TSTP Solution File: SEV210^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV210^5 : 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 : n024.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 0.38s
% 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_v,type,
v: a ).
thf(ty_eigen__0,type,
eigen__0: a > a > a > $o ).
thf(ty_cZ,type,
cZ: a ).
thf(ty_u,type,
u: a ).
thf(ty_y,type,
y: a ).
thf(ty_x,type,
x: a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a,X3: a] :
( ( ~ ( ( ( X1 = cZ )
=> ( X2 != X3 ) )
=> ~ ( ( X2 = cZ )
=> ( 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 @ y )
= ( cP @ x @ y ) )
=> ( ( cP @ u @ v )
!= ( cP @ u @ v ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ( ~ ( ( ( ( cP @ x @ y )
= cZ )
=> ( ( cP @ u @ v )
!= X1 ) )
=> ~ ( ( ( cP @ u @ v )
= cZ )
=> ( ( cP @ x @ y )
!= X1 ) ) )
=> ~ ! [X2: a,X3: a,X4: a,X5: a,X6: a,X7: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ y )
= ( cP @ X2 @ X3 ) )
=> ( ( cP @ u @ v )
!= ( cP @ X4 @ X5 ) ) )
=> ( X1
!= ( cP @ X6 @ X7 ) ) )
=> ~ ( eigen__0 @ X2 @ X4 @ X6 ) )
=> ~ ( eigen__0 @ X3 @ X5 @ X7 ) ) )
=> ( eigen__0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( cP @ x @ y )
= ( cP @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP2
=> ( ( cP @ u @ v )
!= ( cP @ u @ v ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a,X3: a,X4: a] :
( ~ ( ~ ( ~ ( sP4
=> ( ( cP @ u @ v )
!= ( cP @ X1 @ X2 ) ) )
=> ( ( cP @ u @ v )
!= ( cP @ X3 @ X4 ) ) )
=> ~ ( eigen__0 @ x @ X1 @ X3 ) )
=> ~ ( eigen__0 @ y @ X2 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ sP5
=> ~ ( eigen__0 @ x @ u @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ~ $false
=> ~ sP1 )
=> ( eigen__0 @ x @ u @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: a,X3: a,X4: a,X5: a,X6: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ y )
= ( cP @ X1 @ X2 ) )
=> ( ( cP @ u @ v )
!= ( cP @ X3 @ X4 ) ) )
=> ( ( cP @ u @ v )
!= ( cP @ X5 @ X6 ) ) )
=> ~ ( eigen__0 @ X1 @ X3 @ X5 ) )
=> ~ ( eigen__0 @ X2 @ X4 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a,X3: a,X4: a,X5: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ y )
= ( cP @ x @ X1 ) )
=> ( ( cP @ u @ v )
!= ( cP @ X2 @ X3 ) ) )
=> ( ( cP @ u @ v )
!= ( cP @ X4 @ X5 ) ) )
=> ~ ( eigen__0 @ x @ X2 @ X4 ) )
=> ~ ( eigen__0 @ X1 @ X3 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a,X2: a] :
( ~ ( ~ ( ~ sP2
=> ( ( cP @ u @ v )
!= ( cP @ X1 @ X2 ) ) )
=> ~ ( eigen__0 @ x @ u @ X1 ) )
=> ~ ( eigen__0 @ y @ v @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> $false ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( ~ ( ( ( ( cP @ x @ y )
= cZ )
=> ( ( cP @ u @ v )
!= ( cP @ u @ v ) ) )
=> ~ ( ( ( cP @ u @ v )
= cZ )
=> ( ( cP @ x @ y )
!= ( cP @ u @ v ) ) ) )
=> ~ sP9 )
=> ( eigen__0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a,X2: a] :
( ( ~ ( ( ( ( cP @ x @ y )
= cZ )
=> ( X1 != X2 ) )
=> ~ ( ( X1 = cZ )
=> ( ( cP @ x @ y )
!= X2 ) ) )
=> ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a,X8: a] :
( ~ ( ~ ( ~ ( ( ( cP @ x @ y )
= ( 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 @ y ) @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ x @ u @ u ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y @ v @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__0 @ ( cP @ x @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( cP @ u @ v )
= ( cP @ u @ v ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ( ( ( cP @ x @ y )
= cZ )
=> ~ sP18 )
=> ~ ( ( ( cP @ u @ v )
= cZ )
=> ( ( cP @ x @ y )
!= ( cP @ u @ v ) ) ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__0 @ y @ v @ v ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ sP12
=> ~ sP1 )
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP12
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ u @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP7
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: a,X2: a,X3: a] :
( ~ ( ~ ( ~ ( sP4
=> ( ( cP @ u @ v )
!= ( cP @ u @ X1 ) ) )
=> ( ( cP @ u @ v )
!= ( cP @ X2 @ X3 ) ) )
=> ~ ( eigen__0 @ x @ u @ X2 ) )
=> ~ ( eigen__0 @ y @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a] :
( ~ ( ~ ( ~ sP2
=> ( ( cP @ u @ v )
!= ( cP @ u @ X1 ) ) )
=> ~ sP15 )
=> ~ ( eigen__0 @ y @ v @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(cS_LEM1E_pme,conjecture,
( ~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ( sP23
=> ( sP16
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ( sP23
=> ( sP16
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cS_LEM1E_pme]) ).
thf(h1,assumption,
~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP23
=> ( sP16
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ ),
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP23,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP16
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP16,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ sP22
=> sP17 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
sP18,
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
sP4,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP25
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP11
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP26
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP24
| sP7
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP5
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP5
| sP2
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| ~ sP4
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( sP19
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP23
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP8
| sP22
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP16
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP21
| sP22
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP22
| sP12
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
~ sP12,
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP3
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP13
| ~ sP19
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,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,h7,h9,h15,h13]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h14,h15])],[h12,24,h14,h15]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,25,h12,h13]) ).
thf(27,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)],[h10,26,h11]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,27,h9,h10]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h2,28,h7,h8]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,29,h5,h6]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,30,h3,h4]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,31,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
!= cZ )
=> ~ ! [X1: a,X2: a,X3: a,X4: a] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ~ ( ( X1 = X2 )
=> ( X3 != X4 ) ) ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( X1 @ cZ )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( X1 @ X3 ) )
=> ( X1 @ ( cP @ X2 @ X3 ) ) ) )
=> ( !! @ X1 ) ) )
=> ( sP23
=> ( sP16
=> ! [X1: a > a > a > $o] :
( ~ ( ~ sP12
=> ~ ! [X2: a,X3: a,X4: a] :
( ( ~ ( ( ( X2 = cZ )
=> ( X3 != X4 ) )
=> ~ ( ( X3 = cZ )
=> ( 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 @ y ) @ ( cP @ u @ v ) @ ( cP @ u @ v ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[32,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV210^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.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 : Tue Jun 28 12:30:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % Mode: mode213
% 0.18/0.38 % Inferences: 31
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------