%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU267+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 14:35:41 EDT 2022

% Result   : Theorem 149.76s 150.00s
% Output   : Refutation 149.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   10 (   4 unt;   0 nHn;  10 RR)
%            Number of literals    :   18 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(421,axiom,
    ( ~ equal(pair_second(ordered_pair(skc18,skc19)),skc19)
    | ~ equal(pair_first(ordered_pair(skc16,skc17)),skc16) ),
    file('SEU267+2.p',unknown),
    [] ).

cnf(423,axiom,
    ( ~ equal(u,pair_first(v))
    | ~ equal(v,ordered_pair(w,x))
    | equal(u,w) ),
    file('SEU267+2.p',unknown),
    [] ).

cnf(427,axiom,
    ( ~ equal(u,pair_second(v))
    | ~ equal(v,ordered_pair(w,x))
    | equal(u,x) ),
    file('SEU267+2.p',unknown),
    [] ).

cnf(13057,plain,
    ( ~ equal(u,pair_second(ordered_pair(v,w)))
    | equal(u,w) ),
    inference(eqr,[status(thm),theory(equality)],[427]),
    [iquote('0:EqR:427.1')] ).

cnf(13107,plain,
    ( ~ equal(u,pair_first(ordered_pair(v,w)))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[423]),
    [iquote('0:EqR:423.1')] ).

cnf(53891,plain,
    equal(pair_second(ordered_pair(u,v)),v),
    inference(eqr,[status(thm),theory(equality)],[13057]),
    [iquote('0:EqR:13057.0')] ).

cnf(53895,plain,
    ( ~ equal(skc19,skc19)
    | ~ equal(pair_first(ordered_pair(skc16,skc17)),skc16) ),
    inference(rew,[status(thm),theory(equality)],[53891,421]),
    [iquote('0:Rew:53891.0,421.0')] ).

cnf(53900,plain,
    ~ equal(pair_first(ordered_pair(skc16,skc17)),skc16),
    inference(obv,[status(thm),theory(equality)],[53895]),
    [iquote('0:Obv:53895.0')] ).

cnf(54169,plain,
    equal(pair_first(ordered_pair(u,v)),u),
    inference(eqr,[status(thm),theory(equality)],[13107]),
    [iquote('0:EqR:13107.0')] ).

cnf(54172,plain,
    $false,
    inference(unc,[status(thm)],[54169,53900]),
    [iquote('0:UnC:54169.0,53900.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU267+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n003.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 : Sun Jun 19 21:53:59 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 149.76/150.00  
% 149.76/150.00  SPASS V 3.9 
% 149.76/150.00  SPASS beiseite: Proof found.
% 149.76/150.00  % SZS status Theorem
% 149.76/150.00  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 149.76/150.00  SPASS derived 44884 clauses, backtracked 22 clauses, performed 3 splits and kept 21796 clauses.
% 149.76/150.00  SPASS allocated 147268 KBytes.
% 149.76/150.00  SPASS spent	0:2:26.84 on the problem.
% 149.76/150.00  		0:00:00.04 for the input.
% 149.76/150.00  		0:0:13.59 for the FLOTTER CNF translation.
% 149.76/150.00  		0:00:01.45 for inferences.
% 149.76/150.00  		0:00:02.55 for the backtracking.
% 149.76/150.00  		0:02:07.49 for the reduction.
% 149.76/150.00  
% 149.76/150.00  
% 149.76/150.00  Here is a proof with depth 2, length 10 :
% 149.76/150.00  % SZS output start Refutation
% See solution above
% 149.76/150.00  Formulae used in the proof : t7_mcart_1 d1_mcart_1 d2_mcart_1
% 149.76/150.00  
%------------------------------------------------------------------------------