TSTP Solution File: SET921+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 05:29:49 EDT 2022

% Result   : Theorem 0.10s 0.32s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   28 (  13 unt;   3 nHn;  28 RR)
%            Number of literals    :   51 (   0 equ;  27 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    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ( in(skc5,skc6)
    | in(skc5,set_difference(skc6,singleton(skc7))) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ equal(skc7,skc5)
    | in(skc5,set_difference(skc6,singleton(skc7))) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ in(u,v)
    | ~ equal(v,set_difference(w,x))
    | in(u,w) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ in(skc5,skc6)
    | ~ in(skc5,set_difference(skc6,singleton(skc7)))
    | equal(skc7,skc5) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ in(u,w)
    | ~ equal(v,set_difference(x,w)) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ in(u,v)
    | ~ equal(w,set_difference(v,x))
    | in(u,w)
    | in(u,x) ),
    file('SET921+1.p',unknown),
    [] ).

cnf(17,plain,
    ~ in(skc5,set_difference(skc6,singleton(skc7))),
    inference(spt,[spt(split,[position(s1)])],[10]),
    [iquote('1:Spt:10.1')] ).

cnf(18,plain,
    in(skc5,skc6),
    inference(mrr,[status(thm)],[4,17]),
    [iquote('1:MRR:4.1,17.0')] ).

cnf(19,plain,
    ~ equal(skc7,skc5),
    inference(mrr,[status(thm)],[5,17]),
    [iquote('1:MRR:5.1,17.0')] ).

cnf(21,plain,
    ( ~ equal(u,v)
    | in(u,singleton(v)) ),
    inference(eqr,[status(thm),theory(equality)],[8]),
    [iquote('0:EqR:8.1')] ).

cnf(24,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[7]),
    [iquote('0:EqR:7.1')] ).

cnf(28,plain,
    ( ~ in(u,set_difference(v,w))
    | in(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[9]),
    [iquote('0:EqR:9.1')] ).

cnf(29,plain,
    ( ~ in(u,set_difference(v,w))
    | ~ in(u,w) ),
    inference(eqr,[status(thm),theory(equality)],[12]),
    [iquote('0:EqR:12.2')] ).

cnf(35,plain,
    ( ~ in(u,v)
    | in(u,set_difference(v,w))
    | in(u,w) ),
    inference(eqr,[status(thm),theory(equality)],[13]),
    [iquote('0:EqR:13.1')] ).

cnf(36,plain,
    ( ~ in(skc5,skc6)
    | in(skc5,singleton(skc7)) ),
    inference(res,[status(thm),theory(equality)],[35,17]),
    [iquote('1:Res:35.1,17.0')] ).

cnf(42,plain,
    in(skc5,singleton(skc7)),
    inference(mrr,[status(thm)],[36,18]),
    [iquote('1:MRR:36.0,18.0')] ).

cnf(44,plain,
    equal(skc7,skc5),
    inference(res,[status(thm),theory(equality)],[42,24]),
    [iquote('1:Res:42.0,24.0')] ).

cnf(45,plain,
    $false,
    inference(mrr,[status(thm)],[44,19]),
    [iquote('1:MRR:44.0,19.0')] ).

cnf(46,plain,
    in(skc5,set_difference(skc6,singleton(skc7))),
    inference(spt,[spt(split,[position(sa)])],[45,17]),
    [iquote('1:Spt:45.0,10.1,17.0')] ).

cnf(47,plain,
    ( ~ in(skc5,skc6)
    | equal(skc7,skc5) ),
    inference(spt,[spt(split,[position(s2)])],[10]),
    [iquote('1:Spt:45.0,10.0,10.2')] ).

cnf(49,plain,
    ~ in(skc5,singleton(skc7)),
    inference(res,[status(thm),theory(equality)],[46,29]),
    [iquote('1:Res:46.0,29.0')] ).

cnf(50,plain,
    in(skc5,skc6),
    inference(res,[status(thm),theory(equality)],[46,28]),
    [iquote('1:Res:46.0,28.0')] ).

cnf(51,plain,
    equal(skc7,skc5),
    inference(mrr,[status(thm)],[47,50]),
    [iquote('1:MRR:47.0,50.0')] ).

cnf(53,plain,
    ~ in(skc5,singleton(skc5)),
    inference(rew,[status(thm),theory(equality)],[51,49]),
    [iquote('1:Rew:51.0,49.0')] ).

cnf(57,plain,
    ~ equal(skc5,skc5),
    inference(res,[status(thm),theory(equality)],[21,53]),
    [iquote('1:Res:21.1,53.0')] ).

cnf(58,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[57]),
    [iquote('1:Obv:57.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.07  % Command  : run_spass %d %s
% 0.07/0.26  % Computer : n009.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 600
% 0.07/0.26  % DateTime : Sun Jul 10 20:56:07 EDT 2022
% 0.07/0.26  % CPUTime  : 
% 0.10/0.32  
% 0.10/0.32  SPASS V 3.9 
% 0.10/0.32  SPASS beiseite: Proof found.
% 0.10/0.32  % SZS status Theorem
% 0.10/0.32  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.10/0.32  SPASS derived 35 clauses, backtracked 4 clauses, performed 1 splits and kept 48 clauses.
% 0.10/0.32  SPASS allocated 85245 KBytes.
% 0.10/0.32  SPASS spent	0:00:00.06 on the problem.
% 0.10/0.32  		0:00:00.02 for the input.
% 0.10/0.32  		0:00:00.02 for the FLOTTER CNF translation.
% 0.10/0.32  		0:00:00.00 for inferences.
% 0.10/0.32  		0:00:00.00 for the backtracking.
% 0.10/0.32  		0:00:00.00 for the reduction.
% 0.10/0.32  
% 0.10/0.32  
% 0.10/0.32  Here is a proof with depth 3, length 28 :
% 0.10/0.32  % SZS output start Refutation
% See solution above
% 0.10/0.32  Formulae used in the proof : t64_zfmisc_1 d1_tarski antisymmetry_r2_hidden d4_xboole_0
% 0.10/0.32  
%------------------------------------------------------------------------------