%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET023-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 : Tue Jul 19 05:22:44 EDT 2022

% Result   : Unsatisfiable 0.49s 0.66s
% Output   : Refutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   4 unt;   0 nHn;  11 RR)
%            Number of literals    :   21 (   0 equ;  12 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    ( ~ little_set(u)
    | ~ little_set(v)
    | equal(second(ordered_pair(v,u)),u) ),
    file('SET023-3.p',unknown),
    [] ).

cnf(8,axiom,
    ordered_pair_predicate(a),
    file('SET023-3.p',unknown),
    [] ).

cnf(9,axiom,
    ~ little_set(second(a)),
    file('SET023-3.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ ordered_pair_predicate(u)
    | little_set(f2(u)) ),
    file('SET023-3.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ ordered_pair_predicate(u)
    | little_set(f3(u)) ),
    file('SET023-3.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ ordered_pair_predicate(u)
    | equal(ordered_pair(f2(u),f3(u)),u) ),
    file('SET023-3.p',unknown),
    [] ).

cnf(1362,plain,
    ( ~ ordered_pair_predicate(u)
    | ~ little_set(f3(u))
    | ~ little_set(f2(u))
    | equal(f3(u),second(u)) ),
    inference(spr,[status(thm),theory(equality)],[22,6]),
    [iquote('0:SpR:22.1,6.2')] ).

cnf(1369,plain,
    ( ~ ordered_pair_predicate(u)
    | equal(f3(u),second(u)) ),
    inference(ssi,[status(thm)],[1362,20,21]),
    [iquote('0:SSi:1362.2,1362.1,20.1,21.1')] ).

cnf(1370,plain,
    ( ~ ordered_pair_predicate(u)
    | little_set(second(u)) ),
    inference(rew,[status(thm),theory(equality)],[1369,21]),
    [iquote('0:Rew:1369.1,21.1')] ).

cnf(1384,plain,
    ~ ordered_pair_predicate(a),
    inference(res,[status(thm),theory(equality)],[1370,9]),
    [iquote('0:Res:1370.1,9.0')] ).

cnf(1386,plain,
    $false,
    inference(ssi,[status(thm)],[1384,8]),
    [iquote('0:SSi:1384.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET023-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n004.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 : Mon Jul 11 01:57:52 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.49/0.66  
% 0.49/0.66  SPASS V 3.9 
% 0.49/0.66  SPASS beiseite: Proof found.
% 0.49/0.66  % SZS status Theorem
% 0.49/0.66  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.49/0.66  SPASS derived 1084 clauses, backtracked 13 clauses, performed 6 splits and kept 989 clauses.
% 0.49/0.66  SPASS allocated 77234 KBytes.
% 0.49/0.66  SPASS spent	0:00:00.29 on the problem.
% 0.49/0.66  		0:00:00.04 for the input.
% 0.49/0.66  		0:00:00.00 for the FLOTTER CNF translation.
% 0.49/0.66  		0:00:00.02 for inferences.
% 0.49/0.66  		0:00:00.01 for the backtracking.
% 0.49/0.66  		0:00:00.19 for the reduction.
% 0.49/0.66  
% 0.49/0.66  
% 0.49/0.66  Here is a proof with depth 1, length 11 :
% 0.49/0.66  % SZS output start Refutation
% See solution above
% 0.49/0.66  Formulae used in the proof : property_of_second an_ordered_pair_predicate prove_second_component_is_small ordered_pair_predicate1 ordered_pair_predicate2 ordered_pair_predicate3
% 0.49/0.66  
%------------------------------------------------------------------------------