TSTP Solution File: SEU895^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU895^5 : 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 : 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 : 600s
% DateTime : Tue Jul 19 14:10:44 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_eigen__2,type,
eigen__2: b ).
thf(ty_eigen__1,type,
eigen__1: b ).
thf(ty_eigen__0,type,
eigen__0: a ).
thf(ty_y,type,
y: b > $o ).
thf(ty_eigen__3,type,
eigen__3: b ).
thf(ty_f,type,
f: b > a ).
thf(ty_x,type,
x: b > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: b] :
( ( x @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( y @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ~ ( x @ eigen__3 )
=> sP2 )
=> ( eigen__0
!= ( f @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0
= ( f @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( x @ eigen__3 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( y @ eigen__1 )
=> ( eigen__0
!= ( f @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( x @ eigen__1 )
=> ( eigen__0
!= ( f @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: b] :
( ( ~ ( x @ X1 )
=> ( y @ X1 ) )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( x @ eigen__2 )
=> ( y @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__0
= ( f @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b] :
( ( y @ X1 )
=> ( eigen__0
!= ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( y @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( x @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0
= ( f @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( x @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP9
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cX5202_pme,conjecture,
( ( ^ [X1: a] :
~ ! [X2: b] :
( ( ~ ( x @ X2 )
=> ( y @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
( ! [X2: b] :
( ( x @ X2 )
=> ( X1
!= ( f @ X2 ) ) )
=> ~ ! [X2: b] :
( ( y @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ^ [X1: a] :
~ ! [X2: b] :
( ( ~ ( x @ X2 )
=> ( y @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
!= ( ^ [X1: a] :
( ! [X2: b] :
( ( x @ X2 )
=> ( X1
!= ( f @ X2 ) ) )
=> ~ ! [X2: b] :
( ( y @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cX5202_pme]) ).
thf(h1,assumption,
~ ! [X1: a] :
( ( ~ ! [X2: b] :
( ( ~ ( x @ X2 )
=> ( y @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ! [X2: b] :
( ( x @ X2 )
=> ( X1
!= ( f @ X2 ) ) )
=> ~ ! [X2: b] :
( ( y @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
( ~ sP8 )
!= ( sP1
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h4,assumption,
( sP1
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP8,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ( ~ sP15
=> sP12 )
=> ~ sP10 ),
introduced(assumption,[]) ).
thf(h8,assumption,
( ~ sP15
=> sP12 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP10,
introduced(assumption,[]) ).
thf(h10,assumption,
sP15,
introduced(assumption,[]) ).
thf(h11,assumption,
sP12,
introduced(assumption,[]) ).
thf(h12,assumption,
sP1,
introduced(assumption,[]) ).
thf(h13,assumption,
sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| ~ sP15
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h10,h8,h9,h7,h3,h4,h2,h1,h0])],[1,2,h10,h9,h12]) ).
thf(4,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,3,h12,h13]) ).
thf(5,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| ~ sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h8,h9,h7,h3,h4,h2,h1,h0])],[5,6,h11,h9,h13]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h8,h9,h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h4,7,h12,h13]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h7,h3,h4,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h8,4,8,h10,h11]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,9,h8,h9]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h3,10,h7]) ).
thf(h14,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h16,assumption,
~ ( sP13
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h17,assumption,
sP13,
introduced(assumption,[]) ).
thf(h18,assumption,
sP14,
introduced(assumption,[]) ).
thf(12,plain,
( sP9
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP16
| ~ sP9
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h16,h14,h5,h6,h2,h1,h0])],[12,13,14,h5,h17,h18]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h14,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,15,h17,h18]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h5,h6,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__2)],[h14,16,h16]) ).
thf(h19,assumption,
~ ( sP2
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP2,
introduced(assumption,[]) ).
thf(h21,assumption,
sP4,
introduced(assumption,[]) ).
thf(18,plain,
( sP5
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP3
| ~ sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h20,h21,h19,h15,h5,h6,h2,h1,h0])],[18,19,20,h5,h20,h21]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h15,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,21,h20,h21]) ).
thf(23,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h5,h6,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__3)],[h15,22,h19]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h6,17,23,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])],[h2,11,24,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] :
( ( ~ ( x @ X2 )
=> ( y @ X2 ) )
=> ( X1
!= ( f @ X2 ) ) ) )
= ( ^ [X1: a] :
( ! [X2: b] :
( ( x @ X2 )
=> ( X1
!= ( f @ X2 ) ) )
=> ~ ! [X2: b] :
( ( y @ X2 )
=> ( X1
!= ( f @ X2 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU895^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 20 01:38:59 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % Mode: mode213
% 0.21/0.41 % Inferences: 16
% 0.21/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------