%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG248^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n001.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 01:12:11 PM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 58
% Syntax : Number of formulae : 68 ( 20 unt; 0 typ; 8 def)
% Number of atoms : 179 ( 31 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 280 ( 35 ~; 27 |; 0 &; 153 @)
% ( 25 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 36 con; 0-2 aty)
% Number of variables : 60 ( 8 ^; 52 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_eigen__2,type,
eigen__2: term > $o ).
thf(ty_eigen__0,type,
eigen__0: term > $o ).
thf(ty_eigen__5,type,
eigen__5: subst ).
thf(ty_eigen__3,type,
eigen__3: term ).
thf(ty_one,type,
one: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(h0,assumption,
! [X1: term > $o,X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: term] :
~ ! [X2: subst] :
( ( eigen__0 @ X1 )
=> ( ! [X3: term] :
( ( eigen__2 @ X3 )
= ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) )
=> ( eigen__2 @ one ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( term > $o ) > $o,X2: term > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: term > $o] :
~ ! [X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( X2 @ one ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: term > $o] :
~ ! [X2: term,X3: subst] :
( ( eigen__0 @ X2 )
=> ( ! [X4: term] :
( ( X1 @ X4 )
= ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) )
=> ( X1 @ one ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(h2,assumption,
! [X1: subst > $o,X2: subst] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__2
@ ^ [X1: subst] :
~ ( ( eigen__0 @ eigen__3 )
=> ( ! [X2: term] :
( ( eigen__2 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__3 @ X1 ) ) ) )
=> ( eigen__2 @ one ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: term,X2: subst] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: subst] :
( ( eigen__0 @ eigen__3 )
=> ( ! [X2: term] :
( ( eigen__2 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__3 @ X1 ) ) ) )
=> ( eigen__2 @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0 @ ( sub @ one @ ( push @ eigen__3 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( eigen__2 @ one )
= sP3 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o] :
( ( ( eigen__2 @ one )
= X1 )
=> ~ X1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__2 @ one )
= sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ( sub @ one @ ( push @ eigen__3 @ eigen__5 ) )
= eigen__3 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: term,X2: subst] :
( ( eigen__0 @ X1 )
=> ( ! [X3: term] :
( ( eigen__2 @ X3 )
= ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) )
=> ( eigen__2 @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: term] :
( ( ( sub @ one @ ( push @ eigen__3 @ eigen__5 ) )
= X1 )
=> ~ ( eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: subst] :
( ( sub @ one @ ( push @ eigen__3 @ X1 ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> ( ! [X1: term] :
( ( eigen__2 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__3 @ eigen__5 ) ) ) )
=> ( eigen__2 @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( sub @ one @ ( push @ eigen__3 @ eigen__5 ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: term,X2: term > $o] :
( ( X2 @ X1 )
=> ! [X3: term] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: term] :
( ( eigen__2 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__3 @ eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( X2 @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP16
=> ( eigen__2 @ one ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP1
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP3
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $o > $o] :
( ( X1 @ ( eigen__2 @ one ) )
=> ! [X2: $o] :
( ( ( eigen__2 @ one )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: term > $o] :
( ( X1 @ ( sub @ one @ ( push @ eigen__3 @ eigen__5 ) ) )
=> ! [X2: term] :
( ( ( sub @ one @ ( push @ eigen__3 @ eigen__5 ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: term > $o,X2: term,X3: subst] :
( ( eigen__0 @ X2 )
=> ( ! [X4: term] :
( ( X1 @ X4 )
= ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) )
=> ( X1 @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( eigen__2 @ one )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__2 @ one ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(def_axvarcons,definition,
axvarcons = sP1 ).
thf(def_pushprop_p_and_p_prime,definition,
( pushprop_p_and_p_prime
= ( ^ [X1: term,X2: subst,X3: term > $o,X4: term > $o] :
! [X5: term] :
( ( X4 @ X5 )
= ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) ).
thf(def_pushprop_lem1v2,definition,
( pushprop_lem1v2
= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( X1 @ X3 )
=> ( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( X2 @ one ) ) ) ) ) ).
thf(def_pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( axvarcons
=> pushprop_lem1v2 ) ) ).
thf(thm,conjecture,
sP19 ).
thf(h3,negated_conjecture,
~ sP19,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
( ~ sP8
| ~ sP14
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP20
| sP3
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP22
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP11
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| ~ sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP24
| sP25
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP21
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP16
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
sP12,
inference(eq_ind,[status(thm)],[]) ).
thf(15,plain,
( sP18
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP13
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
sP15,
inference(eq_ind,[status(thm)],[]) ).
thf(20,plain,
( sP2
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).
thf(21,plain,
( sP9
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(22,plain,
( sP23
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(23,plain,
( sP17
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(24,plain,
( sP19
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP19
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,h3]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[26,h2]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[27,h1]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
sP19,
inference(contra,[status(thm),contra(discharge,[h3])],[26,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG248^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.14/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.35 % CPULimit : 300
% 0.21/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Wed Oct 8 23:20:08 EDT 2025
% 0.21/0.35 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.21/0.43 % Inferences: 26
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------