%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO385^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 03:23:21 PM UTC 2025
% Result : Theorem 1.07s 1.27s
% Output : Proof 1.07s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_f,type,
f: $i > $i ).
thf(ty_b,type,
b: $i ).
thf(ty_cQ_1,type,
cQ_1: $i > $i > $i > $o ).
thf(ty_d,type,
d: $i ).
thf(ty_c,type,
c: $i ).
thf(ty_cP_1,type,
cP_1: $i > $i > $o ).
thf(ty_cP_2,type,
cP_2: $i > $i > $o ).
thf(ty_cQ_3,type,
cQ_3: $i > $i > $i > $o ).
thf(ty_a,type,
a: $i ).
thf(ty_cQ_2,type,
cQ_2: $i > $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ X1 @ X2 @ X3 )
=> ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_2 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_3 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ ( cP_2 @ ( f @ a ) @ a ) )
=> ~ ( cP_2 @ ( f @ b ) @ b ) )
=> ~ ( cP_2 @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( cP_2 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( cP_2 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cQ_3 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
~ ( cQ_3 @ a @ b @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ ( cP_2 @ ( f @ a ) @ a ) )
=> ~ ( cP_2 @ ( f @ b ) @ b ) )
=> ~ ( cP_2 @ ( f @ c ) @ X1 ) )
=> ( cQ_3 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ( cQ_2 @ a @ b @ c )
=> ~ ( cP_2 @ ( f @ a ) @ a ) )
=> ~ ( cP_2 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( cP_2 @ b @ b )
=> ( cP_2 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( cP_2 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP4
=> ( cP_2 @ ( f @ a ) @ a ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( cP_2 @ c @ X1 )
=> ( cP_2 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ b @ X1 )
=> ~ ( cP_2 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_2 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_3 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( cP_2 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ X1 )
=> ~ ( cP_1 @ ( f @ a ) @ X2 ) )
=> ~ ( cP_1 @ ( f @ b ) @ X3 ) )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ( cQ_2 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP3
=> ~ ( cP_1 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( cP_2 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP3
=> ~ ( cP_1 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_1 @ ( f @ c ) @ X2 ) )
=> ( cQ_2 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( cQ_2 @ a @ b @ c )
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ b @ c )
=> ~ ( cP_1 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_1 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_1 @ ( f @ c ) @ X3 ) )
=> ( cQ_2 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP17
=> ~ ( cP_1 @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( cP_1 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( cP_2 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_2 @ a @ X1 @ X2 )
=> ~ ( cP_2 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_2 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_2 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_3 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( cP_1 @ X1 @ X2 )
=> ( cP_1 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ~ ( ~ sP17
=> ~ ( cP_1 @ ( f @ c ) @ X1 ) )
=> ( cQ_2 @ a @ b @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( cP_1 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP20
=> ~ ( cP_2 @ ( f @ b ) @ X1 ) )
=> ~ ( cP_2 @ ( f @ c ) @ X2 ) )
=> ( cQ_3 @ a @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( cP_1 @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i] :
( ( cP_2 @ X1 @ X2 )
=> ( cP_2 @ ( f @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( cP_1 @ c @ X1 )
=> ( cP_1 @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( cP_1 @ b @ b )
=> ( cP_1 @ ( f @ b ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP11
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_3 @ X1 @ X2 @ X3 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP22
=> ( cQ_2 @ a @ b @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ sP2
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ X1 @ X2 @ X3 )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
=> ~ ( cP_1 @ ( f @ X3 ) @ X6 ) )
=> ( cQ_2 @ X4 @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i,X2: $i] :
~ ( cQ_3 @ a @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( cP_1 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( cP_2 @ b @ X1 )
=> ( cP_2 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP28
=> sP30 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ( cQ_1 @ a @ X1 @ X2 )
=> ~ ( cP_1 @ ( f @ a ) @ X3 ) )
=> ~ ( cP_1 @ ( f @ X1 ) @ X4 ) )
=> ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
=> ( cQ_2 @ X3 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( cP_1 @ ( f @ b ) @ b ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( cP_1 @ ( f @ a ) @ a ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( cQ_1 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP23
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ( cP_1 @ b @ X1 )
=> ( cP_1 @ ( f @ b ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i] :
( ( cP_2 @ a @ X1 )
=> ( cP_2 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( cP_1 @ a @ X1 )
=> ( cP_1 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( cQ_2 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( sP51
=> ~ ( cP_2 @ ( f @ a ) @ X1 ) )
=> ~ ( cP_2 @ ( f @ b ) @ X2 ) )
=> ~ ( cP_2 @ ( f @ c ) @ X3 ) )
=> ( cQ_3 @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(cTHM409_2,conjecture,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ ! [X1: $i] : ( cP_2 @ d @ X1 ) )
=> ~ sP31 )
=> ~ sP1 )
=> ~ sP35 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ ! [X1: $i] : ( cP_2 @ d @ X1 ) )
=> ~ sP31 )
=> ~ sP1 )
=> ~ sP35 ),
inference(assume_negation,[status(cth)],[cTHM409_2]) ).
