%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET912+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 05:29:45 EDT 2022

% Result   : Theorem 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   9 unt;   0 nHn;  14 RR)
%            Number of literals    :   20 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    in(skc7,skc5),
    file('SET912+1.p',unknown),
    [] ).

cnf(3,axiom,
    in(skc6,skc5),
    file('SET912+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET912+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET912+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ subset(u,v)
    | equal(set_intersection2(u,v),u) ),
    file('SET912+1.p',unknown),
    [] ).

cnf(13,axiom,
    ~ equal(set_intersection2(unordered_pair(skc7,skc6),skc5),unordered_pair(skc7,skc6)),
    file('SET912+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ in(u,v)
    | ~ in(w,v)
    | subset(unordered_pair(u,w),v) ),
    file('SET912+1.p',unknown),
    [] ).

cnf(15,plain,
    ~ equal(set_intersection2(skc5,unordered_pair(skc6,skc7)),unordered_pair(skc6,skc7)),
    inference(rew,[status(thm),theory(equality)],[8,13,7]),
    [iquote('0:Rew:8.0,13.0,7.0,13.0')] ).

cnf(19,plain,
    ( ~ in(u,skc5)
    | subset(unordered_pair(skc6,u),skc5) ),
    inference(res,[status(thm),theory(equality)],[3,14]),
    [iquote('0:Res:3.0,14.1')] ).

cnf(26,plain,
    subset(unordered_pair(skc6,skc7),skc5),
    inference(res,[status(thm),theory(equality)],[2,19]),
    [iquote('0:Res:2.0,19.0')] ).

cnf(52,plain,
    ( ~ subset(u,v)
    | equal(set_intersection2(v,u),u) ),
    inference(spr,[status(thm),theory(equality)],[10,8]),
    [iquote('0:SpR:10.1,8.0')] ).

cnf(98,plain,
    ( ~ subset(unordered_pair(skc6,skc7),skc5)
    | ~ equal(unordered_pair(skc6,skc7),unordered_pair(skc6,skc7)) ),
    inference(spl,[status(thm),theory(equality)],[52,15]),
    [iquote('0:SpL:52.1,15.0')] ).

cnf(100,plain,
    ~ subset(unordered_pair(skc6,skc7),skc5),
    inference(obv,[status(thm),theory(equality)],[98]),
    [iquote('0:Obv:98.1')] ).

cnf(101,plain,
    $false,
    inference(mrr,[status(thm)],[100,26]),
    [iquote('0:MRR:100.0,26.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET912+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.32  % Computer : n013.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Sun Jul 10 04:57:59 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 82 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.18/0.42  SPASS allocated 85116 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.42  		0:00:00.04 for the input.
% 0.18/0.42  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.00 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 2, length 14 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : t53_zfmisc_1 commutativity_k2_tarski commutativity_k3_xboole_0 t28_xboole_1 t38_zfmisc_1
% 0.18/0.42  
%------------------------------------------------------------------------------