TSTP Solution File: ITP010^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP010^1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : Sun Jul 17 00:28:24 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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
% 0.07/0.11 % Problem : ITP010^1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jun 3 20:54:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 0
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------