%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM691^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 02:11:49 PM UTC 2025
% Result : Theorem 1.10s 1.36s
% Output : Proof 1.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_z,type,
z: nat ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_u,type,
u: nat ).
thf(ty_y,type,
y: nat ).
thf(ty_more,type,
more: nat > nat > $o ).
thf(ty_x,type,
x: nat ).
thf(sP1,plain,
( sP1
<=> ( ~ ( more @ x @ y )
=> ( x = y ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( more @ z @ u ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat,X2: nat] :
( ( more @ x @ y )
=> ( ( ~ ( more @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( more @ ( pl @ x @ X1 ) @ ( pl @ y @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( ~ ( more @ X1 @ X2 )
=> ( X1 = X2 ) )
=> ( ( more @ X3 @ X4 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat] :
( sP1
=> ( ( more @ z @ X1 )
=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( ~ ( more @ x @ X1 )
=> ( x = X1 ) )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ x @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat,X2: nat] :
( sP1
=> ( ( more @ X1 @ X2 )
=> ( more @ ( pl @ x @ X1 ) @ ( pl @ y @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP1
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( more @ X1 @ X2 )
=> ( ( ~ ( more @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( more @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( more @ x @ X1 )
=> ( ( ~ ( more @ X2 @ X3 )
=> ( X2 = X3 ) )
=> ( more @ ( pl @ x @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: nat] :
( sP12
=> ( ( ~ ( more @ z @ X1 )
=> ( z = X1 ) )
=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( z = u ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP3
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> ( sP16
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP2
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP16
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(satz23,conjecture,
sP18 ).
thf(h0,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[satz23]) ).
thf(1,plain,
( ~ sP9
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| ~ sP1
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP4
| ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP5
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP14
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP17
| ~ sP12
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP20
| ~ sP16
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP1
| sP12
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP16
| sP3
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( sP19
| ~ sP21
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP18
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP18
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(satz22b,axiom,
sP11 ).
thf(satz22a,axiom,
sP6 ).
thf(n,axiom,
sP16 ).
thf(m,axiom,
sP1 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,satz22b,satz22a,n,m,h0]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM691^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 22:54:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.10/1.36 % SZS status Theorem
% 1.10/1.36 % Mode: mode506
% 1.10/1.36 % Inferences: 19472
% 1.10/1.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------