%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM705^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n001.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 Oct 9 02:11:53 PM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_p,type,
p: nat > $o ).
thf(ty_eigen__1,type,
eigen__1: nat ).
thf(ty_eigen__0,type,
eigen__0: nat ).
thf(ty_some,type,
some: ( nat > $o ) > $o ).
thf(ty_lessis,type,
lessis: nat > nat > $o ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(sP1,plain,
( sP1
<=> ( p @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( lessis @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( lessis @ eigen__0 @ eigen__1 )
=> ( ~ ( more @ eigen__1 @ eigen__0 )
=> ( eigen__1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( some @ p )
=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( some @ p ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( more @ eigen__1 @ eigen__0 )
=> ( eigen__1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( lessis @ eigen__0 @ X1 )
=> ( ~ ( more @ X1 @ eigen__0 )
=> ( X1 = eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat > $o] :
( ( some @ X1 )
=> ( some
@ ^ [X2: nat] :
~ ( ! [X3: nat] :
( ( X1 @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( p @ eigen__0 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: nat] :
( ( lessis @ eigen__1 @ X1 )
=> ~ ( more @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat,X2: nat] :
( ( lessis @ X1 @ X2 )
=> ( ~ ( more @ X2 @ X1 )
=> ( X2 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP1
=> ( lessis @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: nat] :
( ( p @ X1 )
=> ( lessis @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( lessis @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( some
@ ^ [X1: nat] :
~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: nat,X2: nat] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP2
=> ~ ( more @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: nat] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( more @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( p @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(satz27a,conjecture,
~ ( ! [X1: nat,X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP20 ) ).
thf(h0,negated_conjecture,
( ! [X1: nat,X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP20 ),
inference(assume_negation,[status(cth)],[satz27a]) ).
thf(h1,assumption,
~ ! [X1: nat,X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: nat] :
( ~ ( sP8
=> ~ sP25 )
=> ( ~ ( ! [X2: nat] :
( ( p @ X2 )
=> ( lessis @ X1 @ X2 ) )
=> ~ ( p @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( sP8
=> ~ sP25 )
=> ( ~ ( sP17
=> ~ sP1 )
=> sP19 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP8
=> ~ sP25 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( sP17
=> ~ sP1 )
=> sP19 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP8,
introduced(assumption,[]) ).
thf(h8,assumption,
sP25,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP17
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP19,
introduced(assumption,[]) ).
thf(h11,assumption,
sP17,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP18
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP7
| sP24
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP12
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP22
| ~ sP2
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| ~ sP1
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP11
| ~ sP25
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP17
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP15
| ~ sP14
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP23
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP21
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
sP21,
inference(eq_sym,[status(thm)],[]) ).
thf(satz14,axiom,
sP13 ).
thf(satz10d,axiom,
sP4 ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,satz14,satz10d,h7,h8,h11,h12,h10]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,16,h11,h12]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h6,17,h9,h10]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,18,h7,h8]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,19,h5,h6]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,20,h4]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,21,h3]) ).
thf(23,plain,
( ~ sP10
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP5
| ~ sP6
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(s,axiom,
sP6 ).
thf(satz27,axiom,
sP10 ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h0])],[23,24,s,satz27,h2]) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,22,25,h1,h2]) ).
thf(0,theorem,
~ ( ! [X1: nat,X2: nat] :
( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X1 @ X3 ) )
=> ~ ( p @ X1 ) )
=> ( ~ ( ! [X3: nat] :
( ( p @ X3 )
=> ( lessis @ X2 @ X3 ) )
=> ~ ( p @ X2 ) )
=> ( X1 = X2 ) ) )
=> ~ sP20 ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM705^1 : TPTP v9.2.0. Released v3.7.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n001.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 : Wed Oct 8 22:47:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 77
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------