TSTP Solution File: NUM721^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM721^1 : 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 : n024.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 13:55:41 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_z,type,
z: nat ).
thf(ty_u,type,
u: nat ).
thf(ty_y,type,
y: nat ).
thf(ty_ts,type,
ts: nat > nat > nat ).
thf(ty_some,type,
some: ( nat > $o ) > $o ).
thf(ty_diffprop,type,
diffprop: nat > nat > nat > $o ).
thf(ty_x,type,
x: nat ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( some @ ( diffprop @ X1 @ X2 ) )
=> ( ( some @ ( diffprop @ X3 @ X4 ) )
=> ( some @ ( diffprop @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat] :
( ( some @ ( diffprop @ y @ x ) )
=> ( ( some @ ( diffprop @ u @ X1 ) )
=> ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( some @ ( diffprop @ u @ z ) )
=> ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( some @ ( diffprop @ y @ x ) )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( some @ ( diffprop @ y @ X1 ) )
=> ( ( some @ ( diffprop @ X2 @ X3 ) )
=> ( some @ ( diffprop @ ( ts @ y @ X2 ) @ ( ts @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( some @ ( diffprop @ u @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat,X2: nat] :
( ( some @ ( diffprop @ y @ x ) )
=> ( ( some @ ( diffprop @ X1 @ X2 ) )
=> ( some @ ( diffprop @ ( ts @ y @ X1 ) @ ( ts @ x @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( some @ ( diffprop @ y @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(satz34a,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[satz34a]) ).
thf(1,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| ~ sP9
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| ~ sP6
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(l,axiom,
sP9 ).
thf(k,axiom,
sP6 ).
thf(satz34,axiom,
sP1 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,l,k,satz34,h0]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM721^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n024.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 : Thu Jul 7 21:47:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 2
% 0.12/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------