TSTP Solution File: SEV107^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV107^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Aug 31 19:32:38 EDT 2023
% Result : Theorem 1.02s 1.20s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 134
% Syntax : Number of formulae : 153 ( 24 unt; 14 typ; 9 def)
% Number of atoms : 432 ( 9 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 965 ( 337 ~; 65 |; 0 &; 351 @)
% ( 55 <=>; 157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 70 usr; 68 con; 0-2 aty)
% Number of variables : 105 ( 9 ^; 96 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_z,type,
z: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__36,type,
eigen__36: a ).
thf(ty_cS,type,
cS: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__15,type,
eigen__15: a ).
thf(ty_cR,type,
cR: a > a > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_f,type,
f: a > $i > $o ).
thf(ty_eigen__19,type,
eigen__19: $i ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ! [X3: a] :
( ~ ( f @ X1 @ eigen__2 )
=> ~ ( ~ ( f @ X3 @ eigen__2 )
=> ~ ( cR @ X1 @ z ) ) )
=> ~ ! [X3: a] :
( ~ ( f @ X2 @ eigen__2 )
=> ~ ( ~ ( f @ X3 @ eigen__2 )
=> ~ ( cR @ X2 @ z ) ) ) )
=> ( cR @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a] :
~ ~ ! [X2: $i] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( f @ eigen__6 @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ eigen__6 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( f @ z @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ z @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i] :
~ ~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: $i] :
~ ! [X2: a,X3: a] :
( ~ ( ! [X4: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X4 @ X1 )
=> ~ ( cR @ X2 @ z ) ) )
=> ~ ! [X4: a] :
( ~ ( f @ X3 @ X1 )
=> ~ ( ~ ( f @ X4 @ X1 )
=> ~ ( cR @ X3 @ z ) ) ) )
=> ( cR @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ! [X2: a] :
( ~ ( f @ eigen__3 @ eigen__2 )
=> ~ ( ~ ( f @ X2 @ eigen__2 )
=> ~ ( cR @ eigen__3 @ z ) ) )
=> ~ ! [X2: a] :
( ~ ( f @ X1 @ eigen__2 )
=> ~ ( ~ ( f @ X2 @ eigen__2 )
=> ~ ( cR @ X1 @ z ) ) ) )
=> ( cR @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__36,definition,
( eigen__36
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( f @ eigen__1 @ eigen__19 )
=> ~ ( ~ ( f @ X1 @ eigen__19 )
=> ~ ( cR @ eigen__1 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__36])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__1
@ ^ [X1: $i] :
~ ~ ( f @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( f @ eigen__4 @ eigen__2 )
=> ~ ( ~ ( f @ z @ eigen__2 )
=> ~ ( cR @ eigen__4 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a,X2: a,X3: $i] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( f @ eigen__4 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cR @ eigen__3 @ z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( sP3
=> ~ ( f @ eigen__3 @ eigen__2 ) )
=> ( cR @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: a] :
~ ! [X2: $i] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) )
=> ~ ! [X1: $i,X2: a,X3: a] :
( ~ ( ! [X4: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X4 @ X1 )
=> ~ ( cR @ X2 @ z ) ) )
=> ~ ! [X4: a] :
( ~ ( f @ X3 @ X1 )
=> ~ ( ~ ( f @ X4 @ X1 )
=> ~ ( cR @ X3 @ z ) ) ) )
=> ( cR @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
~ ! [X2: $i] :
~ ! [X3: a] :
( ~ ( f @ X1 @ X2 )
=> ~ ( ~ ( f @ X3 @ X2 )
=> ~ ( cR @ X1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP3
=> ~ ( f @ eigen__3 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( cR @ eigen__3 @ eigen__3 )
=> ~ ( cR @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f @ eigen__6 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( f @ eigen__3 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP3
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ sP3
=> ~ ( ~ sP11
=> ~ ( cR @ eigen__4 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] : ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
~ ( f @ eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ~ ( f @ z @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ z @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( f @ eigen__1 @ eigen__19 )
=> ~ ( ~ ( f @ eigen__36 @ eigen__19 )
=> ~ ( cR @ eigen__1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cR @ eigen__3 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a] :
( ~ ( ( cR @ eigen__4 @ z )
=> ~ ( cR @ X1 @ z ) )
=> ( cR @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( f @ z @ eigen__2 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( cR @ eigen__4 @ z )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a,X2: a] :
( ~ ( ( cR @ eigen__4 @ X1 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( cR @ eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cR @ z @ z ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP21
=> ( cR @ eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( f @ eigen__1 @ eigen__19 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP11
=> ~ ( cR @ eigen__4 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP11
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a,X2: a] :
( ~ ( ( cR @ eigen__3 @ X1 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( cR @ eigen__3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP10
=> ~ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( cR @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( cR @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ~ sP3
=> ~ ( ~ ( f @ X1 @ eigen__2 )
=> ~ ( cR @ eigen__4 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( cR @ eigen__4 @ z ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: a,X2: a] :
( ~ ( ! [X3: a] :
( ~ ( f @ X1 @ eigen__2 )
=> ~ ( ~ ( f @ X3 @ eigen__2 )
=> ~ ( cR @ X1 @ z ) ) )
=> ~ ! [X3: a] :
( ~ ( f @ X2 @ eigen__2 )
=> ~ ( ~ ( f @ X3 @ eigen__2 )
=> ~ ( cR @ X2 @ z ) ) ) )
=> ( cR @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a,X2: $i] :
( ~ ( ( f @ eigen__4 @ X2 )
=> ~ ( f @ X1 @ X2 ) )
=> ( cR @ eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: a] :
~ ! [X2: a] :
( ~ ( f @ X1 @ eigen__0 )
=> ~ ( ~ ( f @ X2 @ eigen__0 )
=> ~ ( cR @ X1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i,X2: a,X3: a] :
( ~ ( ! [X4: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X4 @ X1 )
=> ~ ( cR @ X2 @ z ) ) )
=> ~ ! [X4: a] :
( ~ ( f @ X3 @ X1 )
=> ~ ( ~ ( f @ X4 @ X1 )
=> ~ ( cR @ X3 @ z ) ) ) )
=> ( cR @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ~ ( ( f @ eigen__4 @ X1 )
=> ~ ( f @ eigen__3 @ X1 ) )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP9
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( f @ z @ eigen__0 )
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP11
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: a] :
( ~ ( sP18
=> ~ ( cR @ X1 @ eigen__3 ) )
