TSTP Solution File: NUM707^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM707^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : 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 : 600s
% DateTime : Mon Jul 18 13:55:32 EDT 2022
% Result : Theorem 1.59s 1.99s
% Output : Proof 1.59s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_pl,type,
pl: nat > nat > nat ).
thf(ty_y,type,
y: nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_ts,type,
ts: nat > nat > nat ).
thf(ty_x,type,
x: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat] :
( ( ts @ X1 @ ( suc @ X2 ) )
= ( pl @ ( ts @ X1 @ X2 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( ( ts @ x @ ( suc @ y ) )
= X1 )
=> ( X1
= ( ts @ x @ ( suc @ y ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
( ( ts @ x @ ( suc @ X1 ) )
= ( pl @ ( ts @ x @ X1 ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ts @ x @ ( suc @ y ) )
= ( pl @ ( ts @ x @ y ) @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( pl @ ( ts @ x @ y ) @ x )
= ( ts @ x @ ( suc @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat,X2: nat] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(satz28f,conjecture,
sP5 ).
thf(h0,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[satz28f]) ).
thf(1,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| ~ sP4
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
sP7,
inference(eq_sym,[status(thm)],]) ).
thf(satz28b,axiom,
sP1 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,satz28b,h0]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM707^1 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 15:13:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.59/1.99 % SZS status Theorem
% 1.59/1.99 % Mode: mode213
% 1.59/1.99 % Inferences: 3326
% 1.59/1.99 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------