TSTP Solution File: SET600^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET600^5 : 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 : n019.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 04:54:16 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% 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(ty_eigen__4,type,
eigen__4: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(sP1,plain,
( sP1
<=> ( ( ^ [X1: a] :
( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) ) )
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( eigen__0 @ eigen__4 )
=> sP2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( eigen__0 @ eigen__2 )
=> ( eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( eigen__0 @ eigen__4 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__0
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP5 = $false ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__1 @ X1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP12 = $false ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__1 @ eigen__5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1
= ( ^ [X1: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__1 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> $false ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(cBOOL_PROP_59_pme,conjecture,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] : sP17 ) )
= ( ~ ( ( X1
= ( ^ [X3: a] : sP17 ) )
=> ( X2
!= ( ^ [X3: a] : sP17 ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] : sP17 ) )
= ( ~ ( ( X1
= ( ^ [X3: a] : sP17 ) )
=> ( X2
!= ( ^ [X3: a] : sP17 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cBOOL_PROP_59_pme]) ).
thf(h1,assumption,
~ ! [X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( eigen__0 @ X2 )
=> ( X1 @ X2 ) ) )
= ( ^ [X2: a] : sP17 ) )
= ( ~ ( sP7
=> ( X1
!= ( ^ [X2: a] : sP17 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP1
!= ( ~ ( sP7
=> ~ sP15 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP7
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
( sP7
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h10,assumption,
sP11 != sP17,
introduced(assumption,[]) ).
thf(h11,assumption,
sP11,
introduced(assumption,[]) ).
thf(h12,assumption,
sP17,
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| ~ sP5
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h9,h7,h3,h4,h2,h1,h0])],[1,2,3,4,5,h3,h11]) ).
thf(7,plain,
$false,
inference(tab_false,[status(thm),assumptions([h13,h14,h10,h9,h7,h3,h4,h2,h1,h0])],[h14]) ).
thf(8,plain,
$false,
inference(tab_be,[status(thm),assumptions([h10,h9,h7,h3,h4,h2,h1,h0]),tab_be(discharge,[h11,h12]),tab_be(discharge,[h13,h14])],[h10,6,7,h11,h12,h13,h14]) ).
thf(9,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h3,h4,h2,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__2)],[h9,8,h10]) ).
thf(10,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_fe(discharge,[h9])],[h7,9,h9]) ).
thf(h15,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h16,assumption,
sP2 != sP17,
introduced(assumption,[]) ).
thf(h17,assumption,
sP2,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(11,plain,
( sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP3
| ~ sP6
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP1
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h12,h16,h15,h8,h3,h4,h2,h1,h0])],[11,12,13,14,15,h3,h17]) ).
thf(17,plain,
$false,
inference(tab_false,[status(thm),assumptions([h18,h14,h16,h15,h8,h3,h4,h2,h1,h0])],[h14]) ).
thf(18,plain,
$false,
inference(tab_be,[status(thm),assumptions([h16,h15,h8,h3,h4,h2,h1,h0]),tab_be(discharge,[h17,h12]),tab_be(discharge,[h18,h14])],[h16,16,17,h17,h12,h18,h14]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__4)],[h15,18,h16]) ).
thf(20,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h8,h3,h4,h2,h1,h0]),tab_fe(discharge,[h15])],[h8,19,h15]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h4,10,20,h7,h8]) ).
thf(h19,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h20,assumption,
( ~ sP12
=> sP16 )
!= sP17,
introduced(assumption,[]) ).
thf(h21,assumption,
( ~ sP12
=> sP16 ),
introduced(assumption,[]) ).
thf(h22,assumption,
~ ( ~ sP12
=> sP16 ),
introduced(assumption,[]) ).
thf(h23,assumption,
sP12,
introduced(assumption,[]) ).
thf(h24,assumption,
sP16,
introduced(assumption,[]) ).
thf(h25,assumption,
sP7,
introduced(assumption,[]) ).
thf(h26,assumption,
sP15,
introduced(assumption,[]) ).
thf(22,plain,
( ~ sP13
| ~ sP12
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP7
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h26,h23,h21,h12,h20,h19,h5,h6,h2,h1,h0])],[22,23,24,25,h23,h25]) ).
thf(27,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h21,h12,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h6,26,h25,h26]) ).
thf(28,plain,
~ sP17,
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP14
| ~ sP16
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP9
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP15
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h26,h24,h21,h12,h20,h19,h5,h6,h2,h1,h0])],[28,29,30,31,h24,h26]) ).
thf(33,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h21,h12,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h25,h26])],[h6,32,h25,h26]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h21,h12,h20,h19,h5,h6,h2,h1,h0]),tab_imp(discharge,[h23]),tab_imp(discharge,[h24])],[h21,27,33,h23,h24]) ).
thf(h27,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h28,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(35,plain,
$false,
inference(tab_false,[status(thm),assumptions([h27,h28,h22,h14,h20,h19,h5,h6,h2,h1,h0])],[h14]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h14,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h22,35,h27,h28]) ).
thf(37,plain,
$false,
inference(tab_be,[status(thm),assumptions([h20,h19,h5,h6,h2,h1,h0]),tab_be(discharge,[h21,h12]),tab_be(discharge,[h22,h14])],[h20,34,36,h21,h12,h22,h14]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h5,h6,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,37,h20]) ).
thf(39,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_fe(discharge,[h19])],[h5,38,h19]) ).
thf(40,plain,
$false,
inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,21,39,h3,h4,h5,h6]) ).
thf(41,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,40,h2]) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,41,h1]) ).
thf(0,theorem,
! [X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
= ( ^ [X3: a] : sP17 ) )
= ( ~ ( ( X1
= ( ^ [X3: a] : sP17 ) )
=> ( X2
!= ( ^ [X3: a] : sP17 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[42,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET600^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n019.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 : Sat Jul 9 23:21:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % Mode: mode213
% 0.19/0.38 % Inferences: 164
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------