TSTP Solution File: ALG265^2 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ALG265^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n019.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 : Thu Jul 14 17:57:50 EDT 2022

% Result   : Theorem 1.03s 1.24s
% Output   : Proof 1.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   62 (  22 unt;   0 typ;   5 def)
%            Number of atoms       :  342 (  28 equ;   0 cnn)
%            Maximal formula atoms :   27 (   5 avg)
%            Number of connectives :  466 (  38   ~;  37   |;   0   &; 356   @)
%                                         (   0 <=>;  34  =>;   1  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   34 (  32 usr;  33 con; 0-2 aty)
%            Number of variables   :   85 (   2   ^  83   !;   0   ?;  85   :)

% Comments : 
%------------------------------------------------------------------------------
thf(def_axclos,definition,
    ( axclos
    = ( ! [X1: term,X2: subst,X3: subst] :
          ( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
          = ( sub @ X1 @ ( comp @ X2 @ X3 ) ) ) ) ) ).

thf(def_axmap,definition,
    ( axmap
    = ( ! [X1: term,X2: subst,X3: subst] :
          ( ( comp @ ( push @ X1 @ X2 ) @ X3 )
          = ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) ) ) ) ).

thf(def_hoaslam,definition,
    ( hoaslam
    = ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).

thf(def_hoasinduction_lem3aa,definition,
    ( hoasinduction_lem3aa
    = ( ! [X1: subst > term > subst > $o] :
          ( ! [X2: subst > term > term] :
              ( ! [X3: subst,X4: term,X5: subst] :
                  ( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
                  = ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
             => ( ! [X3: term] :
                    ( ( X1 @ id @ X3 @ id )
                   => ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
               => ( X1 @ id @ ( hoaslam @ id @ X2 ) @ id ) ) )
         => ! [X2: term] :
              ( ! [X3: term] :
                  ( ( X1 @ id @ X3 @ id )
                 => ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
             => ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).

thf(def_hoasinduction_lem3aa_lthm,definition,
    ( hoasinduction_lem3aa_lthm
    = ( axclos
     => ( axmap
       => hoasinduction_lem3aa ) ) ) ).

thf(thm,conjecture,
    ( ! [X1: term,X2: subst,X3: subst] :
        ( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
        = ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
   => ( ! [X1: term,X2: subst,X3: subst] :
          ( ( comp @ ( push @ X1 @ X2 ) @ X3 )
          = ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
     => ! [X1: subst > term > subst > $o] :
          ( ! [X2: subst > term > term] :
              ( ! [X3: subst,X4: term,X5: subst] :
                  ( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
                  = ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
             => ( ! [X3: term] :
                    ( ( X1 @ id @ X3 @ id )
                   => ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
               => ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
         => ! [X2: term] :
              ( ! [X3: term] :
                  ( ( X1 @ id @ X3 @ id )
                 => ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
             => ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ! [X1: term,X2: subst,X3: subst] :
          ( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
          = ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
     => ( ! [X1: term,X2: subst,X3: subst] :
            ( ( comp @ ( push @ X1 @ X2 ) @ X3 )
            = ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
       => ! [X1: subst > term > subst > $o] :
            ( ! [X2: subst > term > term] :
                ( ! [X3: subst,X4: term,X5: subst] :
                    ( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
                    = ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
               => ( ! [X3: term] :
                      ( ( X1 @ id @ X3 @ id )
                     => ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
                 => ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
           => ! [X2: term] :
                ( ! [X3: term] :
                    ( ( X1 @ id @ X3 @ id )
                   => ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
               => ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(ax1151,axiom,
    ( p1
    | ~ p3 ),
    file('<stdin>',ax1151) ).

thf(ax1153,axiom,
    ~ p1,
    file('<stdin>',ax1153) ).

thf(ax1149,axiom,
    ( p3
    | ~ p5 ),
    file('<stdin>',ax1149) ).

thf(ax1146,axiom,
    ( p5
    | ~ p8 ),
    file('<stdin>',ax1146) ).

thf(ax1093,axiom,
    ( ~ p9
    | p61 ),
    file('<stdin>',ax1093) ).

thf(ax1145,axiom,
    ( p8
    | p9 ),
    file('<stdin>',ax1145) ).

