%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 05:29:48 EDT 2022

% Result   : Theorem 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   19 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ in(skc5,skc6),
    file('SET920+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET920+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(set_intersection2(unordered_pair(skc5,skc7),skc6),unordered_pair(skc5,skc7)),
    file('SET920+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(v,x))
    | in(u,w) ),
    file('SET920+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(u,v)
    | ~ equal(v,set_intersection2(w,x))
    | in(u,w) ),
    file('SET920+1.p',unknown),
    [] ).

cnf(21,plain,
    equal(set_intersection2(skc6,unordered_pair(skc5,skc7)),unordered_pair(skc5,skc7)),
    inference(rew,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Rew:6.0,8.0')] ).

cnf(28,plain,
    ( ~ equal(u,skc5)
    | in(u,set_intersection2(skc6,unordered_pair(skc5,skc7))) ),
    inference(res,[status(thm),theory(equality)],[21,9]),
    [iquote('0:Res:21.0,9.1')] ).

cnf(32,plain,
    ( ~ in(u,unordered_pair(skc5,skc7))
    | in(u,skc6) ),
    inference(res,[status(thm),theory(equality)],[21,11]),
    [iquote('0:Res:21.0,11.1')] ).

cnf(38,plain,
    ( ~ equal(u,skc5)
    | in(u,unordered_pair(skc5,skc7)) ),
    inference(rew,[status(thm),theory(equality)],[21,28]),
    [iquote('0:Rew:21.0,28.1')] ).

cnf(42,plain,
    ~ in(skc5,unordered_pair(skc5,skc7)),
    inference(res,[status(thm),theory(equality)],[32,3]),
    [iquote('0:Res:32.1,3.0')] ).

cnf(58,plain,
    ~ equal(skc5,skc5),
    inference(res,[status(thm),theory(equality)],[38,42]),
    [iquote('0:Res:38.1,42.0')] ).

cnf(60,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[58]),
    [iquote('0:Obv:58.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 14:44:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 31 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.19/0.44  SPASS allocated 85325 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.44  		0:00:00.04 for the input.
% 0.19/0.44  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.00 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 3, length 12 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : t63_zfmisc_1 commutativity_k3_xboole_0 d2_tarski idempotence_k3_xboole_0 d3_xboole_0
% 0.19/0.44  
%------------------------------------------------------------------------------