%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 14:37:27 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   8 unt;   0 nHn;  11 RR)
%            Number of literals    :   14 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    op_equiv,
    file('LCL512+1.p',unknown),
    [] ).

cnf(9,axiom,
    kn2,
    file('LCL512+1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equivalence_1,
    file('LCL512+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ kn2
    | is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
    file('LCL512+1.p',unknown),
    [] ).

cnf(44,axiom,
    ( ~ is_a_theorem(implies__dfg(equiv__dfg(skc82,skc81),implies__dfg(skc82,skc81)))
    | equivalence_1 ),
    file('LCL512+1.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ op_equiv
    | equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
    file('LCL512+1.p',unknown),
    [] ).

cnf(73,plain,
    is_a_theorem(implies__dfg(and__dfg(u,v),u)),
    inference(mrr,[status(thm)],[30,9]),
    [iquote('0:MRR:30.0,9.0')] ).

cnf(76,plain,
    ~ is_a_theorem(implies__dfg(equiv__dfg(skc82,skc81),implies__dfg(skc82,skc81))),
    inference(mrr,[status(thm)],[44,12]),
    [iquote('0:MRR:44.1,12.0')] ).

cnf(88,plain,
    equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
    inference(mrr,[status(thm)],[58,6]),
    [iquote('0:MRR:58.0,6.0')] ).

cnf(225,plain,
    is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(u,v))),
    inference(spr,[status(thm),theory(equality)],[88,73]),
    [iquote('0:SpR:88.0,73.0')] ).

cnf(231,plain,
    $false,
    inference(unc,[status(thm)],[225,76]),
    [iquote('0:UnC:225.0,76.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL512+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n008.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 : Mon Jul  4 09:27:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.47  
% 0.19/0.47  SPASS V 3.9 
% 0.19/0.47  SPASS beiseite: Proof found.
% 0.19/0.47  % SZS status Theorem
% 0.19/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.47  SPASS derived 125 clauses, backtracked 0 clauses, performed 0 splits and kept 133 clauses.
% 0.19/0.47  SPASS allocated 97873 KBytes.
% 0.19/0.47  SPASS spent	0:00:00.12 on the problem.
% 0.19/0.47  		0:00:00.04 for the input.
% 0.19/0.47  		0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.47  		0:00:00.00 for inferences.
% 0.19/0.47  		0:00:00.00 for the backtracking.
% 0.19/0.47  		0:00:00.02 for the reduction.
% 0.19/0.47  
% 0.19/0.47  
% 0.19/0.47  Here is a proof with depth 1, length 11 :
% 0.19/0.47  % SZS output start Refutation
% See solution above
% 0.19/0.47  Formulae used in the proof : rosser_op_equiv rosser_kn2 hilbert_equivalence_1 kn2 equivalence_1 op_equiv
% 0.19/0.47  
%------------------------------------------------------------------------------