%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET619^5 : 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 : n013.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 02:26:06 PM UTC 2025
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__1,type,
eigen__1: a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > $o ).
thf(sP1,plain,
( sP1
<=> ( eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(cBOOL_PROP_95_pme,conjecture,
! [X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_95_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o] :
( ( ^ [X2: a] :
( ~ ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] :
( ~ ( ( ( eigen__0 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ( ( X1 @ X2 )
=> ( eigen__0 @ X2 ) ) )
=> ~ ( ( eigen__0 @ X2 )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ( ^ [X1: a] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
!= ( ^ [X1: a] :
( ~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) )
=> ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: a] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
= ( ~ ( ( ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
=> ~ ( ( eigen__1 @ X1 )
=> ( eigen__0 @ X1 ) ) )
=> ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ~ sP2
=> sP1 )
!= ( ~ ( ( sP2
=> sP1 )
=> ~ ( sP1
=> sP2 ) )
=> ~ ( sP2
=> ~ sP1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( ( sP2
=> sP1 )
=> ~ ( sP1
=> sP2 ) )
=> ~ ( sP2
=> ~ sP1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ( ( sP2
=> sP1 )
=> ~ ( sP1
=> sP2 ) )
=> ~ ( sP2
=> ~ sP1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP2,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ( sP2
=> sP1 )
=> ~ ( sP1
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
( sP2
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h13,assumption,
( sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h14,assumption,
( sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h16,h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,1,2,h15,h16]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h9,h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h9,h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(6,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,4,5,h15,h16]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h15,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h9])],[h14,3,6,h16,h9]) ).
thf(8,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h16,h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,8,9,h15,h16]) ).
thf(11,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h9,h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h9,h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(13,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,11,12,h15,h16]) ).
thf(14,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h9])],[h14,10,13,h16,h9]) ).
thf(15,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h10])],[h13,7,14,h15,h10]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,15,h13,h14]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h6,16,h11,h12]) ).
thf(18,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(19,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h16,h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(20,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,18,19,h15,h16]) ).
thf(21,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h9,h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h9,h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(23,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,21,22,h15,h16]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h15,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h9])],[h14,20,23,h16,h9]) ).
thf(25,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(26,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h16,h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,25,26,h15,h16]) ).
thf(28,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h9,h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(29,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h16,h9,h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(30,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h12,28,29,h15,h16]) ).
thf(31,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h10,h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h9])],[h14,27,30,h16,h9]) ).
thf(32,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h10])],[h13,24,31,h15,h10]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,32,h13,h14]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h6,33,h11,h12]) ).
thf(35,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h5,17,34,h9,h10]) ).
thf(h17,assumption,
( ( sP2
=> sP1 )
=> ~ ( sP1
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( sP2
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP2
=> sP1 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( sP1
=> sP2 ),
introduced(assumption,[]) ).
thf(36,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h16,h19,h17,h15,h16,h7,h8,h4,h3,h2,h1,h0])],[h9,h15]) ).
thf(37,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h17,h15,h16,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h16])],[h19,36,h9,h16]) ).
thf(38,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h10,h15,h20,h17,h15,h16,h7,h8,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h17,h15,h16,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h15])],[h20,38,h10,h15]) ).
thf(40,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h17,h15,h16,h7,h8,h4,h3,h2,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h20])],[h17,37,39,h19,h20]) ).
thf(41,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h9,h10,h18,h15,h16,h7,h8,h4,h3,h2,h1,h0])],[h10,h16]) ).
thf(42,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h15,h16,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h18,41,h9,h10]) ).
thf(43,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h15,h16,h7,h8,h4,h3,h2,h1,h0]),tab_imp(discharge,[h17]),tab_imp(discharge,[h18])],[h8,40,42,h17,h18]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h7,43,h15,h16]) ).
thf(45,plain,
$false,
inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,35,44,h5,h6,h7,h8]) ).
thf(46,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,45,h4]) ).
thf(47,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,46,h3]) ).
thf(48,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,47,h2]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,48,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] :
( ~ ( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[49,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SET619^5 : TPTP v9.2.0. Released v4.0.0.
% 0.05/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n013.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 14:47:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 0
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------