%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG250^3 : 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 : n027.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 01:12:12 PM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 41
% Syntax : Number of formulae : 52 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 166 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 341 ( 26 ~; 18 |; 0 &; 222 @)
% ( 17 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 27 con; 0-2 aty)
% Number of variables : 74 ( 9 ^; 65 !; 0 ?; 74 :)
% 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 ).
thf(ty_eigen__1,type,
eigen__1: term > $o ).
thf(ty_eigen__0,type,
eigen__0: term > $o ).
thf(ty_eigen__5,type,
eigen__5: term ).
thf(ty_eigen__3,type,
eigen__3: subst ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_var,type,
var: term > $o ).
thf(h0,assumption,
! [X1: subst > $o,X2: subst] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: subst] :
~ ( ! [X2: term] :
( ( eigen__1 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( eigen__1 @ X2 ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) ) ) ) ) ),
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__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: term > $o] :
~ ! [X2: term,X3: subst] :
( ! [X4: term] :
( ( X1 @ X4 )
= ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: term] :
( ( var @ X4 )
=> ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: term > $o] :
~ ! [X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h2,assumption,
! [X1: term > $o,X2: term] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__2
@ ^ [X1: term] :
~ ! [X2: subst] :
( ! [X3: term] :
( ( eigen__1 @ X3 )
= ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) )
=> ( ! [X3: term] :
( ( var @ X3 )
=> ( eigen__1 @ X3 ) )
=> ! [X3: term] :
( ( var @ X3 )
=> ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__2
@ ^ [X1: term] :
~ ( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: term > $o,X2: term,X3: subst] :
( ! [X4: term] :
( ( X1 @ X4 )
= ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: term] :
( ( var @ X4 )
=> ( eigen__0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o > $o] :
( ( X1 @ ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) )
=> ! [X2: $o] :
( ( X2
= ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: term] :
( ( var @ X1 )
=> ( eigen__1 @ X1 ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__1 @ eigen__5 )
= ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ( var @ eigen__5 )
=> ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) )
=> ! [X1: $o] :
( ( X1
= ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) )
=> ~ ( ( var @ eigen__5 )
=> X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o] :
( ( X1
= ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) )
=> ~ ( ( var @ eigen__5 )
=> X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: term] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( var @ eigen__5 )
=> ( eigen__1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: term] :
( ( eigen__1 @ X1 )
= ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP4
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__0 @ ( sub @ X1 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: term,X2: subst] :
( ! [X3: term] :
( ( eigen__1 @ X3 )
= ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) )
=> ( ! [X3: term] :
( ( var @ X3 )
=> ( eigen__1 @ X3 ) )
=> ! [X3: term] :
( ( var @ X3 )
=> ( eigen__0 @ ( sub @ X3 @ ( push @ X1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ! [X5: term] :
( ( X2 @ X5 )
= ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: term] :
( ( var @ X1 )
=> ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( var @ eigen__5 )
=> ( eigen__0 @ ( sub @ eigen__5 @ ( push @ eigen__2 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o,X2: $o > $o] :
( ( X2 @ X1 )
=> ! [X3: $o] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: subst] :
( ! [X2: term] :
( ( eigen__1 @ X2 )
= ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) )
=> ( sP14
=> ! [X2: term] :
( ( var @ X2 )
=> ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__2 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
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_lem3v2,definition,
( pushprop_lem3v2
= ( ! [X1: term > $o,X2: term > $o,X3: term,X4: subst] :
( ( pushprop_p_and_p_prime @ X3 @ X4 @ X1 @ X2 )
=> ( ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ X5 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X1 @ ( sub @ X5 @ ( push @ X3 @ X4 ) ) ) ) ) ) ) ) ).
thf(def_pushprop_lem3v2_lthm,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2 ).
thf(thm,conjecture,
sP13 ).
thf(h3,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[thm]) ).
thf(1,plain,
( ~ sP14
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| ~ sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP15
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP16
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
sP16,
inference(eq_ind_sym,[status(thm)],[]) ).
thf(9,plain,
( sP11
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).
thf(10,plain,
( sP3
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP3
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP7
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP7
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP17
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(15,plain,
( sP12
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2]) ).
thf(16,plain,
( sP1
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(17,plain,
( sP13
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(18,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,h3]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[18,h2]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[19,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h3])],[18,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG250^3 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.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 23:40:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.20/0.42 % Inferences: 20
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------