%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COL027-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 : Fri Jul 15 00:42:26 EDT 2022

% Result   : Unsatisfiable 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    6 (   6 unt;   0 nHn;   6 RR)
%            Number of literals    :    6 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(apply(apply(apply(b,u),v),w),apply(u,apply(v,w))),
    file('COL027-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(apply(apply(apply(h,u),v),w),apply(apply(apply(u,v),w),v)),
    file('COL027-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(apply(combinator,u),u),
    file('COL027-1.p',unknown),
    [] ).

cnf(15,plain,
    equal(apply(apply(apply(h,apply(b,u)),v),w),apply(apply(u,apply(v,w)),v)),
    inference(spr,[status(thm),theory(equality)],[1,2]),
    [iquote('0:SpR:1.0,2.0')] ).

cnf(249,plain,
    equal(apply(apply(apply(h,apply(b,apply(b,u))),v),w),apply(u,apply(apply(v,w),v))),
    inference(spr,[status(thm),theory(equality)],[15,1]),
    [iquote('0:SpR:15.0,1.0')] ).

cnf(277,plain,
    $false,
    inference(unc,[status(thm)],[249,3]),
    [iquote('0:UnC:249.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : COL027-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 : Tue May 31 15:55:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.50  
% 0.20/0.50  SPASS V 3.9 
% 0.20/0.50  SPASS beiseite: Proof found.
% 0.20/0.50  % SZS status Theorem
% 0.20/0.50  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.50  SPASS derived 219 clauses, backtracked 0 clauses, performed 0 splits and kept 134 clauses.
% 0.20/0.50  SPASS allocated 63817 KBytes.
% 0.20/0.50  SPASS spent	0:00:00.14 on the problem.
% 0.20/0.50  		0:00:00.03 for the input.
% 0.20/0.50  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.50  		0:00:00.01 for inferences.
% 0.20/0.50  		0:00:00.00 for the backtracking.
% 0.20/0.50  		0:00:00.08 for the reduction.
% 0.20/0.50  
% 0.20/0.50  
% 0.20/0.50  Here is a proof with depth 2, length 6 :
% 0.20/0.50  % SZS output start Refutation
% See solution above
% 0.20/0.50  Formulae used in the proof : b_definition h_definition prove_fixed_point
% 0.20/0.50  
%------------------------------------------------------------------------------