TSTP Solution File: SET924+1 by CSE---1.6

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE---1.6
% Problem  : SET924+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d

% Computer : n029.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  : 300s
% DateTime : Thu Aug 31 14:31:43 EDT 2023

% Result   : Theorem 0.20s 0.64s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET924+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35  % Computer : n029.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    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 13:07:39 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.55  start to proof:theBenchmark
% 0.20/0.63  %-------------------------------------------
% 0.20/0.63  % File        :CSE---1.6
% 0.20/0.63  % Problem     :theBenchmark
% 0.20/0.63  % Transform   :cnf
% 0.20/0.63  % Format      :tptp:raw
% 0.20/0.63  % Command     :java -jar mcs_scs.jar %d %s
% 0.20/0.63  
% 0.20/0.63  % Result      :Theorem 0.010000s
% 0.20/0.63  % Output      :CNFRefutation 0.010000s
% 0.20/0.63  %-------------------------------------------
% 0.20/0.63  %------------------------------------------------------------------------------
% 0.20/0.63  % File     : SET924+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.63  % Domain   : Set theory
% 0.20/0.63  % Problem  : difference(singleton(A),B) = singleton(A) <=> ~ in(A,B)
% 0.20/0.63  % Version  : [Urb06] axioms : Especial.
% 0.20/0.63  % English  :
% 0.20/0.63  
% 0.20/0.63  % Refs     : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.63  %          : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.63  % Source   : [Urb06]
% 0.20/0.63  % Names    : zfmisc_1__t67_zfmisc_1 [Urb06]
% 0.20/0.63  
% 0.20/0.63  % Status   : Theorem
% 0.20/0.63  % Rating   : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0
% 0.20/0.63  % Syntax   : Number of formulae    :    5 (   2 unt;   0 def)
% 0.20/0.63  %            Number of atoms       :    8 (   2 equ)
% 0.20/0.63  %            Maximal formula atoms :    2 (   1 avg)
% 0.20/0.63  %            Number of connectives :    7 (   4   ~;   0   |;   0   &)
% 0.20/0.63  %                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
% 0.20/0.63  %            Maximal formula depth :    5 (   4 avg)
% 0.20/0.64  %            Maximal term depth    :    3 (   1 avg)
% 0.20/0.64  %            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
% 0.20/0.64  %            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
% 0.20/0.64  %            Number of variables   :    8 (   6   !;   2   ?)
% 0.20/0.64  % SPC      : FOF_THM_RFO_SEQ
% 0.20/0.64  
% 0.20/0.64  % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.64  %            library, www.mizar.org
% 0.20/0.64  %------------------------------------------------------------------------------
% 0.20/0.64  fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.64      ! [A,B] :
% 0.20/0.64        ( in(A,B)
% 0.20/0.64       => ~ in(B,A) ) ).
% 0.20/0.64  
% 0.20/0.64  fof(rc1_xboole_0,axiom,
% 0.20/0.64      ? [A] : empty(A) ).
% 0.20/0.64  
% 0.20/0.64  fof(rc2_xboole_0,axiom,
% 0.20/0.64      ? [A] : ~ empty(A) ).
% 0.20/0.64  
% 0.20/0.64  fof(t67_zfmisc_1,conjecture,
% 0.20/0.64      ! [A,B] :
% 0.20/0.64        ( set_difference(singleton(A),B) = singleton(A)
% 0.20/0.64      <=> ~ in(A,B) ) ).
% 0.20/0.64  
% 0.20/0.64  fof(l34_zfmisc_1,axiom,
% 0.20/0.64      ! [A,B] :
% 0.20/0.64        ( set_difference(singleton(A),B) = singleton(A)
% 0.20/0.64      <=> ~ in(A,B) ) ).
% 0.20/0.64  
% 0.20/0.64  %------------------------------------------------------------------------------
% 0.20/0.64  %-------------------------------------------
% 0.20/0.64  % Proof found
% 0.20/0.64  % SZS status Theorem for theBenchmark
% 0.20/0.64  % SZS output start Proof
% 0.20/0.64  %ClaNum:16(EqnAxiom:9)
% 0.20/0.64  %VarNum:14(SingletonVarNum:6)
% 0.20/0.64  %MaxLitNum:2
% 0.20/0.64  %MaxfuncDepth:2
% 0.20/0.64  %SharedTerms:12
% 0.20/0.64  %goalClause: 12 14
% 0.20/0.64  [10]P1(a1)
% 0.20/0.64  [11]~P1(a2)
% 0.20/0.64  [12]~P2(a3,a5)+E(f6(f4(a3),a5),f4(a3))
% 0.20/0.64  [14]P2(a3,a5)+~E(f6(f4(a3),a5),f4(a3))
% 0.20/0.64  [15]~P2(x152,x151)+~P2(x151,x152)
% 0.20/0.64  [13]P2(x131,x132)+E(f6(f4(x131),x132),f4(x131))
% 0.20/0.64  [16]~P2(x161,x162)+~E(f6(f4(x161),x162),f4(x161))
% 0.20/0.64  %EqnAxiom
% 0.20/0.64  [1]E(x11,x11)
% 0.20/0.64  [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64  [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64  [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 0.20/0.64  [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53))
% 0.20/0.64  [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62))
% 0.20/0.64  [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.20/0.64  [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.20/0.64  [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.20/0.64  
% 0.20/0.64  %-------------------------------------------
% 0.20/0.64  cnf(28,plain,
% 0.20/0.64     (~E(f6(f4(a3),a5),f4(a3))),
% 0.20/0.64     inference(scs_inference,[],[14,16])).
% 0.20/0.64  cnf(29,plain,
% 0.20/0.64     (~P2(a3,a5)),
% 0.20/0.64     inference(scs_inference,[],[28,12])).
% 0.20/0.64  cnf(30,plain,
% 0.20/0.64     (P2(a3,a5)),
% 0.20/0.64     inference(scs_inference,[],[28,13])).
% 0.20/0.64  cnf(39,plain,
% 0.20/0.64     ($false),
% 0.20/0.64     inference(scs_inference,[],[30,29]),
% 0.20/0.64     ['proof']).
% 0.20/0.64  % SZS output end Proof
% 0.20/0.64  % Total time :0.010000s
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