thf(h1,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ ! [X1: $i] : ( cP_2 @ d @ X1 ) )
=> ~ sP31 )
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP35,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ ! [X1: $i] : ( cP_2 @ d @ X1 ) )
=> ~ sP31 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ ! [X1: $i] : ( cP_2 @ d @ X1 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP31,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 ),
introduced(assumption,[]) ).
thf(h8,assumption,
! [X1: $i] : ( cP_2 @ d @ X1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP11,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP15,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP4,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP38,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP26,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 ),
introduced(assumption,[]) ).
thf(h20,assumption,
! [X1: $i] : ( cP_1 @ d @ X1 ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP28,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP46
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP40,
introduced(assumption,[]) ).
thf(h25,assumption,
sP46,
introduced(assumption,[]) ).
thf(h26,assumption,
sP23,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| sP20
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP20
| ~ sP51
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP9
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP37
| sP2
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP29
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP52
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP17
| sP3
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP3
| ~ sP46
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP22
| sP17
| ~ sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP36
| sP22
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP27
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP19
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP21
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP14
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP16
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP25
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP43
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP7
| ~ sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP12
| ~ sP4
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP47
| ~ sP23
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP39
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP49
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP50
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP35
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP31
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP26
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP1
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP38
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP10
| ~ sP15
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP33
| ~ sP40
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP41
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP48
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP31
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP26
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP34
| ~ sP11
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP42
| ~ sP28
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP13
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP32
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP31
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP26
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,h25,h26,h24,h22,h18,h16,h14,h12,h10,h6,h4,h2]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h23,42,h25,h26]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h23,h24])],[h21,43,h23,h24]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h19,44,h21,h22]) ).
thf(46,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h17,45,h19,h20]) ).
thf(47,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h15,46,h17,h18]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h13,47,h15,h16]) ).
thf(49,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,48,h13,h14]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,49,h11,h12]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,50,h9,h10]) ).
thf(52,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,51,h7,h8]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,52,h5,h6]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,53,h3,h4]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,54,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP23 )
=> ~ sP40 )
=> ~ sP28 )
=> ~ ! [X1: $i] : ( cP_1 @ d @ X1 ) )
=> ~ sP26 )
=> ~ sP38 )
=> ~ sP4 )
=> ~ sP15 )
=> ~ sP11 )
=> ~ ! [X1: $i] : ( cP_2 @ d @ X1 ) )
=> ~ sP31 )
=> ~ sP1 )
=> ~ sP35 ),
inference(contra,[status(thm),contra(discharge,[h0])],[55,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO385^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Oct 9 01:20:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.07/1.27 % SZS status Theorem
% 1.07/1.27 % Mode: cade22grackle2xfee4
% 1.07/1.27 % Steps: 25923
% 1.07/1.27 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------