%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUN023^1 : TPTP v9.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n007.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 02:13:11 PM UTC 2025
% Result : Theorem 112.35s 112.56s
% Output : Proof 112.35s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_zero,type,
zero: $i ).
thf(ty_s,type,
s: $i > $i ).
thf(ty_ite,type,
ite: $o > $i > $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $o,X2: $i,X3: $i] :
( ~ X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ X1 )
= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( s @ zero )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ ( s @ zero ) ) )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( ( s @ zero )
= ( s @ zero ) )
=> ( ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ X1
@ X2 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( s @ zero )
= zero ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ~ sP6
=> ( ( ite @ sP6 @ X1 @ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ite @ sP6 @ zero @ ( s @ zero ) )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP6
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( zero = zero ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( s @ zero )
= ( s @ zero ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP8
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $o,X2: $i,X3: $i] :
( X1
=> ( ( ite @ X1 @ X2 @ X3 )
= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i > $i] :
( ( ( X1 @ zero )
= ( s @ zero ) )
=> ( ( X1 @ ( s @ zero ) )
!= zero ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ sP6
=> ( ( ite @ sP6 @ zero @ X1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP11
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(n8,conjecture,
( ~ ( sP13
=> ~ sP1 )
=> ~ sP14 ) ).
thf(h0,negated_conjecture,
~ ( ~ ( sP13
=> ~ sP1 )
=> ~ sP14 ),
inference(assume_negation,[status(cth)],[n8]) ).
thf(h1,assumption,
~ ( sP13
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP14,
introduced(assumption,[]) ).
thf(h3,assumption,
sP13,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP13
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP2
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP16
| ~ sP11
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP6
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP12
| ~ sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP15
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP14
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
sP10,
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP3
| ~ sP11
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP11
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h4,h2]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,15,h3,h4]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,16,h1,h2]) ).
thf(0,theorem,
( ~ ( sP13
=> ~ sP1 )
=> ~ sP14 ),
inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUN023^1 : TPTP v9.2.0. Released v6.4.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.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 13:47:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 112.35/112.56 % SZS status Theorem
% 112.35/112.56 % Mode: mode447
% 112.35/112.56 % Inferences: 1782
% 112.35/112.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------