%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU896^5 : TPTP v9.2.0. 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 : 300s
% DateTime : Thu Oct 9 02:52:54 PM UTC 2025
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__1,type,
eigen__1: b ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_y,type,
y: b ).
thf(ty_g,type,
g: b > a ).
thf(ty_x,type,
x: b ).
thf(sP1,plain,
( sP1
<=> ( eigen__0
= ( g @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: b] :
( ( ( X1 != x )
=> ( X1 = y ) )
=> ( eigen__0
!= ( g @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( y != x )
=> ( y = y ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( x != x )
=> ( x = y ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( x = x ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( eigen__0
!= ( g @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( g @ eigen__1 )
= ( g @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP5
=> ( x = y ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( g @ eigen__1 )
= ( g @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0
= ( g @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0
= ( g @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 = y ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1 = x ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( y = y ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cTHM500_pme,conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
= ( ^ [X1: a] :
( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
!= ( ^ [X1: a] :
( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM500_pme]) ).
thf(h1,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
= ( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ~ sP2 )
!= ( ~ sP1
=> sP11 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ sP1
=> sP11 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ~ sP13
=> sP12 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP13
=> sP12 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP10,
introduced(assumption,[]) ).
thf(h10,assumption,
sP13,
introduced(assumption,[]) ).
thf(h11,assumption,
sP12,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
sP15,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| sP1
| ~ sP15
| ~ sP9 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h8,h9,h7,h3,h4,h2,h1,h0])],[1,2,3,h10,h9,h12]) ).
thf(5,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,4,h12,h13]) ).
thf(6,plain,
( sP7
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
sP15,
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP10
| sP11
| ~ sP15
| ~ sP7 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h8,h9,h7,h3,h4,h2,h1,h0])],[6,7,8,h11,h9,h13]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h8,h9,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,9,h12,h13]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h7,h3,h4,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,5,10,h10,h11]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,11,h8,h9]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h3,12,h7]) ).
thf(h14,assumption,
sP1,
introduced(assumption,[]) ).
thf(h15,assumption,
sP11,
introduced(assumption,[]) ).
thf(14,plain,
sP5,
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP4
| ~ sP8
| ~ sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h5,h6,h2,h1,h0])],[14,15,16,17,h5,h14]) ).
thf(19,plain,
sP14,
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP3
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP6
| ~ sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h5,h6,h2,h1,h0])],[19,20,21,22,h5,h15]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h6,18,23,h14,h15]) ).
thf(25,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,13,24,h3,h4,h5,h6]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,25,h2]) ).
thf(27,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,26,h1]) ).
thf(0,theorem,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ( X2 != x )
=> ( X2 = y ) )
=> ( X1
!= ( g @ X2 ) ) ) )
= ( ^ [X1: a] :
( ( X1
!= ( g @ x ) )
=> ( X1
= ( g @ y ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU896^5 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 21:17:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % Mode: mode213
% 0.22/0.40 % Inferences: 41
% 0.22/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------