TSTP Solution File: ITP124^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP124^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n018.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 : Sun Jul 17 00:29:11 EDT 2022

% Result   : Theorem 3.19s 3.46s
% Output   : Proof 3.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   42 (  24 unt;   0 typ;   0 def)
%            Number of atoms       :  224 (  27 equ;   0 cnn)
%            Maximal formula atoms :    2 (   5 avg)
%            Number of connectives :  261 (  17   ~;  12   |;   0   &; 226   @)
%                                         (   0 <=>;   5  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;  20 con; 0-2 aty)
%            Number of variables   :   52 (   0   ^  52   !;   0   ?;  52   :)

% Comments : 
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
    ( ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 )
    = ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ) ).

thf(h0,negated_conjecture,
    ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 )
 != ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(pax1,axiom,
    ( p1
   => ! [X14: a,X6: a,X4: a] :
        ( ( finf @ ( finf @ X14 @ X6 ) @ X4 )
        = ( finf @ X14 @ ( finf @ X6 @ X4 ) ) ) ),
    file('<stdin>',pax1) ).

thf(nax76,axiom,
    ( p76
   <= ( ( fmodula1144073633_aux_a @ finf @ fsup @ fb @ fc @ fa2 )
      = ( fmodula1144073633_aux_a @ finf @ fsup @ fa2 @ fb @ fc ) ) ),
    file('<stdin>',nax76) ).

thf(ax0,axiom,
    ~ p76,
    file('<stdin>',ax0) ).

thf(pax9,axiom,
    ( p9
   => ! [X14: a,X6: a,X4: a] :
        ( ( fmodula1144073633_aux_a @ finf @ fsup @ X14 @ X6 @ X4 )
        = ( finf @ ( finf @ ( fsup @ X14 @ X6 ) @ ( fsup @ X6 @ X4 ) ) @ ( fsup @ X4 @ X14 ) ) ) ),
    file('<stdin>',pax9) ).

thf(ax75,axiom,
    p1,
    file('<stdin>',ax75) ).

thf(pax5,axiom,
    ( p5
   => ! [X14: a,X6: a] :
        ( ( fsup @ X14 @ X6 )
        = ( fsup @ X6 @ X14 ) ) ),
    file('<stdin>',pax5) ).

thf(pax3,axiom,
    ( p3
   => ! [X14: a,X6: a,X4: a] :
        ( ( finf @ X14 @ ( finf @ X6 @ X4 ) )
        = ( finf @ X6 @ ( finf @ X14 @ X4 ) ) ) ),
    file('<stdin>',pax3) ).

thf(pax2,axiom,
    ( p2
   => ! [X14: a,X6: a] :
        ( ( finf @ X14 @ X6 )
        = ( finf @ X6 @ X14 ) ) ),
    file('<stdin>',pax2) ).

thf(ax67,axiom,
    p9,
    file('<stdin>',ax67) ).

thf(ax71,axiom,
    p5,
    file('<stdin>',ax71) ).

thf(ax73,axiom,
    p3,
    file('<stdin>',ax73) ).

thf(ax74,axiom,
    p2,
    file('<stdin>',ax74) ).

thf(c_0_12,plain,
    ! [X363: a,X364: a,X365: a] :
      ( ~ p1
      | ( ( finf @ ( finf @ X363 @ X364 ) @ X365 )
        = ( finf @ X363 @ ( finf @ X364 @ X365 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1])])]) ).

thf(c_0_13,plain,
    ( ( ( fmodula1144073633_aux_a @ finf @ fsup @ fb @ fc @ fa2 )
     != ( fmodula1144073633_aux_a @ finf @ fsup @ fa2 @ fb @ fc ) )
    | p76 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax76])]) ).

thf(c_0_14,plain,
    ~ p76,
    inference(fof_simplification,[status(thm)],[ax0]) ).

thf(c_0_15,plain,
    ! [X307: a,X308: a,X309: a] :
      ( ~ p9
      | ( ( fmodula1144073633_aux_a @ finf @ fsup @ X307 @ X308 @ X309 )
        = ( finf @ ( finf @ ( fsup @ X307 @ X308 ) @ ( fsup @ X308 @ X309 ) ) @ ( fsup @ X309 @ X307 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])]) ).

thf(c_0_16,plain,
    ! [X1: a,X2: a,X4: a] :
      ( ( ( finf @ ( finf @ X1 @ X2 ) @ X4 )
        = ( finf @ X1 @ ( finf @ X2 @ X4 ) ) )
      | ~ p1 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_17,plain,
    p1,
    inference(split_conjunct,[status(thm)],[ax75]) ).