thf(pax4,axiom,
    ( p4
   => ! [X130: term,X129: subst,X131: subst] :
        ( ( fcomp @ ( fpush @ X130 @ X129 ) @ X131 )
        = ( fpush @ ( fsub @ X130 @ X131 ) @ ( fcomp @ X129 @ X131 ) ) ) ),
    file('<stdin>',pax4) ).

thf(ax1150,axiom,
    ( p3
    | p4 ),
    file('<stdin>',ax1150) ).

thf(pax2,axiom,
    ( p2
   => ! [X130: term,X129: subst,X131: subst] :
        ( ( fsub @ ( fsub @ X130 @ X129 ) @ X131 )
        = ( fsub @ X130 @ ( fcomp @ X129 @ X131 ) ) ) ),
    file('<stdin>',pax2) ).

thf(ax1152,axiom,
    ( p1
    | p2 ),
    file('<stdin>',ax1152) ).

thf(ax1082,axiom,
    ( ~ p61
    | ~ p73
    | p14 ),
    file('<stdin>',ax1082) ).

thf(nax73,axiom,
    ( p73
   <= ! [X82: subst,X78: term,X60: subst] :
        ( ( fsub @ ( fsub @ f__3 @ ( fpush @ X78 @ X82 ) ) @ X60 )
        = ( fsub @ f__3 @ ( fpush @ ( fsub @ X78 @ X60 ) @ ( fcomp @ X82 @ X60 ) ) ) ) ),
    file('<stdin>',nax73) ).

thf(ax1140,axiom,
    ( p10
    | ~ p14 ),
    file('<stdin>',ax1140) ).

thf(ax1144,axiom,
    ( p8
    | ~ p10 ),
    file('<stdin>',ax1144) ).

thf(c_0_14,plain,
    ( p1
    | ~ p3 ),
    inference(fof_simplification,[status(thm)],[ax1151]) ).

thf(c_0_15,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax1153]) ).

thf(c_0_16,plain,
    ( p3
    | ~ p5 ),
    inference(fof_simplification,[status(thm)],[ax1149]) ).

thf(c_0_17,plain,
    ( p1
    | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_18,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_19,plain,
    ( p5
    | ~ p8 ),
    inference(fof_simplification,[status(thm)],[ax1146]) ).

thf(c_0_20,plain,
    ( p3
    | ~ p5 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_21,plain,
    ~ p3,
    inference(sr,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_22,plain,
    ( p5
    | ~ p8 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_23,plain,
    ~ p5,
    inference(sr,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_24,plain,
    ( ~ p9
    | p61 ),
    inference(fof_simplification,[status(thm)],[ax1093]) ).

thf(c_0_25,plain,
    ( p8
    | p9 ),
    inference(split_conjunct,[status(thm)],[ax1145]) ).

thf(c_0_26,plain,
    ~ p8,
    inference(sr,[status(thm)],[c_0_22,c_0_23]) ).

thf(c_0_27,plain,
    ! [X1080: term,X1081: subst,X1082: subst] :
      ( ~ p4
      | ( ( fcomp @ ( fpush @ X1080 @ X1081 ) @ X1082 )
        = ( fpush @ ( fsub @ X1080 @ X1082 ) @ ( fcomp @ X1081 @ X1082 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])]) ).

thf(c_0_28,plain,
    ( p3
    | p4 ),
    inference(split_conjunct,[status(thm)],[ax1150]) ).

thf(c_0_29,plain,
    ! [X1086: term,X1087: subst,X1088: subst] :
      ( ~ p2
      | ( ( fsub @ ( fsub @ X1086 @ X1087 ) @ X1088 )
        = ( fsub @ X1086 @ ( fcomp @ X1087 @ X1088 ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])]) ).

thf(c_0_30,plain,
    ( p1
    | p2 ),
    inference(split_conjunct,[status(thm)],[ax1152]) ).

thf(c_0_31,plain,
    ( ~ p61
    | ~ p73
    | p14 ),
    inference(fof_simplification,[status(thm)],[ax1082]) ).

