%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN391^4 : 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 : n018.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 03:18:11 PM UTC 2025
% Result : Theorem 1.03s 1.35s
% Output : Proof 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 68
% Syntax : Number of formulae : 74 ( 26 unt; 0 typ; 21 def)
% Number of atoms : 336 ( 21 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 681 ( 126 ~; 31 |; 0 &; 333 @)
% ( 23 <=>; 166 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 47 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 147 ( 29 ^; 118 !; 0 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_p2,type,
p2: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_p1,type,
p1: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p2 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p2 @ X4 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p1 @ X5 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p2 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) )
=> ( ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) )
=> ~ ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( irel @ eigen__1 @ eigen__1 )
=> ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p2 @ X1 ) ) )
=> ~ ( ~ ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> ~ ( sP3
=> sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( p2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p2 @ X4 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p1 @ X5 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p2 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP10
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( irel @ eigen__1 @ eigen__1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP3
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( irel @ eigen__1 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP5
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP20
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP9
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
iand = mand ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
ivalid = !! ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(pel9,conjecture,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ~ ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p2 @ X4 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p1 @ X5 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p2 @ X5 ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ sP15,
inference(assume_negation,[status(cth)],[pel9]) ).
thf(1,plain,
( ~ sP3
| sP9
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP16
| sP10
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP23
| sP9
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP7
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP7
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP19
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP19
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP5
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP12
| ~ sP17
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP14
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP6
| ~ sP20
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP18
| ~ sP20
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP2
| sP10
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP10
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP22
| ~ sP20
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP1
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP11
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( sP4
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP4
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP8
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(21,plain,
( sP21
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP21
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP15
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(refl_axiom,axiom,
sP1 ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,refl_axiom,h1]) ).
thf(25,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[24,h0]) ).
thf(0,theorem,
! [X1: $i] :
( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ~ ~ ( ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p1 @ X4 ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) )
=> ~ ( ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( p2 @ X4 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p1 @ X5 ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( p2 @ X5 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[24,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN391^4 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.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 15:08:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.03/1.35 % SZS status Theorem
% 1.03/1.35 % Mode: mode506
% 1.03/1.35 % Inferences: 38836
% 1.03/1.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------