thf(c_0_18,plain,
    ! [X343: a,X344: a] :
      ( ~ p5
      | ( ( fsup @ X343 @ X344 )
        = ( fsup @ X344 @ X343 ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).

thf(c_0_19,plain,
    ! [X353: a,X354: a,X355: a] :
      ( ~ p3
      | ( ( finf @ X353 @ ( finf @ X354 @ X355 ) )
        = ( finf @ X354 @ ( finf @ X353 @ X355 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])]) ).

thf(c_0_20,plain,
    ! [X359: a,X360: a] :
      ( ~ p2
      | ( ( finf @ X359 @ X360 )
        = ( finf @ X360 @ X359 ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).

thf(c_0_21,plain,
    ( p76
    | ( ( fmodula1144073633_aux_a @ finf @ fsup @ fb @ fc @ fa2 )
     != ( fmodula1144073633_aux_a @ finf @ fsup @ fa2 @ fb @ fc ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_22,plain,
    ~ p76,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_23,plain,
    ! [X4: a,X2: a,X1: a] :
      ( ( ( fmodula1144073633_aux_a @ finf @ fsup @ X1 @ X2 @ X4 )
        = ( finf @ ( finf @ ( fsup @ X1 @ X2 ) @ ( fsup @ X2 @ X4 ) ) @ ( fsup @ X4 @ X1 ) ) )
      | ~ p9 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_24,plain,
    ! [X1: a,X2: a,X4: a] :
      ( ( finf @ ( finf @ X1 @ X2 ) @ X4 )
      = ( finf @ X1 @ ( finf @ X2 @ X4 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).

thf(c_0_25,plain,
    p9,
    inference(split_conjunct,[status(thm)],[ax67]) ).

thf(c_0_26,plain,
    ! [X2: a,X1: a] :
      ( ( ( fsup @ X1 @ X2 )
        = ( fsup @ X2 @ X1 ) )
      | ~ p5 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_27,plain,
    p5,
    inference(split_conjunct,[status(thm)],[ax71]) ).

thf(c_0_28,plain,
    ! [X1: a,X2: a,X4: a] :
      ( ( ( finf @ X1 @ ( finf @ X2 @ X4 ) )
        = ( finf @ X2 @ ( finf @ X1 @ X4 ) ) )
      | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_29,plain,
    p3,
    inference(split_conjunct,[status(thm)],[ax73]) ).

thf(c_0_30,plain,
    ! [X2: a,X1: a] :
      ( ( ( finf @ X1 @ X2 )
        = ( finf @ X2 @ X1 ) )
      | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_31,plain,
    p2,
    inference(split_conjunct,[status(thm)],[ax74]) ).

thf(c_0_32,plain,
    ( fmodula1144073633_aux_a @ finf @ fsup @ fa2 @ fb @ fc )
 != ( fmodula1144073633_aux_a @ finf @ fsup @ fb @ fc @ fa2 ),
    inference(sr,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_33,plain,
    ! [X4: a,X2: a,X1: a] :
      ( ( fmodula1144073633_aux_a @ finf @ fsup @ X1 @ X2 @ X4 )
      = ( finf @ ( fsup @ X1 @ X2 ) @ ( finf @ ( fsup @ X2 @ X4 ) @ ( fsup @ X4 @ X1 ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

thf(c_0_34,plain,
    ! [X2: a,X1: a] :
      ( ( fsup @ X1 @ X2 )
      = ( fsup @ X2 @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).

thf(c_0_35,plain,
    ! [X1: a,X2: a,X4: a] :
      ( ( finf @ X1 @ ( finf @ X2 @ X4 ) )
      = ( finf @ X2 @ ( finf @ X1 @ X4 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

thf(c_0_36,plain,
    ! [X2: a,X1: a] :
      ( ( finf @ X1 @ X2 )
      = ( finf @ X2 @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).

thf(c_0_37,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_33]),c_0_34]),c_0_36])]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h0])],]) ).

thf(0,theorem,
    ( ( modula1144073633_aux_a @ inf @ sup @ b @ c @ a2 )
    = ( modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ITP124^1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  2 17:00:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 3.19/3.46  % SZS status Theorem
% 3.19/3.46  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.19/3.46  % Inferences: 1
% 3.19/3.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------