%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COL026-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 0.19s 0.48s
% Output   : Refutation 0.19s
% 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    :    5 (   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('COL026-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(apply(apply(w1,u),v),apply(apply(v,u),u)),
    file('COL026-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(apply(combinator,u),u),
    file('COL026-1.p',unknown),
    [] ).

cnf(21,plain,
    equal(apply(apply(w1,u),apply(apply(b,v),w)),apply(apply(v,apply(w,u)),u)),
    inference(spr,[status(thm),theory(equality)],[1,2]),
    [iquote('0:SpR:1.0,2.0')] ).

cnf(281,plain,
    equal(apply(apply(w1,u),apply(apply(b,apply(b,v)),w)),apply(v,apply(apply(w,u),u))),
    inference(spr,[status(thm),theory(equality)],[21,1]),
    [iquote('0:SpR:21.0,1.0')] ).

cnf(320,plain,
    $false,
    inference(unc,[status(thm)],[281,3]),
    [iquote('0:UnC:281.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : COL026-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue May 31 13:27:08 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 240 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.19/0.48  SPASS allocated 63758 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.48  		0:00:00.04 for the input.
% 0.19/0.48  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.01 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.07 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 2, length 6 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : b_definition w1_definition prove_fixed_point
% 0.19/0.48  
%------------------------------------------------------------------------------