TSTP Solution File: ITP047^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP047^1 : 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 : n020.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 00:28:53 EDT 2022

% Result   : Theorem 4.27s 4.49s
% Output   : Proof 4.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   48 (  18 unt;  21 typ;   0 def)
%            Number of atoms       :  129 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  171 (  12   ~;   6   |;   0   &; 150   @)
%                                         (   0 <=>;   2  =>;   1  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    8 (   8 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  29 usr;  21 con; 0-4 aty)
%            Number of variables   :    9 (   0   ^   9   !;   0   ?;   9   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_option1457017436_r_l_v,type,
    option1457017436_r_l_v: $tType ).

thf(ty_l,type,
    l: $tType ).

thf(ty_produc1156025366_r_l_v,type,
    produc1156025366_r_l_v: $tType ).

thf(ty_cntxt_r_l_v,type,
    cntxt_r_l_v: $tType ).

thf(ty_option_val_r_l_v,type,
    option_val_r_l_v: $tType ).

thf(ty_produc1164766533_r_l_v,type,
    produc1164766533_r_l_v: $tType ).

thf(ty_expr_r_l_v,type,
    expr_r_l_v: $tType ).

thf(ty_r,type,
    r: $tType ).

thf(ty_produc297528454_r_l_v,type,
    produc297528454_r_l_v: ( l > option_val_r_l_v ) > produc1164766533_r_l_v > produc1156025366_r_l_v ).

thf(ty_s,type,
    s: r > option1457017436_r_l_v ).

thf(ty_eigen__0,type,
    eigen__0: r ).

thf(ty_fun_up709272714_r_l_v,type,
    fun_up709272714_r_l_v: ( r > option1457017436_r_l_v ) > r > option1457017436_r_l_v > r > option1457017436_r_l_v ).

thf(ty_produc1834103605_r_l_v,type,
    produc1834103605_r_l_v: ( l > option_val_r_l_v ) > expr_r_l_v > produc1164766533_r_l_v ).

thf(ty_e,type,
    e: cntxt_r_l_v ).

thf(ty_e2,type,
    e2: expr_r_l_v ).

thf(ty_r2,type,
    r2: r ).

thf(ty_rfork_r_l_v,type,
    rfork_r_l_v: expr_r_l_v > expr_r_l_v ).

thf(ty_tau,type,
    tau: l > option_val_r_l_v ).

thf(ty_some_P1807977723_r_l_v,type,
    some_P1807977723_r_l_v: produc1156025366_r_l_v > option1457017436_r_l_v ).

thf(ty_plug_r_l_v,type,
    plug_r_l_v: cntxt_r_l_v > expr_r_l_v > expr_r_l_v ).

thf(ty_sigma,type,
    sigma: l > option_val_r_l_v ).

thf(conj_0,conjecture,
    ( s
    = ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    s
 != ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ ! [X1: r] :
        ( ( s @ X1 )
        = ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) @ X1 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( s @ eigen__0 )
 != ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) @ eigen__0 ),
    introduced(assumption,[]) ).

thf(pax1,axiom,
    ( p1
   => ( ( fs @ fr2 )
      = ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) ) ) ),
    file('<stdin>',pax1) ).

thf(pax5,axiom,
    ( p5
   => ! [X225: r > option1457017436_r_l_v,X226: r] :
        ( ( ffun_up709272714_r_l_v @ X225 @ X226 @ ( X225 @ X226 ) )
        = X225 ) ),
    file('<stdin>',pax5) ).

thf(nax112,axiom,
    ( p112
   <= ( ( fs @ f__0 )
      = ( ffun_up709272714_r_l_v @ fs @ fr2 @ ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) ) @ f__0 ) ) ),
    file('<stdin>',nax112) ).

thf(ax111,axiom,
    p1,
    file('<stdin>',ax111) ).

thf(ax107,axiom,
    p5,
    file('<stdin>',ax107) ).

thf(ax0,axiom,
    ~ p112,
    file('<stdin>',ax0) ).

thf(c_0_6,plain,
    ( ~ p1
    | ( ( fs @ fr2 )
      = ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[pax1]) ).

thf(c_0_7,plain,
    ! [X939: r > option1457017436_r_l_v,X940: r] :
      ( ~ p5
      | ( ( ffun_up709272714_r_l_v @ X939 @ X940 @ ( X939 @ X940 ) )
        = X939 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).

thf(c_0_8,plain,
    ( ( ( fs @ f__0 )
     != ( ffun_up709272714_r_l_v @ fs @ fr2 @ ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) ) @ f__0 ) )
    | p112 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax112])]) ).

thf(c_0_9,plain,
    ( ( ( fs @ fr2 )
      = ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) ) )
    | ~ p1 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,plain,
    p1,
    inference(split_conjunct,[status(thm)],[ax111]) ).

thf(c_0_11,plain,
    ! [X5: r,X4: r > option1457017436_r_l_v] :
      ( ( ( ffun_up709272714_r_l_v @ X4 @ X5 @ ( X4 @ X5 ) )
        = X4 )
      | ~ p5 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_12,plain,
    p5,
    inference(split_conjunct,[status(thm)],[ax107]) ).

thf(c_0_13,plain,
    ~ p112,
    inference(fof_simplification,[status(thm)],[ax0]) ).

thf(c_0_14,plain,
    ( p112
    | ( ( fs @ f__0 )
     != ( ffun_up709272714_r_l_v @ fs @ fr2 @ ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) ) @ f__0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,plain,
    ( ( fsome_P1807977723_r_l_v @ ( fproduc297528454_r_l_v @ fsigma @ ( fproduc1834103605_r_l_v @ ftau @ ( fplug_r_l_v @ fe @ ( frfork_r_l_v @ fe2 ) ) ) ) )
    = ( fs @ fr2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).

thf(c_0_16,plain,
    ! [X5: r,X4: r > option1457017436_r_l_v] :
      ( ( ffun_up709272714_r_l_v @ X4 @ X5 @ ( X4 @ X5 ) )
      = X4 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).

thf(c_0_17,plain,
    ~ p112,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_18,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),c_0_17]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h2,h1,h0])],]) ).

thf(2,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,1,h2]) ).

thf(3,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,2,h1]) ).

thf(0,theorem,
    ( s
    = ( fun_up709272714_r_l_v @ s @ r2 @ ( some_P1807977723_r_l_v @ ( produc297528454_r_l_v @ sigma @ ( produc1834103605_r_l_v @ tau @ ( plug_r_l_v @ e @ ( rfork_r_l_v @ e2 ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ITP047^1 : TPTP v8.1.0. Released v7.5.0.
% 0.00/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33  % Computer : n020.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Thu Jun  2 12:09:23 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 4.27/4.49  % SZS status Theorem
% 4.27/4.49  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 4.27/4.49  % Inferences: 1
% 4.27/4.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------