%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU151+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 14:34:24 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   7 unt;   3 nHn;  16 RR)
%            Number of literals    :   31 (   0 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ equal(skc8,skc6),
    file('SEU151+3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(skc7,skc6),
    file('SEU151+3.p',unknown),
    [] ).

cnf(5,axiom,
    equal(unordered_pair(skc8,skc7),unordered_pair(skc6,skc9)),
    file('SEU151+3.p',unknown),
    [] ).

cnf(6,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SEU151+3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(x,v))
    | in(u,w) ),
    file('SEU151+3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ equal(v,unordered_pair(w,x))
    | equal(u,x)
    | equal(u,w) ),
    file('SEU151+3.p',unknown),
    [] ).

cnf(14,plain,
    equal(unordered_pair(skc7,skc8),unordered_pair(skc6,skc9)),
    inference(rew,[status(thm),theory(equality)],[6,5]),
    [iquote('0:Rew:6.0,5.0')] ).

cnf(30,plain,
    ( ~ in(u,unordered_pair(skc6,skc9))
    | equal(u,skc8)
    | equal(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[14,12]),
    [iquote('0:Res:14.0,12.1')] ).

cnf(43,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(w,v)) ),
    inference(eqr,[status(thm),theory(equality)],[9]),
    [iquote('0:EqR:9.1')] ).

cnf(49,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(v,w)) ),
    inference(spr,[status(thm),theory(equality)],[6,43]),
    [iquote('0:SpR:6.0,43.1')] ).

cnf(91,plain,
    ( ~ equal(u,skc6)
    | equal(u,skc8)
    | equal(u,skc7) ),
    inference(res,[status(thm),theory(equality)],[49,30]),
    [iquote('0:Res:49.1,30.0')] ).

cnf(163,plain,
    ( ~ equal(u,skc6)
    | ~ equal(u,skc6)
    | equal(u,skc7) ),
    inference(spl,[status(thm),theory(equality)],[91,3]),
    [iquote('0:SpL:91.1,3.0')] ).

cnf(168,plain,
    ( ~ equal(u,skc6)
    | equal(u,skc7) ),
    inference(obv,[status(thm),theory(equality)],[163]),
    [iquote('0:Obv:163.0')] ).

cnf(199,plain,
    ( ~ equal(u,skc6)
    | ~ equal(u,skc6) ),
    inference(spl,[status(thm),theory(equality)],[168,4]),
    [iquote('0:SpL:168.1,4.0')] ).

cnf(202,plain,
    ~ equal(u,skc6),
    inference(obv,[status(thm),theory(equality)],[199]),
    [iquote('0:Obv:199.0')] ).

cnf(203,plain,
    $false,
    inference(aed,[status(thm),theory(equality)],[3,202]),
    [iquote('0:AED:3.0,202.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU151+3 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n014.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 : Sun Jun 19 22:24:18 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 169 clauses, backtracked 0 clauses, performed 1 splits and kept 87 clauses.
% 0.19/0.45  SPASS allocated 85252 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.45  		0:00:00.03 for the input.
% 0.19/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.01 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 5, length 16 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : t10_zfmisc_1 commutativity_k2_tarski d2_tarski antisymmetry_r2_hidden
% 0.19/0.45  
%------------------------------------------------------------------------------