%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN055^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 03:17:41 PM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_cG,type,
cG: $i > $o ).
thf(ty_cP,type,
cP: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_cR,type,
cR: $i > $o ).
thf(ty_cF,type,
cF: $i > $o ).
thf(ty_cQ,type,
cQ: $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ( cQ @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( cQ @ eigen__0 )
=> ~ ( cP @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( cP @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( cG @ eigen__1 )
=> ~ ( cR @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cF @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP3
=> ( cQ @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( cP @ eigen__1 )
=> ~ ( ( cG @ eigen__1 )
=> ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( ( cG @ X1 )
=> ~ ( cF @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( cQ @ X1 )
=> ~ ( cP @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cQ @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( cP @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( cG @ eigen__1 )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( cF @ X1 )
=> ~ ( ~ ( cG @ X1 )
=> ~ ( cR @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cG @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(cPELL25,conjecture,
( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
~ ( cP @ X1 )
=> ~ sP14 )
=> ~ sP8 )
=> ~ ( ~ sP1
=> ~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( cR @ X1 ) ) ) )
=> ~ sP10 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
~ ( cP @ X1 )
=> ~ sP14 )
=> ~ sP8 )
=> ~ ( ~ sP1
=> ~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( cR @ X1 ) ) ) )
=> ~ sP10 ),
inference(assume_negation,[status(cth)],[cPELL25]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ! [X1: $i] :
~ ( cP @ X1 )
=> ~ sP14 )
=> ~ sP8 )
=> ~ ( ~ sP1
=> ~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( cR @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP10,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ! [X1: $i] :
~ ( cP @ X1 )
=> ~ sP14 )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ~ sP1
=> ~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( cR @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ! [X1: $i] :
~ ( cP @ X1 )
=> ~ sP14 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP8,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: $i] :
~ ( cP @ X1 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP14,
introduced(assumption,[]) ).
thf(h9,assumption,
sP3,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( cR @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| ~ sP11
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP1
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP6
| ~ sP3
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,h9,h10,h2]) ).
thf(h12,assumption,
~ ( sP12
=> ~ ( cR @ eigen__1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
sP12,
introduced(assumption,[]) ).
thf(h14,assumption,
cR @ eigen__1,
introduced(assumption,[]) ).
thf(6,plain,
( sP4
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP14
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP9
| ~ sP5
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP13
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP7
| ~ sP12
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[6,7,8,9,10,11,12,h8,h6,h13]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,13,h13,h14]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,14,h12]) ).
thf(16,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h4,5,15,h10,h11]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__0)],[h7,16,h9]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,17,h7,h8]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,18,h5,h6]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,19,h3,h4]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ! [X1: $i] :
~ ( cP @ X1 )
=> ~ sP14 )
=> ~ sP8 )
=> ~ ( ~ sP1
=> ~ ! [X1: $i] :
( ( cP @ X1 )
=> ~ ( cR @ X1 ) ) ) )
=> ~ sP10 ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN055^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32 % Computer : n002.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 8 14:57:23 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 41
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------