TSTP Solution File: ITP066^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP066^1 : 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 : n022.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 00:28:58 EDT 2022

% Result   : Theorem 3.27s 3.47s
% Output   : Proof 3.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   37 (  22 unt;   0 typ;   0 def)
%            Number of atoms       :  280 (  24 equ;   0 cnn)
%            Maximal formula atoms :    2 (   7 avg)
%            Number of connectives :  290 (  15   ~;  10   |;   0   &; 260   @)
%                                         (   0 <=>;   4  =>;   1  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   30 (  28 usr;  29 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
    ( v_a
    = ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ) ).

thf(h0,negated_conjecture,
    v_a
 != ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(pax5,axiom,
    ( p5
   => ! [X49: a,X51: a,X48: tree_a,X26: tree_a,X52: a,X53: tree_a,X30: tree_a] :
        ( ( fheapIm837449470Leaf_a @ ( ft_a @ X49 @ ( ft_a @ X51 @ X48 @ X26 ) @ ( ft_a @ X52 @ X53 @ X30 ) ) )
        = ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X51 @ X48 @ X26 ) ) ) @ ( ft_a @ X49 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X51 @ X48 @ X26 ) ) ) @ ( ft_a @ X52 @ X53 @ X30 ) ) ) ) ),
    file('<stdin>',pax5) ).

thf(pax3,axiom,
    ( p3
   => ( ft_a2
      = ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ),
    file('<stdin>',pax3) ).

thf(pax1,axiom,
    ( p1
   => ( ( fproduc686083979Tree_a @ fv_a @ ft_a2 )
      = ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ) ),
    file('<stdin>',pax1) ).

thf(pax10,axiom,
    ( p10
   => ! [X44: a,X41: tree_a] :
        ( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X44 @ X41 ) )
        = X44 ) ),
    file('<stdin>',pax10) ).

thf(ax45,axiom,
    p5,
    file('<stdin>',ax45) ).

thf(ax47,axiom,
    p3,
    file('<stdin>',ax47) ).

thf(ax49,axiom,
    p1,
    file('<stdin>',ax49) ).

thf(nax46,axiom,
    ( p46
   <= ( fv_a
      = ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) ) ),
    file('<stdin>',nax46) ).

thf(ax4,axiom,
    ~ p46,
    file('<stdin>',ax4) ).

thf(ax40,axiom,
    p10,
    file('<stdin>',ax40) ).

thf(c_0_10,plain,
    ! [X304: a,X305: a,X306: tree_a,X307: tree_a,X308: a,X309: tree_a,X310: tree_a] :
      ( ~ p5
      | ( ( fheapIm837449470Leaf_a @ ( ft_a @ X304 @ ( ft_a @ X305 @ X306 @ X307 ) @ ( ft_a @ X308 @ X309 @ X310 ) ) )
        = ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X305 @ X306 @ X307 ) ) ) @ ( ft_a @ X304 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X305 @ X306 @ X307 ) ) ) @ ( ft_a @ X308 @ X309 @ X310 ) ) ) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])]) ).

thf(c_0_11,plain,
    ( ~ p3
    | ( ft_a2
      = ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ),
    inference(fof_nnf,[status(thm)],[pax3]) ).

thf(c_0_12,plain,
    ( ~ p1
    | ( ( fproduc686083979Tree_a @ fv_a @ ft_a2 )
      = ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[pax1]) ).

thf(c_0_13,plain,
    ! [X282: a,X283: tree_a] :
      ( ~ p10
      | ( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X282 @ X283 ) )
        = X282 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])]) ).

thf(c_0_14,plain,
    ! [X1: a,X2: a,X3: tree_a,X4: tree_a,X5: tree_a,X6: a,X8: tree_a] :
      ( ( ( fheapIm837449470Leaf_a @ ( ft_a @ X1 @ ( ft_a @ X2 @ X3 @ X4 ) @ ( ft_a @ X6 @ X5 @ X8 ) ) )
        = ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X2 @ X3 @ X4 ) ) ) @ ( ft_a @ X1 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X2 @ X3 @ X4 ) ) ) @ ( ft_a @ X6 @ X5 @ X8 ) ) ) )
      | ~ p5 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    p5,
    inference(split_conjunct,[status(thm)],[ax45]) ).

thf(c_0_16,plain,
    ( ( ft_a2
      = ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) )
    | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_17,plain,
    p3,
    inference(split_conjunct,[status(thm)],[ax47]) ).

thf(c_0_18,plain,
    ( ( ( fproduc686083979Tree_a @ fv_a @ ft_a2 )
      = ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) ) )
    | ~ p1 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_19,plain,
    p1,
    inference(split_conjunct,[status(thm)],[ax49]) ).

thf(c_0_20,plain,
    ( ( fv_a
     != ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) )
    | p46 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax46])]) ).

thf(c_0_21,plain,
    ~ p46,
    inference(fof_simplification,[status(thm)],[ax4]) ).

thf(c_0_22,plain,
    ! [X3: tree_a,X1: a] :
      ( ( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X1 @ X3 ) )
        = X1 )
      | ~ p10 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_23,plain,
    p10,
    inference(split_conjunct,[status(thm)],[ax40]) ).

thf(c_0_24,plain,
    ! [X1: a,X2: a,X3: tree_a,X4: tree_a,X5: tree_a,X6: a,X8: tree_a] :
      ( ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X1 @ X3 @ X4 ) ) ) @ ( ft_a @ X2 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ X1 @ X3 @ X4 ) ) ) @ ( ft_a @ X6 @ X5 @ X8 ) ) )
      = ( fheapIm837449470Leaf_a @ ( ft_a @ X2 @ ( ft_a @ X1 @ X3 @ X4 ) @ ( ft_a @ X6 @ X5 @ X8 ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).

thf(c_0_25,plain,
    ( ( ft_a @ fv3 @ ( fproduct_snd_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) )
    = ft_a2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).

thf(c_0_26,plain,
    ( ( fheapIm837449470Leaf_a @ ( ft_a @ fv3 @ ( ft_a @ fv1 @ fl1 @ fr1 ) @ ( ft_a @ fv2 @ fl2 @ fr2 ) ) )
    = ( fproduc686083979Tree_a @ fv_a @ ft_a2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).

thf(c_0_27,plain,
    ( p46
    | ( fv_a
     != ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_28,plain,
    ~ p46,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_29,plain,
    ! [X3: tree_a,X1: a] :
      ( ( fproduct_fst_a_Tree_a @ ( fproduc686083979Tree_a @ X1 @ X3 ) )
      = X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).

thf(c_0_30,plain,
    ( ( fproduc686083979Tree_a @ ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) ) @ ft_a2 )
    = ( fproduc686083979Tree_a @ fv_a @ ft_a2 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

thf(c_0_31,plain,
    ( fproduct_fst_a_Tree_a @ ( fheapIm837449470Leaf_a @ ( ft_a @ fv1 @ fl1 @ fr1 ) ) )
 != fv_a,
    inference(sr,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_32,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]),c_0_31]),
    [proof] ).

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

thf(0,theorem,
    ( v_a
    = ( product_fst_a_Tree_a @ ( heapIm837449470Leaf_a @ ( t_a @ v1 @ l1 @ r1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ITP066^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n022.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  : 600
% 0.13/0.35  % DateTime : Thu Jun  2 16:42:06 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 3.27/3.47  % SZS status Theorem
% 3.27/3.47  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.27/3.47  % Inferences: 1
% 3.27/3.47  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------