TSTP Solution File: SEU705^2 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU705^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 Aug 31 17:22:35 EDT 2023
% Result : Theorem 20.24s 20.62s
% Output : Proof 20.24s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_subset,type,
subset: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(sP1,plain,
( sP1
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( subset
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) )
@ eigen__0 )
=> ( ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) ) )
=> ( in @ X1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP1
=> ~ ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o] : ( subset @ ( dsetconstr @ eigen__0 @ X1 ) @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( subset
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ( subset
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X3 != eigen__3 ) ) ) )
@ X1 )
=> ( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X3 != eigen__3 ) ) ) ) )
=> ( in @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP9
=> ( ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
@ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( eigen__1
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X4 != X2 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( eigen__1
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X4 != X2 ) ) ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
@ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP16
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP15
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP13
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(def_subsetE,definition,
( subsetE
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( subset @ X1 @ X2 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) ) ) ) ) ).
thf(def_sepSubset,definition,
( sepSubset
= ( ! [X1: $i,X2: $i > $o] :
( subset
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ X1 ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_theprop,definition,
( theprop
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( singleton @ X1 )
@ ( in @ ( setunion @ X1 ) @ X1 ) ) ) ) ).
thf(def_ifSingleton,definition,
( ifSingleton
= ( ! [X1: $i,X2: $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X1 )
@ ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ( (~) @ X2 )
& ( X5 = X4 ) ) ) ) ) ) ) ) ) ).
thf(def_if,definition,
( if
= ( ^ [X1: $i,X2: $o,X3: $i,X4: $i] :
( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
& ( X5 = X3 ) )
| ( ( (~) @ X2 )
& ( X5 = X4 ) ) ) ) ) ) ) ).
thf(ifp,conjecture,
( sP2
=> ( sP12
=> ( sP6
=> ( sP21
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP2
=> ( sP12
=> ( sP6
=> ( sP21
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[ifp]) ).
thf(h1,assumption,
sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP12
=> ( sP6
=> ( sP21
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP12,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP6
=> ( sP21
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP21
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP21,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) )
@ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X2 ) ) ) ) )
@ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP16
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) )
@ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP16,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in
@ ( setunion
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) )
@ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP1
=> sP17 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| ~ sP1
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| ~ sP13
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| ~ sP9
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| ~ sP16
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP14
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP19
| sP15
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP2
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP12
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP6
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP21
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1,h3,h5,h7,h12,h15,h16]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,16,h15,h16]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,17,h14]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,18,h12,h13]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h10,19,h11]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,20,h10]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h8,21,h9]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,22,h7,h8]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,23,h5,h6]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,24,h3,h4]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,25,h1,h2]) ).
thf(0,theorem,
( sP2
=> ( sP12
=> ( sP6
=> ( sP21
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in
@ ( setunion
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) )
@ X1 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU705^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n015.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 Aug 23 17:45:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.24/20.62 % SZS status Theorem
% 20.24/20.62 % Mode: cade22grackle2x798d
% 20.24/20.62 % Steps: 3155
% 20.24/20.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------