TSTP Solution File: SET927+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 05:29:53 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   28 (  10 unt;   7 nHn;  28 RR)
%            Number of literals    :   55 (   0 equ;  25 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(5,axiom,
    ( ~ in(skc5,skc7)
    | equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ in(u,v)
    | ~ equal(set_difference(unordered_pair(u,w),v),singleton(u)) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( equal(skc6,skc5)
    | in(skc6,skc7)
    | equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equal(set_difference(unordered_pair(u,v),w),singleton(u))
    | equal(u,v)
    | in(v,w) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ in(u,v)
    | in(w,v)
    | equal(set_difference(unordered_pair(w,u),v),singleton(w)) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ equal(u,v)
    | in(u,w)
    | equal(set_difference(unordered_pair(u,v),w),singleton(u)) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(skc6,skc7)
    | ~ equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5))
    | in(skc5,skc7) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ equal(skc6,skc5)
    | ~ equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5))
    | in(skc5,skc7) ),
    file('SET927+1.p',unknown),
    [] ).

cnf(13,plain,
    ( ~ equal(skc6,skc5)
    | ~ equal(singleton(skc5),singleton(skc5))
    | in(skc5,skc7) ),
    inference(rew,[status(thm),theory(equality)],[10,12]),
    [iquote('0:Rew:10.1,12.1')] ).

cnf(14,plain,
    ( ~ equal(skc6,skc5)
    | in(skc5,skc7) ),
    inference(obv,[status(thm),theory(equality)],[13]),
    [iquote('0:Obv:13.1')] ).

cnf(15,plain,
    ( ~ in(skc6,skc7)
    | ~ equal(singleton(skc5),singleton(skc5))
    | in(skc5,skc7) ),
    inference(rew,[status(thm),theory(equality)],[9,11]),
    [iquote('0:Rew:9.1,11.1')] ).

cnf(16,plain,
    ( ~ in(skc6,skc7)
    | in(skc5,skc7) ),
    inference(obv,[status(thm),theory(equality)],[15]),
    [iquote('0:Obv:15.1')] ).

cnf(17,plain,
    equal(skc6,skc5),
    inference(spt,[spt(split,[position(s1)])],[7]),
    [iquote('1:Spt:7.0')] ).

cnf(18,plain,
    ( ~ in(skc5,skc7)
    | equal(set_difference(unordered_pair(skc5,skc5),skc7),singleton(skc5)) ),
    inference(rew,[status(thm),theory(equality)],[17,5]),
    [iquote('1:Rew:17.0,5.1')] ).

cnf(20,plain,
    ( ~ equal(skc5,skc5)
    | in(skc5,skc7) ),
    inference(rew,[status(thm),theory(equality)],[17,14]),
    [iquote('1:Rew:17.0,14.0')] ).

cnf(21,plain,
    in(skc5,skc7),
    inference(obv,[status(thm),theory(equality)],[20]),
    [iquote('1:Obv:20.0')] ).

cnf(22,plain,
    equal(set_difference(unordered_pair(skc5,skc5),skc7),singleton(skc5)),
    inference(mrr,[status(thm)],[18,21]),
    [iquote('1:MRR:18.0,21.0')] ).

cnf(34,plain,
    ( ~ in(skc5,skc7)
    | ~ equal(singleton(skc5),singleton(skc5)) ),
    inference(spl,[status(thm),theory(equality)],[22,6]),
    [iquote('1:SpL:22.0,6.1')] ).

cnf(35,plain,
    ~ in(skc5,skc7),
    inference(obv,[status(thm),theory(equality)],[34]),
    [iquote('1:Obv:34.1')] ).

cnf(36,plain,
    $false,
    inference(mrr,[status(thm)],[35,21]),
    [iquote('1:MRR:35.0,21.0')] ).

cnf(37,plain,
    ~ equal(skc6,skc5),
    inference(spt,[spt(split,[position(sa)])],[36,17]),
    [iquote('1:Spt:36.0,7.0,17.0')] ).

cnf(38,plain,
    ( in(skc6,skc7)
    | equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)) ),
    inference(spt,[spt(split,[position(s2)])],[7]),
    [iquote('1:Spt:36.0,7.1,7.2')] ).

cnf(39,plain,
    ~ in(skc5,skc7),
    inference(mrr,[status(thm)],[5,6]),
    [iquote('0:MRR:5.1,6.1')] ).

cnf(40,plain,
    ~ in(skc6,skc7),
    inference(mrr,[status(thm)],[16,39]),
    [iquote('0:MRR:16.1,39.0')] ).

cnf(41,plain,
    equal(set_difference(unordered_pair(skc5,skc6),skc7),singleton(skc5)),
    inference(mrr,[status(thm)],[38,40]),
    [iquote('1:MRR:38.0,40.0')] ).

cnf(66,plain,
    ( ~ equal(singleton(skc5),singleton(skc5))
    | equal(skc6,skc5)
    | in(skc6,skc7) ),
    inference(spl,[status(thm),theory(equality)],[41,8]),
    [iquote('1:SpL:41.0,8.0')] ).

cnf(68,plain,
    ( equal(skc6,skc5)
    | in(skc6,skc7) ),
    inference(obv,[status(thm),theory(equality)],[66]),
    [iquote('1:Obv:66.0')] ).

cnf(69,plain,
    $false,
    inference(mrr,[status(thm)],[68,37,40]),
    [iquote('1:MRR:68.0,68.1,37.0,40.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n027.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 : Mon Jul 11 05:11:18 EDT 2022
% 0.13/0.35  % 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 42 clauses, backtracked 5 clauses, performed 1 splits and kept 30 clauses.
% 0.19/0.45  SPASS allocated 85109 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.45  		0:00:00.04 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  		0:00:00.00 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 2, length 28 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : t70_zfmisc_1 l39_zfmisc_1
% 0.19/0.45  
%------------------------------------------------------------------------------