TSTP Solution File: LCL955^24 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL955^24 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n001.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 Aug 31 08:06:05 EDT 2023
% Result : Theorem 1.46s 1.66s
% Output : Proof 1.46s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_gt,type,
gt: $i > $i > mworld > $o ).
thf(ty_plus,type,
plus: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(ty_pv65,type,
pv65: $i ).
thf(ty_tptp_float_0_001,type,
tptp_float_0_001: $i ).
thf(ty_loopcounter,type,
loopcounter: $i ).
thf(ty_n1,type,
n1: $i ).
thf(ty_true,type,
true: mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_eigen__151,type,
eigen__151: mworld ).
thf(ty_eigen__152,type,
eigen__152: mworld ).
thf(ty_geq,type,
geq: $i > $i > mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( true @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( mrel @ mactual @ eigen__2 )
=> ( true @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( mrel @ mactual @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( true @ eigen__152 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mrel @ mactual @ eigen__152 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( true @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( mrel @ mactual @ eigen__152 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] : ( mrel @ mactual @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( mrel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( eiw_di @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(cl5_nebula_array_0028,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( geq @ pv65 @ tptp_float_0_001 @ X2 ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X4 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( true @ X3 ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( geq @ pv65 @ tptp_float_0_001 @ X2 ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X4 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( true @ X3 ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0028]) ).
thf(h1,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( geq @ pv65 @ tptp_float_0_001 @ X1 ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( geq @ pv65 @ tptp_float_0_001 @ X1 ) )
=> ~ ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( geq @ pv65 @ tptp_float_0_001 @ X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) )
=> ~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( true @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( mrel @ eigen__0 @ eigen__151 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__151 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__151 @ X1 )
=> ( true @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
mrel @ eigen__0 @ eigen__151,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( ! [X1: mworld] :
( ( mrel @ eigen__151 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__151 @ X1 )
=> ( true @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
! [X1: mworld] :
( ( mrel @ eigen__151 @ X1 )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__151 @ X1 )
=> ( true @ X1 ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ( mrel @ eigen__151 @ eigen__152 )
=> sP4 ),
introduced(assumption,[]) ).
thf(h14,assumption,
mrel @ eigen__151 @ eigen__152,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP8
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP9
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(ttrue,axiom,
sP1 ).
thf(mrel_universal,axiom,
sP7 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h9,h10,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,h15,ttrue,mrel_universal]) ).
thf(6,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h9,h10,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,5,h14,h15]) ).
thf(7,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__152)],[h12,6,h13]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,7,h11,h12]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,8,h9,h10]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__151)],[h6,9,h8]) ).
thf(h16,assumption,
~ ( ( mrel @ eigen__0 @ eigen__1 )
=> ( ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( true @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h17,assumption,
mrel @ eigen__0 @ eigen__1,
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X1 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( true @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X1 ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ ! [X1: mworld] :
( ( mrel @ eigen__1 @ X1 )
=> ( true @ X1 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ( mrel @ eigen__1 @ eigen__2 )
=> sP6 ),
introduced(assumption,[]) ).
thf(h22,assumption,
mrel @ eigen__1 @ eigen__2,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(11,plain,
( ~ sP2
| ~ sP3
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h22,h23,h21,h19,h20,h17,h18,h16,h7,h4,h5,h2,h3,h1,h0])],[11,12,13,14,h23,ttrue,mrel_universal]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h17,h18,h16,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,15,h22,h23]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h17,h18,h16,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__2)],[h20,16,h21]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,17,h19,h20]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,18,h17,h18]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__1)],[h7,19,h16]) ).
thf(21,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[h5,10,20,h6,h7]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,21,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,22,h2,h3]) ).
thf(24,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,23,h1]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( geq @ pv65 @ tptp_float_0_001 @ X2 ) )
=> ~ ( ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X4 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( true @ X3 ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( gt @ ( plus @ n1 @ loopcounter ) @ n1 @ X3 ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( true @ X3 ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL955^24 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n001.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 : Thu Aug 24 18:37:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.46/1.66 % SZS status Theorem
% 1.46/1.66 % Mode: cade22sinegrackle2x6978
% 1.46/1.66 % Steps: 38705
% 1.46/1.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------