%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP010^4 : TPTP v9.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 01:46:28 PM UTC 2025
% Result : Theorem 2.28s 2.50s
% Output : Proof 2.28s
% Verified :
% SZS Type : Derivation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 201 ( 19 ~; 0 |; 0 &; 182 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_u,type,
u: $tType ).
thf(ty_d,type,
d: $tType ).
thf(ty_du,type,
du: $tType ).
thf(ty_eigen__2,type,
eigen__2: u ).
thf(ty_j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(ty_s,type,
s: d > u > du ).
thf(ty_tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(ty_eigen__1,type,
eigen__1: d ).
thf(ty_eigen__0,type,
eigen__0: d ).
thf(ty_eigen__3,type,
eigen__3: u ).
thf(ty_tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(ty_c_2Ecardinal_2Ecardleq_2E2,type,
c_2Ecardinal_2Ecardleq_2E2: du > du > u ).
thf(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
! [X1: d,X2: d,X3: u,X4: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: d,X2: d,X3: u,X4: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm_2Ecardinal_2ECARD__NOT__LE]) ).
thf(h1,assumption,
~ ! [X1: d,X2: u,X3: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: u,X2: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ eigen__1 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ eigen__1 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ eigen__2 ) @ ( s @ ( tyop_2Emin_2Efun @ eigen__1 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ eigen__2 ) @ ( s @ ( tyop_2Emin_2Efun @ eigen__1 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ eigen__2 ) @ ( s @ ( tyop_2Emin_2Efun @ eigen__1 @ tyop_2Emin_2Ebool ) @ eigen__3 ) ) ) ) )
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ eigen__0 @ tyop_2Emin_2Ebool ) @ eigen__2 ) @ ( s @ ( tyop_2Emin_2Efun @ eigen__1 @ tyop_2Emin_2Ebool ) @ eigen__3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_negrefl,[status(thm),assumptions([h4,h3,h2,h1,h0])],[h4]) ).
thf(2,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__3)],[h3,1,h4]) ).
thf(3,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,2,h3]) ).
thf(4,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,3,h2]) ).
thf(5,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).
thf(0,theorem,
! [X1: d,X2: d,X3: u,X4: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) )
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecardinal_2Ecardleq_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP010^4 : TPTP v9.2.0. Bugfixed v7.5.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n008.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 18:28:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.28/2.50 % SZS status Theorem
% 2.28/2.50 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.28/2.50 % Inferences: 0
% 2.28/2.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------