TSTP Solution File: SET975+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 05:30:10 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   25 (  12 unt;   2 nHn;  25 RR)
%            Number of literals    :   42 (   0 equ;  23 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    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    ( equal(skc8,skc6)
    | in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9)) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( in(skc7,skc9)
    | in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9)) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
    | in(u,w) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ in(ordered_pair(u,v),cartesian_product2(w,x))
    | in(v,x) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ in(u,v)
    | ~ in(w,x)
    | in(ordered_pair(u,w),cartesian_product2(v,x)) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9))
    | ~ equal(skc8,skc6)
    | ~ in(skc7,skc9) ),
    file('SET975+1.p',unknown),
    [] ).

cnf(18,plain,
    in(skc7,skc9),
    inference(mrr,[status(thm)],[8,10]),
    [iquote('0:MRR:8.1,10.0')] ).

cnf(19,plain,
    ( ~ equal(skc8,skc6)
    | ~ in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9)) ),
    inference(mrr,[status(thm)],[16,18]),
    [iquote('0:MRR:16.2,18.0')] ).

cnf(20,plain,
    ( ~ in(u,v)
    | in(ordered_pair(u,skc7),cartesian_product2(v,skc9)) ),
    inference(res,[status(thm),theory(equality)],[18,15]),
    [iquote('0:Res:18.0,15.0')] ).

cnf(34,plain,
    equal(skc8,skc6),
    inference(spt,[spt(split,[position(s1)])],[7]),
    [iquote('1:Spt:7.0')] ).

cnf(35,plain,
    ( ~ equal(skc6,skc6)
    | ~ in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9)) ),
    inference(rew,[status(thm),theory(equality)],[34,19]),
    [iquote('1:Rew:34.0,19.0')] ).

cnf(36,plain,
    ~ in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9)),
    inference(obv,[status(thm),theory(equality)],[35]),
    [iquote('1:Obv:35.0')] ).

cnf(37,plain,
    ~ in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc6),skc9)),
    inference(rew,[status(thm),theory(equality)],[34,36]),
    [iquote('1:Rew:34.0,36.0')] ).

cnf(51,plain,
    ~ in(skc6,singleton(skc6)),
    inference(res,[status(thm),theory(equality)],[20,37]),
    [iquote('1:Res:20.1,37.0')] ).

cnf(56,plain,
    ( ~ equal(u,v)
    | in(u,singleton(v)) ),
    inference(eqr,[status(thm),theory(equality)],[13]),
    [iquote('0:EqR:13.1')] ).

cnf(58,plain,
    ~ equal(skc6,skc6),
    inference(res,[status(thm),theory(equality)],[56,51]),
    [iquote('1:Res:56.1,51.0')] ).

cnf(60,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[58]),
    [iquote('1:Obv:58.0')] ).

cnf(61,plain,
    ~ equal(skc8,skc6),
    inference(spt,[spt(split,[position(sa)])],[60,34]),
    [iquote('1:Spt:60.0,7.0,34.0')] ).

cnf(62,plain,
    in(ordered_pair(skc6,skc7),cartesian_product2(singleton(skc8),skc9)),
    inference(spt,[spt(split,[position(s2)])],[7]),
    [iquote('1:Spt:60.0,7.1')] ).

cnf(64,plain,
    in(skc6,singleton(skc8)),
    inference(res,[status(thm),theory(equality)],[62,9]),
    [iquote('1:Res:62.0,9.0')] ).

cnf(67,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[12]),
    [iquote('0:EqR:12.1')] ).

cnf(69,plain,
    equal(skc8,skc6),
    inference(res,[status(thm),theory(equality)],[64,67]),
    [iquote('1:Res:64.0,67.0')] ).

cnf(70,plain,
    $false,
    inference(mrr,[status(thm)],[69,61]),
    [iquote('1:MRR:69.0,61.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 13:08:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 42 clauses, backtracked 3 clauses, performed 1 splits and kept 41 clauses.
% 0.19/0.43  SPASS allocated 85170 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.43  		0:00:00.03 for the input.
% 0.19/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.00 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 3, length 25 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : t128_zfmisc_1 l55_zfmisc_1 d1_tarski antisymmetry_r2_hidden
% 0.19/0.43  
%------------------------------------------------------------------------------