%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET878+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 05:29:31 EDT 2022

% Result   : Theorem 0.22s 0.45s
% Output   : Refutation 0.22s
% 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    :   18 (   0 equ;  11 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;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET878+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET878+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(set_intersection2(singleton(skc5),unordered_pair(skc5,skc4)),singleton(skc5)),
    file('SET878+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ in(u,v)
    | equal(set_intersection2(v,singleton(u)),singleton(u)) ),
    file('SET878+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(x,v))
    | in(u,w) ),
    file('SET878+1.p',unknown),
    [] ).

cnf(15,plain,
    ~ equal(set_intersection2(singleton(skc5),unordered_pair(skc4,skc5)),singleton(skc5)),
    inference(rew,[status(thm),theory(equality)],[4,7]),
    [iquote('0:Rew:4.0,7.0')] ).

cnf(32,plain,
    ( ~ in(u,v)
    | equal(set_intersection2(singleton(u),v),singleton(u)) ),
    inference(spr,[status(thm),theory(equality)],[8,5]),
    [iquote('0:SpR:8.1,5.0')] ).

cnf(40,plain,
    ( ~ in(skc5,unordered_pair(skc4,skc5))
    | ~ equal(singleton(skc5),singleton(skc5)) ),
    inference(spl,[status(thm),theory(equality)],[32,15]),
    [iquote('0:SpL:32.1,15.0')] ).

cnf(41,plain,
    ~ in(skc5,unordered_pair(skc4,skc5)),
    inference(obv,[status(thm),theory(equality)],[40]),
    [iquote('0:Obv:40.1')] ).

cnf(42,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(w,v)) ),
    inference(eqr,[status(thm),theory(equality)],[10]),
    [iquote('0:EqR:10.1')] ).

cnf(48,plain,
    ~ equal(skc5,skc5),
    inference(res,[status(thm),theory(equality)],[42,41]),
    [iquote('0:Res:42.1,41.0')] ).

cnf(49,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[48]),
    [iquote('0:Obv:48.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET878+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jul  9 23:35:51 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.22/0.45  
% 0.22/0.45  SPASS V 3.9 
% 0.22/0.45  SPASS beiseite: Proof found.
% 0.22/0.45  % SZS status Theorem
% 0.22/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.22/0.45  SPASS derived 30 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.22/0.45  SPASS allocated 85200 KBytes.
% 0.22/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.22/0.45  		0:00:00.03 for the input.
% 0.22/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.45  		0:00:00.00 for inferences.
% 0.22/0.45  		0:00:00.00 for the backtracking.
% 0.22/0.45  		0:00:00.00 for the reduction.
% 0.22/0.45  
% 0.22/0.45  
% 0.22/0.45  Here is a proof with depth 3, length 12 :
% 0.22/0.45  % SZS output start Refutation
% See solution above
% 0.22/0.45  Formulae used in the proof : commutativity_k2_tarski commutativity_k3_xboole_0 t19_zfmisc_1 l32_zfmisc_1 d2_tarski idempotence_k3_xboole_0
% 0.22/0.45  
%------------------------------------------------------------------------------