thf(c_0_32,plain,
    ( p61
    | ~ p9 ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

thf(c_0_33,plain,
    p9,
    inference(sr,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_34,plain,
    ( ( ( fsub @ ( fsub @ f__3 @ ( fpush @ esk412_0 @ esk411_0 ) ) @ esk413_0 )
     != ( fsub @ f__3 @ ( fpush @ ( fsub @ esk412_0 @ esk413_0 ) @ ( fcomp @ esk411_0 @ esk413_0 ) ) ) )
    | p73 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax73])])])]) ).

thf(c_0_35,plain,
    ! [X1: subst,X2: term,X3: subst] :
      ( ( ( fcomp @ ( fpush @ X2 @ X1 ) @ X3 )
        = ( fpush @ ( fsub @ X2 @ X3 ) @ ( fcomp @ X1 @ X3 ) ) )
      | ~ p4 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_36,plain,
    p4,
    inference(sr,[status(thm)],[c_0_28,c_0_21]) ).

thf(c_0_37,plain,
    ! [X1: subst,X2: term,X3: subst] :
      ( ( ( fsub @ ( fsub @ X2 @ X1 ) @ X3 )
        = ( fsub @ X2 @ ( fcomp @ X1 @ X3 ) ) )
      | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_38,plain,
    p2,
    inference(sr,[status(thm)],[c_0_30,c_0_18]) ).

thf(c_0_39,plain,
    ( p14
    | ~ p61
    | ~ p73 ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

thf(c_0_40,plain,
    p61,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).

thf(c_0_41,plain,
    ( p73
    | ( ( fsub @ ( fsub @ f__3 @ ( fpush @ esk412_0 @ esk411_0 ) ) @ esk413_0 )
     != ( fsub @ f__3 @ ( fpush @ ( fsub @ esk412_0 @ esk413_0 ) @ ( fcomp @ esk411_0 @ esk413_0 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_42,plain,
    ! [X3: subst,X2: term,X1: subst] :
      ( ( fpush @ ( fsub @ X2 @ X1 ) @ ( fcomp @ X3 @ X1 ) )
      = ( fcomp @ ( fpush @ X2 @ X3 ) @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).

thf(c_0_43,plain,
    ! [X1: subst,X2: term,X3: subst] :
      ( ( fsub @ X2 @ ( fcomp @ X1 @ X3 ) )
      = ( fsub @ ( fsub @ X2 @ X1 ) @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).

thf(c_0_44,plain,
    ( p10
    | ~ p14 ),
    inference(fof_simplification,[status(thm)],[ax1140]) ).

thf(c_0_45,plain,
    ( p14
    | ~ p73 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).

thf(c_0_46,plain,
    p73,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).

thf(c_0_47,plain,
    ( p8
    | ~ p10 ),
    inference(fof_simplification,[status(thm)],[ax1144]) ).

thf(c_0_48,plain,
    ( p10
    | ~ p14 ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

thf(c_0_49,plain,
    p14,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).

thf(c_0_50,plain,
    ( p8
    | ~ p10 ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_51,plain,
    p10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).

thf(c_0_52,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]),c_0_26]),
    [proof] ).

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

thf(0,theorem,
    ( ! [X1: term,X2: subst,X3: subst] :
        ( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
        = ( sub @ X1 @ ( comp @ X2 @ X3 ) ) )
   => ( ! [X1: term,X2: subst,X3: subst] :
          ( ( comp @ ( push @ X1 @ X2 ) @ X3 )
          = ( push @ ( sub @ X1 @ X3 ) @ ( comp @ X2 @ X3 ) ) )
     => ! [X1: subst > term > subst > $o] :
          ( ! [X2: subst > term > term] :
              ( ! [X3: subst,X4: term,X5: subst] :
                  ( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
                  = ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
             => ( ! [X3: term] :
                    ( ( X1 @ id @ X3 @ id )
                   => ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
               => ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
         => ! [X2: term] :
              ( ! [X3: term] :
                  ( ( X1 @ id @ X3 @ id )
                 => ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
             => ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : ALG265^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n019.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  9 05:20:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.03/1.24  % SZS status Theorem
% 1.03/1.24  % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 1.03/1.24  % Inferences: 275
% 1.03/1.24  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------