TSTP Solution File: SYO052^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO052^2 : 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 : n009.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 : Thu Jul 21 19:29:52 EDT 2022
% Result : Theorem 68.24s 68.40s
% Output : Proof 68.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 90
% Syntax : Number of formulae : 100 ( 42 unt; 9 typ; 37 def)
% Number of atoms : 264 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 538 ( 121 ~; 28 |; 0 &; 255 @)
% ( 24 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 66 usr; 66 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 148 ( 53 ^ 95 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_b,type,
b: $i > $o ).
thf(ty_eigen__316,type,
eigen__316: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_eigen__315,type,
eigen__315: $i ).
thf(ty_eigen__313,type,
eigen__313: $i ).
thf(ty_eigen__41,type,
eigen__41: $i ).
thf(ty_eigen__314,type,
eigen__314: $i ).
thf(ty_eigen__42,type,
eigen__42: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__42,definition,
( eigen__42
= ( eps__0
@ ^ [X1: $i] :
~ ( ( b @ eigen__1 )
=> ( ( r @ X1 @ X1 )
=> ( r @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__42])]) ).
thf(eigendef_eigen__315,definition,
( eigen__315
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( b @ eigen__1 )
=> ~ ( r @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__315])]) ).
thf(eigendef_eigen__316,definition,
( eigen__316
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( b @ eigen__1 )
=> ( r @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__316])]) ).
thf(eigendef_eigen__313,definition,
( eigen__313
= ( eps__0
@ ^ [X1: $i] :
~ ( ( b @ eigen__1 )
=> ~ ( r @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__313])]) ).
thf(eigendef_eigen__41,definition,
( eigen__41
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( b @ eigen__1 )
=> ( ( r @ X1 @ X1 )
=> ( r @ X1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__41])]) ).
thf(eigendef_eigen__314,definition,
( eigen__314
= ( eps__0
@ ^ [X1: $i] :
~ ( ( b @ eigen__1 )
=> ( r @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__314])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ~ ( b @ X1 )
=> ( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ! [X4: $i] :
( ~ ( b @ X1 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ~ ( b @ X1 )
=> ~ ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( b @ eigen__1 )
=> ~ ( r @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( b @ eigen__1 )
=> ( ( r @ X1 @ X1 )
=> ( r @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ~ ( b @ eigen__1 )
=> ~ ( r @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ~ ( b @ eigen__1 )
=> ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: $i] :
( ~ ( b @ eigen__1 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ~ ( b @ eigen__1 )
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: $i] :
( ~ ( b @ eigen__1 )
=> ( r @ X1 @ X1 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> ( ! [X1: $i] :
( ( b @ eigen__1 )
=> ( r @ X1 @ X1 ) )
=> ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( b @ eigen__1 )
=> ( r @ eigen__314 @ eigen__314 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( b @ eigen__1 )
=> ( r @ eigen__316 @ eigen__316 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( b @ eigen__1 )
=> ( ( r @ eigen__42 @ eigen__42 )
=> ( r @ eigen__42 @ eigen__42 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( b @ eigen__1 )
=> ( ( r @ eigen__41 @ eigen__41 )
=> ( r @ eigen__41 @ eigen__41 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ! [X1: $i] :
( ( b @ eigen__1 )
=> ( r @ X1 @ X1 ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $i > $o,X2: $i,X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ( X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X4 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ~ ( b @ eigen__1 )
=> ( ( r @ X2 @ X2 )
=> ( X1 @ X2 ) ) )
=> ( ! [X2: $i] :
( ~ ( b @ eigen__1 )
=> ( r @ X2 @ X2 ) )
=> ~ ! [X2: $i] :
( ~ ( b @ eigen__1 )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ~ ( b @ eigen__1 )
=> ( ( r @ X1 @ X1 )
=> ( r @ X1 @ X1 ) ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( b @ eigen__1 )
=> ( r @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( b @ eigen__1 )
=> ( ( r @ X2 @ X2 )
=> ( X1 @ X2 ) ) )
=> ( sP16
=> ~ ! [X2: $i] :
( ( b @ eigen__1 )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( b @ eigen__1 )
=> ~ ( r @ eigen__313 @ eigen__313 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ~ ( b @ eigen__1 )
=> ( ( r @ X1 @ X1 )
=> ( r @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( b @ X1 )
=> ( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( ! [X4: $i] :
( ( b @ X1 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( b @ X1 )
=> ~ ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( b @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( sP21
=> ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: $i] :
( sP21
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( sP21
=> ~ ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ~ sP21
=> ( r @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ sP21
=> ~ ( r @ eigen__315 @ eigen__315 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
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] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( ~ ( ~ ( X1 @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X3 @ X5 )
=> ~ ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(conj,conjecture,
~ ! [X1: $i > $i > $o,X2: $i,X3: $i > $o,X4: $i > $o] :
( ~ ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ( ~ ~ ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( ~ ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ( X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X4 @ X5 ) ) ) ) ).
thf(h1,negated_conjecture,
sP13,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
( sP18
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP8
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP24
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP9
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP23
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__316]) ).
thf(6,plain,
( sP4
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__315]) ).
thf(7,plain,
( sP16
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__314]) ).
thf(8,plain,
( sP2
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__313]) ).
thf(9,plain,
( sP10
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP3
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__42]) ).
thf(11,plain,
( ~ sP12
| ~ sP16
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP11
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP19
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__41]) ).
thf(14,plain,
( ~ sP6
| ~ sP23
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP15
| ~ sP19
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP14
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP5
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP7
| ~ sP3
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP17
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP22
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP20
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP13
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP13
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h1]) ).
thf(26,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[25,h0]) ).
thf(0,theorem,
~ ! [X1: $i > $i > $o,X2: $i,X3: $i > $o,X4: $i > $o] :
( ~ ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ( ~ ~ ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ( ~ ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ( X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ( X1 @ X2 @ X5 )
=> ~ ( X4 @ X5 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[25,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO052^2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 10:05:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 68.24/68.40 % SZS status Theorem
% 68.24/68.40 % Mode: mode482
% 68.24/68.40 % Inferences: 3747
% 68.24/68.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------