=> ( cR @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ! [X1: a] :
( ~ sP11
=> ~ ( ~ ( f @ X1 @ eigen__2 )
=> ~ sP4 ) )
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a] :
( ~ sP10
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ eigen__6 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP6
=> ~ ! [X1: $i] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
~ ! [X2: a] :
~ ! [X3: a] :
( ~ ( f @ X2 @ X1 )
=> ~ ( ~ ( f @ X3 @ X1 )
=> ~ ( cR @ X2 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
~ ! [X2: a] :
( ~ ( f @ eigen__1 @ X1 )
=> ~ ( ~ ( f @ X2 @ X1 )
=> ~ ( cR @ eigen__1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP44
=> sP31 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: a] :
( ~ ( ! [X2: a] :
( ~ sP11
=> ~ ( ~ ( f @ X2 @ eigen__2 )
=> ~ sP4 ) )
=> ~ ! [X2: a] :
( ~ ( f @ X1 @ eigen__2 )
=> ~ ( ~ ( f @ X2 @ eigen__2 )
=> ~ ( cR @ X1 @ z ) ) ) )
=> ( cR @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ sP10
=> ~ ( ~ ( f @ eigen__15 @ eigen__0 )
=> ~ ( cR @ eigen__6 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( f @ z @ eigen__2 )
=> ~ sP34 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: a] :
( ~ sP25
=> ~ ( ~ ( f @ X1 @ eigen__19 )
=> ~ ( cR @ eigen__1 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: a] :
~ ! [X2: $i] :
~ ( f @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: a] :
( ~ sP11
=> ~ ( ~ ( f @ X1 @ eigen__2 )
=> ~ sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(cTHM552B_pme,conjecture,
( ~ ( sP26
=> ~ sP14 )
=> ( ~ ( ~ ( sP54
=> ~ ! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP2 )
=> ~ sP46 ) ) ).
thf(h2,negated_conjecture,
~ ( ~ ( sP26
=> ~ sP14 )
=> ( ~ ( ~ ( sP54
=> ~ ! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP2 )
=> ~ sP46 ) ),
inference(assume_negation,[status(cth)],[cTHM552B_pme]) ).
thf(h3,assumption,
~ ( sP26
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( sP54
=> ~ ! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP2 )
=> ~ sP46 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP26,
introduced(assumption,[]) ).
thf(h6,assumption,
sP14,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( sP54
=> ~ ! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP46,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP54
=> ~ ! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP2,
introduced(assumption,[]) ).
thf(h11,assumption,
sP54,
introduced(assumption,[]) ).
thf(h12,assumption,
! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( sP17
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP53
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__36]) ).
thf(3,plain,
( ~ sP48
| ~ sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP15
| sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).
thf(5,plain,
( ~ sP54
| ~ sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP51
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP45
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(8,plain,
( ~ sP37
| ~ sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| ~ sP18
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP40
| sP9
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP43
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP8
| ~ sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP5
| sP8
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP29
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP27
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| sP3
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP39
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP21
| ~ sP34
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP24
| sP21
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP26
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP33
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP36
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP19
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP22
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( sP12
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP28
| sP11
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP2
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP26
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP55
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP30
| sP10
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP41
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP16
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(34,plain,
( sP20
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP42
| sP11
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP52
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP1
| sP3
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP14
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP37
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP55
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP33
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( sP44
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP44
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP49
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP49
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP50
| ~ sP49 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(47,plain,
( sP35
| ~ sP50 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(48,plain,
( sP38
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(49,plain,
( sP7
| sP48 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(50,plain,
( ~ sP6
| ~ sP7
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP47
| sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(52,plain,
( ~ sP46
| sP6
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,h5,h6,h11,h10,h8]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,53,h11,h12]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,54,h9,h10]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h4,55,h7,h8]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,56,h5,h6]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,57,h3,h4]) ).
thf(59,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[58,h1]) ).
thf(60,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[59,h0]) ).
thf(0,theorem,
( ~ ( sP26
=> ~ sP14 )
=> ( ~ ( ~ ( sP54
=> ~ ! [X1: a,X2: $i,X3: $i] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP2 )
=> ~ sP46 ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[58,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV107^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n022.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 : 300
% 0.13/0.34 % DateTime : Thu Aug 24 02:09:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.02/1.20 % SZS status Theorem
% 1.02/1.20 % Mode: cade22grackle2xfee4
% 1.02/1.20 % Steps: 12053
% 1.02/1.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------