TSTP Solution File: SEV208^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV208^5 : 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 : n006.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 18:05:22 EDT 2022
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cP,type,
cP: a > a > a ).
thf(ty_z,type,
z: a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a > $o ).
thf(ty_y,type,
y: a ).
thf(ty_w,type,
w: a ).
thf(ty_c0,type,
c0: a ).
thf(ty_x,type,
x: a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ( ~ ( ( ( X1 = c0 )
=> ( X2 != X3 ) )
=> ~ ( ( X2 = c0 )
=> ( X1 != X3 ) ) )
=> ~ ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ~ ( ~ ( ~ ( ( X1
= ( cP @ X4 @ X5 ) )
=> ( X2
!= ( cP @ X6 @ X7 ) ) )
=> ( X3
!= ( cP @ X8 @ X9 ) ) )
=> ~ ( eigen__0 @ X4 @ X6 @ X8 ) )
=> ~ ( eigen__0 @ X5 @ X7 @ X9 ) ) )
=> ( eigen__0 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( cP @ x @ w )
= ( cP @ x @ w ) )
=> ( ( cP @ y @ z )
!= ( cP @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ w )
= ( cP @ x @ X1 ) )
=> ( ( cP @ y @ z )
!= ( cP @ X2 @ X3 ) ) )
=> ( ( cP @ y @ z )
!= ( cP @ X4 @ X5 ) ) )
=> ~ ( eigen__0 @ x @ X2 @ X4 ) )
=> ~ ( eigen__0 @ X1 @ X3 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( ~ ( ( ( ( cP @ x @ w )
= c0 )
=> ( ( cP @ y @ z )
!= X1 ) )
=> ~ ( ( ( cP @ y @ z )
= c0 )
=> ( ( cP @ x @ w )
!= X1 ) ) )
=> ~ ! [X2: a,X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ w )
= ( cP @ X2 @ X3 ) )
=> ( ( cP @ y @ z )
!= ( cP @ X4 @ X5 ) ) )
=> ( X1
!= ( cP @ X6 @ X7 ) ) )
=> ~ ( eigen__0 @ X2 @ X4 @ X6 ) )
=> ~ ( eigen__0 @ X3 @ X5 @ X7 ) ) )
=> ( eigen__0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ~ sP2
=> ( ( cP @ y @ z )
!= ( cP @ y @ z ) ) )
=> ~ ( eigen__0 @ x @ y @ y ) )
=> ~ ( eigen__0 @ w @ z @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> $false ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ y @ z )
= ( cP @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( cP @ x @ w )
= ( cP @ x @ w ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ( ( ( cP @ x @ w )
= c0 )
=> ~ sP7 )
=> ~ ( ( ( cP @ y @ z )
= c0 )
=> ( ( cP @ x @ w )
!= ( cP @ y @ z ) ) ) )
=> ~ ! [X1: a,X2: a,X3: a,X4: a,X5: a,X6: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ w )
= ( cP @ X1 @ X2 ) )
=> ( ( cP @ y @ z )
!= ( cP @ X3 @ X4 ) ) )
=> ( ( cP @ y @ z )
!= ( cP @ X5 @ X6 ) ) )
=> ~ ( eigen__0 @ X1 @ X3 @ X5 ) )
=> ~ ( eigen__0 @ X2 @ X4 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP2
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ~ ( ~ ( ~ sP2
=> ( ( cP @ y @ z )
!= ( cP @ y @ X1 ) ) )
=> ~ ( eigen__0 @ x @ y @ y ) )
=> ~ ( eigen__0 @ w @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a,X2: a] :
( ~ ( ~ ( ~ sP2
=> ( ( cP @ y @ z )
!= ( cP @ X1 @ X2 ) ) )
=> ~ ( eigen__0 @ x @ y @ X1 ) )
=> ~ ( eigen__0 @ w @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP9
=> ( eigen__0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0 @ x @ y @ y ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ w @ z @ z ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP6
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a,X2: a,X3: a,X4: a,X5: a,X6: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ w )
= ( cP @ X1 @ X2 ) )
=> ( ( cP @ y @ z )
!= ( cP @ X3 @ X4 ) ) )
=> ( ( cP @ y @ z )
!= ( cP @ X5 @ X6 ) ) )
=> ~ ( eigen__0 @ X1 @ X3 @ X5 ) )
=> ~ ( eigen__0 @ X2 @ X4 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP6
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ w @ z @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP10
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a,X2: a] :
( ( ~ ( ( ( ( cP @ x @ w )
= c0 )
=> ( X1 != X2 ) )
=> ~ ( ( X1 = c0 )
=> ( ( cP @ x @ w )
!= X2 ) ) )
=> ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a,X8: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ w )
= ( cP @ X3 @ X4 ) )
=> ( X1
!= ( cP @ X5 @ X6 ) ) )
=> ( X2
!= ( cP @ X7 @ X8 ) ) )
=> ~ ( eigen__0 @ X3 @ X5 @ X7 ) )
=> ~ ( eigen__0 @ X4 @ X6 @ X8 ) ) )
=> ( eigen__0 @ ( cP @ x @ w ) @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP16
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP16
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP6
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ x @ y @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ( ~ ( sP8
=> ( ( cP @ y @ z )
!= ( cP @ y @ X1 ) ) )
=> ( ( cP @ y @ z )
!= ( cP @ X2 @ X3 ) ) )
=> ~ ( eigen__0 @ x @ y @ X2 ) )
=> ~ ( eigen__0 @ w @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a,X2: a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( sP8
=> ( ( cP @ y @ z )
!= ( cP @ X1 @ X2 ) ) )
=> ( ( cP @ y @ z )
!= ( cP @ X3 @ X4 ) ) )
=> ~ ( eigen__0 @ x @ X1 @ X3 ) )
=> ~ ( eigen__0 @ w @ X2 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(cS_INCL_LEM1_pme,conjecture,
( ~ ( sP24
=> ~ sP18 )
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP6
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP24
=> ~ sP18 )
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP6
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(assume_negation,[status(cth)],[cS_INCL_LEM1_pme]) ).
thf(h1,assumption,
~ ( sP24
=> ~ sP18 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: a > a > a > $o] :
( ~ ( ~ sP6
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP24,
introduced(assumption,[]) ).
thf(h4,assumption,
sP18,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ sP16
=> sP19 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
sP7,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP8,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP26
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP11
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP20
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP20
| sP10
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP2
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| ~ sP8
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP17
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP9
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP24
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP23
| sP16
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP18
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP22
| sP16
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP16
| sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
~ sP6,
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP1
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP21
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP13
| ~ sP9
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,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,h3,h4,h9,h7]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h6,24,h8,h9]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,25,h6,h7]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,26,h5]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,27,h3,h4]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,28,h1,h2]) ).
thf(0,theorem,
( ~ ( sP24
=> ~ sP18 )
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP6
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = c0 )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = c0 )
=> ( X2 != X4 ) ) )
=> ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
( ~ ( ~ ( ~ ( ( X2
= ( cP @ X5 @ X6 ) )
=> ( X3
!= ( cP @ X7 @ X8 ) ) )
=> ( X4
!= ( cP @ X9 @ X10 ) ) )
=> ~ ( X1 @ X5 @ X7 @ X9 ) )
=> ~ ( X1 @ X6 @ X8 @ X10 ) ) )
=> ( X1 @ X2 @ X3 @ X4 ) ) )
=> ( X1 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SEV208^5 : 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 : n006.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 27 21:22:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % Mode: mode213
% 0.18/0.36 % Inferences: 25
% 0.18/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------