%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWW469^1 : TPTP v9.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 03:11:58 PM UTC 2025
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_state,type,
state: $tType ).
thf(ty_eigen__2,type,
eigen__2: state ).
thf(ty_eigen__1,type,
eigen__1: state ).
thf(ty_eigen__0,type,
eigen__0: state ).
thf(ty_hoare_1821564147gleton,type,
hoare_1821564147gleton: $o ).
thf(sP1,plain,
( sP1
<=> hoare_1821564147gleton ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: state,X2: state] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: state] :
( ( eigen__2 = X1 )
=> ( X1 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__2 = eigen__0 )
=> ( eigen__0 = eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__2 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: state] : ( X1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: state] :
( ( eigen__1 = X1 )
=> ( X1 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP9
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__0 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(conj_1,conjecture,
! [X1: state] :
~ ! [X2: state] : ( X2 = X1 ) ).
thf(h0,negated_conjecture,
~ ! [X1: state] :
~ ! [X2: state] : ( X2 = X1 ),
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(h1,assumption,
sP7,
introduced(assumption,[]) ).
thf(h2,assumption,
sP1,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: state] : ( !! @ ( (=) @ X1 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
! [X1: state] : ( !! @ ( (=) @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( !! @ ( (=) @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP4
| ~ sP11
| ~ sP12 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| ~ sP6
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP10
| ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP2
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
sP2,
inference(eq_sym,[status(thm)],[]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h7,h1]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,11,h7]) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,12,h6]) ).
thf(conj_0,axiom,
sP1 ).
thf(14,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h4,h5,h1,h0])],[conj_0,h4]) ).
thf(fact_0_state__not__singleton__def,axiom,
( sP1
= ( ~ ! [X1: state] : ( !! @ ( (=) @ X1 ) ) ) ) ).
thf(15,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h1,h0]),tab_bq(discharge,[h2,h3]),tab_bq(discharge,[h4,h5])],[fact_0_state__not__singleton__def,13,14,h2,h3,h4,h5]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,15,h1]) ).
thf(0,theorem,
! [X1: state] :
~ ! [X2: state] : ( X2 = X1 ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW469^1 : TPTP v9.2.0. Released v5.3.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n010.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 13:16:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Mode: mode213
% 0.13/0.37 % Inferences: 12
% 0.13/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------