TSTP Solution File: NUM673^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM673^1 : 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 : n004.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 13:55:02 EDT 2022
% Result : Theorem 1.96s 2.18s
% Output : Proof 1.96s
% 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_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 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ( pl @ z @ x )
= ( pl @ x @ z ) )
=> ~ ( more @ ( pl @ x @ z ) @ ( pl @ z @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat > $o] :
( ( X1 @ ( pl @ z @ x ) )
=> ! [X2: nat] :
( ( ( pl @ z @ x )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( more @ ( pl @ x @ z ) @ ( pl @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: nat] :
( ( ( pl @ z @ y )
= X1 )
=> ~ ( more @ ( pl @ x @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( pl @ z @ x )
= ( pl @ x @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: nat,X2: nat] :
( ( more @ x @ X1 )
=> ( more @ ( pl @ x @ X2 ) @ ( pl @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ( pl @ z @ y )
= ( pl @ y @ z ) )
=> ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) )
=> ! [X1: nat] :
( ( ( pl @ z @ x )
= X1 )
=> ~ ( more @ X1 @ ( pl @ z @ y ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat,X2: nat > $o] :
( ( X2 @ X1 )
=> ! [X3: nat] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( more @ ( pl @ z @ x ) @ ( pl @ z @ y ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: nat] :
( ( ( pl @ z @ x )
= X1 )
=> ~ ( more @ X1 @ ( pl @ z @ y ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: nat] :
( sP1
=> ( more @ ( pl @ x @ X1 ) @ ( pl @ y @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP4
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: nat] :
( ( pl @ z @ X1 )
= ( pl @ X1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( pl @ z @ y )
= ( pl @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: nat,X2: nat] :
( ( pl @ X1 @ X2 )
= ( pl @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: nat > $o] :
( ( X1 @ ( pl @ z @ y ) )
=> ! [X2: nat] :
( ( ( pl @ z @ y )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(satz19d,conjecture,
sP13 ).
thf(h0,negated_conjecture,
~ sP13,
inference(assume_negation,[status(cth)],[satz19d]) ).
thf(1,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| ~ sP1
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| ~ sP19
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP17
| sP4
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP21
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP18
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP10
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP20
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| ~ sP6
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP15
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP9
| sP13
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP3
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
sP10,
inference(eq_ind,[status(thm)],]) ).
thf(satz6,axiom,
sP20 ).
thf(satz19a,axiom,
sP11 ).
thf(m,axiom,
sP1 ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,satz6,satz19a,m,h0]) ).
thf(0,theorem,
sP13,
inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM673^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : 600
% 0.13/0.34 % DateTime : Thu Jul 7 18:13:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.18 % SZS status Theorem
% 1.96/2.18 % Mode: mode506
% 1.96/2.18 % Inferences: 93
% 1.96/2.18 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------