TSTP Solution File: SET918+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET918+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 05:29:47 EDT 2022

% Result   : Theorem 0.21s 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (   9 unt;   0 nHn;  17 RR)
%            Number of literals    :   30 (   0 equ;  14 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    in(skc5,skc6),
    file('SET918+1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(skc7,skc5),
    file('SET918+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(unordered_pair(u,v),unordered_pair(v,u)),
    file('SET918+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET918+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(set_intersection2(unordered_pair(skc7,skc5),skc6),singleton(skc7)),
    file('SET918+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET918+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,unordered_pair(v,x))
    | in(u,w) ),
    file('SET918+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ in(u,v)
    | ~ in(u,w)
    | ~ equal(x,set_intersection2(w,v))
    | in(u,x) ),
    file('SET918+1.p',unknown),
    [] ).

cnf(26,plain,
    equal(set_intersection2(skc6,unordered_pair(skc5,skc7)),singleton(skc7)),
    inference(rew,[status(thm),theory(equality)],[7,8,6]),
    [iquote('0:Rew:7.0,8.0,6.0,8.0')] ).

cnf(51,plain,
    ( ~ in(u,skc6)
    | ~ in(u,unordered_pair(skc5,skc7))
    | in(u,singleton(skc7)) ),
    inference(res,[status(thm),theory(equality)],[26,19]),
    [iquote('0:Res:26.0,19.2')] ).

cnf(62,plain,
    ( ~ in(skc5,unordered_pair(skc5,skc7))
    | in(skc5,singleton(skc7)) ),
    inference(res,[status(thm),theory(equality)],[2,51]),
    [iquote('0:Res:2.0,51.0')] ).

cnf(113,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[11]),
    [iquote('0:EqR:11.1')] ).

cnf(135,plain,
    ( ~ equal(u,v)
    | in(u,unordered_pair(v,w)) ),
    inference(eqr,[status(thm),theory(equality)],[13]),
    [iquote('0:EqR:13.1')] ).

cnf(154,plain,
    ( ~ equal(skc5,skc5)
    | in(skc5,singleton(skc7)) ),
    inference(res,[status(thm),theory(equality)],[135,62]),
    [iquote('0:Res:135.1,62.0')] ).

cnf(155,plain,
    in(skc5,singleton(skc7)),
    inference(obv,[status(thm),theory(equality)],[154]),
    [iquote('0:Obv:154.0')] ).

cnf(158,plain,
    equal(skc7,skc5),
    inference(res,[status(thm),theory(equality)],[155,113]),
    [iquote('0:Res:155.0,113.0')] ).

cnf(160,plain,
    $false,
    inference(mrr,[status(thm)],[158,4]),
    [iquote('0:MRR:158.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 23:01:50 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.47  
% 0.21/0.47  SPASS V 3.9 
% 0.21/0.47  SPASS beiseite: Proof found.
% 0.21/0.47  % SZS status Theorem
% 0.21/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.47  SPASS derived 117 clauses, backtracked 0 clauses, performed 0 splits and kept 89 clauses.
% 0.21/0.47  SPASS allocated 85367 KBytes.
% 0.21/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.21/0.47  		0:00:00.03 for the input.
% 0.21/0.47  		0:00:00.05 for the FLOTTER CNF translation.
% 0.21/0.47  		0:00:00.00 for inferences.
% 0.21/0.47  		0:00:00.00 for the backtracking.
% 0.21/0.47  		0:00:00.00 for the reduction.
% 0.21/0.47  
% 0.21/0.47  
% 0.21/0.47  Here is a proof with depth 4, length 17 :
% 0.21/0.47  % SZS output start Refutation
% See solution above
% 0.21/0.48  Formulae used in the proof : t59_zfmisc_1 commutativity_k2_tarski commutativity_k3_xboole_0 d1_tarski idempotence_k3_xboole_0 d2_tarski d3_xboole_0
% 0.21/0.48  
%------------------------------------------------------------------------------