%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COL004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 00:42:23 EDT 2022

% Result   : Unsatisfiable 0.14s 0.42s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   5 unt;   0 nHn;   5 RR)
%            Number of literals    :    5 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(apply(apply(apply(s,u),v),w),apply(apply(u,w),apply(v,w))),
    file('COL004-3.p',unknown),
    [] ).

cnf(2,axiom,
    equal(apply(apply(k,u),v),u),
    file('COL004-3.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x__dfg),y__dfg),apply(y__dfg,apply(apply(x__dfg,x__dfg),y__dfg))),
    file('COL004-3.p',unknown),
    [] ).

cnf(4,plain,
    ~ equal(apply(y__dfg,apply(apply(x__dfg,x__dfg),y__dfg)),apply(y__dfg,apply(apply(x__dfg,x__dfg),y__dfg))),
    inference(rew,[status(thm),theory(equality)],[2,3,1]),
    [iquote('0:Rew:2.0,3.0,1.0,3.0,1.0,3.0,2.0,3.0,2.0,3.0,1.0,3.0,1.0,3.0,1.0,3.0')] ).

cnf(5,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[4]),
    [iquote('0:Obv:4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : COL004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue May 31 12:54:21 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.42  
% 0.14/0.42  SPASS V 3.9 
% 0.14/0.42  SPASS beiseite: Proof found.
% 0.14/0.42  % SZS status Theorem
% 0.14/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.14/0.42  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 3 clauses.
% 0.14/0.42  SPASS allocated 63093 KBytes.
% 0.14/0.42  SPASS spent	0:00:00.05 on the problem.
% 0.14/0.42  		0:00:00.03 for the input.
% 0.14/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.42  		0:00:00.00 for inferences.
% 0.14/0.42  		0:00:00.00 for the backtracking.
% 0.14/0.42  		0:00:00.00 for the reduction.
% 0.14/0.42  
% 0.14/0.42  
% 0.14/0.42  Here is a proof with depth 0, length 5 :
% 0.14/0.42  % SZS output start Refutation
% See solution above
% 0.14/0.42  Formulae used in the proof : s_definition k_definition prove_u_combinator
% 0.14/0.42  
%------------------------------------------------------------------------------