.0,126.0')] ).

cnf(375,plain,
    is_a_theorem(implies__dfg(and__dfg(u,v),v)),
    inference(rew,[status(thm),theory(equality)],[173,365]),
    [iquote('0:Rew:173.0,365.0')] ).

cnf(376,plain,
    $false,
    inference(unc,[status(thm)],[375,78]),
    [iquote('0:UnC:375.0,78.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n028.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 : Sun Jul  3 05:02:33 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.49  
% 0.19/0.49  SPASS V 3.9 
% 0.19/0.49  SPASS beiseite: Proof found.
% 0.19/0.49  % SZS status Theorem
% 0.19/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.49  SPASS derived 228 clauses, backtracked 0 clauses, performed 0 splits and kept 200 clauses.
% 0.19/0.49  SPASS allocated 98130 KBytes.
% 0.19/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.19/0.49  		0:00:00.04 for the input.
% 0.19/0.49  		0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.49  		0:00:00.00 for inferences.
% 0.19/0.49  		0:00:00.00 for the backtracking.
% 0.19/0.49  		0:00:00.02 for the reduction.
% 0.19/0.49  
% 0.19/0.49  
% 0.19/0.49  Here is a proof with depth 3, length 33 :
% 0.19/0.49  % SZS output start Refutation
% See solution above
% 0.19/0.49  Formulae used in the proof : hilbert_op_or hilbert_op_implies_and principia_op_implies_or principia_op_and principia_modus_ponens principia_r2 principia_r3 hilbert_and_2 and_2 r2 r3 op_implies_or op_implies_and modus_ponens op_or op_and
% 0.19/0.49  
%------------------------------------------------------------------------------