TSTP Solution File: SEV104^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV104^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n005.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 : Tue Jul 19 18:04:52 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_cS,type,
cS: b > b > $o ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__1,type,
eigen__1: a ).
thf(ty_z,type,
z: a ).
thf(ty_eigen__0,type,
eigen__0: b ).
thf(ty_cR,type,
cR: a > a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_f,type,
f: a > b > $o ).
thf(sP1,plain,
( sP1
<=> ( ( f @ eigen__1 @ eigen__0 )
=> ~ ( f @ eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a] :
( ~ ( f @ eigen__2 @ eigen__0 )
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ ( cR @ eigen__2 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] : ( cR @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cR @ eigen__1 @ eigen__1 )
=> ~ ( cR @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( f @ eigen__3 @ eigen__0 )
=> ~ ( cR @ eigen__1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a] :
( ~ ( ( cR @ eigen__1 @ X1 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( cR @ eigen__1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( f @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a] :
( ~ ( ( cR @ eigen__1 @ eigen__1 )
=> ~ ( cR @ X1 @ eigen__1 ) )
=> ( cR @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP7
=> ~ ( cR @ eigen__2 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ~ ( ( cR @ eigen__2 @ z )
=> ~ ( cR @ X1 @ z ) )
=> ( cR @ eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b] :
( ~ ( ( f @ eigen__1 @ X1 )
=> ~ ( f @ eigen__2 @ X1 ) )
=> ( cR @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( cR @ eigen__2 @ z )
=> ~ ( cR @ eigen__1 @ z ) )
=> ( cR @ eigen__2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a] :
( ~ ( ( cR @ eigen__2 @ X1 )
=> ~ ( cR @ X2 @ X1 ) )
=> ( cR @ eigen__2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( f @ eigen__2 @ eigen__0 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cR @ eigen__1 @ z ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP7
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( f @ eigen__2 @ eigen__0 )
=> ~ ( ~ ( f @ eigen__3 @ eigen__0 )
=> ~ ( cR @ eigen__2 @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP4
=> ( cR @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( cR @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( cR @ eigen__2 @ z )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( f @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( f @ eigen__3 @ eigen__0 )
=> ~ ( cR @ eigen__2 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP1
=> ( cR @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cR @ eigen__2 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a] :
( ~ sP7
=> ~ ( ~ ( f @ X1 @ eigen__0 )
=> ~ sP15 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a,X2: b] :
( ~ ( ( f @ eigen__1 @ X2 )
=> ~ ( f @ X1 @ X2 ) )
=> ( cR @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( cR @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ( cR @ X1 @ X2 )
=> ~ ( cR @ X3 @ X2 ) )
=> ( cR @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP21
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( cR @ eigen__2 @ z ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a,X2: a,X3: b] :
( ~ ( ( f @ X1 @ X3 )
=> ~ ( f @ X2 @ X3 ) )
=> ( cR @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP7
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(cTHM552D_pme,conjecture,
( ~ ( sP28
=> ~ sP3 )
=> ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP31 )
=> ! [X1: b,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 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP28
=> ~ sP3 )
=> ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP31 )
=> ! [X1: b,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 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM552D_pme]) ).
thf(h1,assumption,
~ ( sP28
=> ~ sP3 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP31 )
=> ! [X1: b,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(assumption,[]) ).
thf(h3,assumption,
sP28,
introduced(assumption,[]) ).
thf(h4,assumption,
sP3,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP31 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: b,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(assumption,[]) ).
thf(h7,assumption,
~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP31,
introduced(assumption,[]) ).
thf(h9,assumption,
! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 ),
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: a,X2: a] :
( ~ ( ! [X3: a] :
( ~ ( f @ X1 @ eigen__0 )
=> ~ ( ~ ( f @ X3 @ eigen__0 )
=> ~ ( cR @ X1 @ z ) ) )
=> ~ ! [X3: a] :
( ~ ( f @ X2 @ eigen__0 )
=> ~ ( ~ ( f @ X3 @ eigen__0 )
=> ~ ( cR @ X2 @ z ) ) ) )
=> ( cR @ X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: a] :
( ~ ( sP25
=> ~ ! [X2: a] :
( ~ ( f @ X1 @ eigen__0 )
=> ~ ( ~ ( f @ X2 @ eigen__0 )
=> ~ ( cR @ X1 @ z ) ) ) )
=> ( cR @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP25
=> ~ sP2 )
=> sP27 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP25
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h16,assumption,
sP25,
introduced(assumption,[]) ).
thf(h17,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP29
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP14
| sP21
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP32
| sP7
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP2
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP25
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( sP22
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP17
| sP21
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP12
| sP20
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP20
| ~ sP30
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP5
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| sP7
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP25
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP3
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP28
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP8
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP18
| sP4
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP4
| ~ sP19
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP28
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP31
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP26
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP11
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP23
| sP1
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP1
| ~ sP7
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,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,h3,h4,h8,h16,h17,h15]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h16,h17])],[h14,29,h16,h17]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h13,30,h14,h15]) ).
thf(32,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,31,h13]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,32,h12]) ).
thf(34,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h6,33,h11]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,34,h9,h10]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,35,h7,h8]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h2,36,h5,h6]) ).
thf(38,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,37,h3,h4]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,38,h1,h2]) ).
thf(0,theorem,
( ~ ( sP28
=> ~ sP3 )
=> ( ~ ( ~ ( ! [X1: a] :
~ ! [X2: b] :
~ ( f @ X1 @ X2 )
=> ~ ! [X1: a,X2: b,X3: b] :
( ~ ( ( f @ X1 @ X2 )
=> ~ ( f @ X1 @ X3 ) )
=> ( cS @ X2 @ X3 ) ) )
=> ~ sP31 )
=> ! [X1: b,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 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[39,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV104^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 28 16:05:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % Mode: mode213
% 0.19/0.48 % Inferences: 750
% 0.19/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------