TSTP Solution File: NUM925^2 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : NUM925^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 Aug 31 11:41:52 EDT 2023
% Result : Theorem 21.08s 21.31s
% Output : Proof 21.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_plus_plus_int,type,
plus_plus_int: int > int > int ).
thf(ty_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(ty_semiri1621563631at_int,type,
semiri1621563631at_int: nat > int ).
thf(ty_pls,type,
pls: int ).
thf(ty_power_power_int,type,
power_power_int: int > nat > int ).
thf(ty_number_number_of_nat,type,
number_number_of_nat: int > nat ).
thf(ty_zero_zero_int,type,
zero_zero_int: int ).
thf(ty_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(ty_n,type,
n: nat ).
thf(ty_bit1,type,
bit1: int > int ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(ty_bit0,type,
bit0: int > int ).
thf(ty_one_one_int,type,
one_one_int: int ).
thf(sP1,plain,
( sP1
<=> ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
= zero_zero_int ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: int] :
( ( ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( X1 = zero_zero_int ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ X1 ) @ zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( zero_zero_int
= ( semiri1621563631at_int @ ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( semiri1621563631at_int @ ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP5
= ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
= zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat] :
( ( ( semiri1621563631at_int @ X1 )
= zero_zero_int )
= ( X1 = zero_zero_nat ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ord_less_int @ ( semiri1621563631at_int @ ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(conj_0,conjecture,
~ sP11 ).
thf(h0,negated_conjecture,
sP11,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP7
| sP12
| ~ sP9
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP4 ),
inference(symeq,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP5
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| ~ sP11
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP3
| ~ sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_288_of__nat__less__0__iff,axiom,
sP3 ).
thf(fact_43_int__eq__0__conv,axiom,
sP10 ).
thf(fact_10_zero__eq__power2,axiom,
sP2 ).
thf(fact_8_zero__power2,axiom,
sP8 ).
thf(fact_0_n1pos,axiom,
sP7 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,h0,fact_288_of__nat__less__0__iff,fact_43_int__eq__0__conv,fact_10_zero__eq__power2,fact_8_zero__power2,fact_0_n1pos]) ).
thf(0,theorem,
~ sP11,
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM925^2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 13:58:20 EDT 2023
% 0.13/0.36 % CPUTime :
% 21.08/21.31 % SZS status Theorem
% 21.08/21.31 % Mode: cade22sinegrackle2xfaf3
% 21.08/21.31 % Steps: 5639
% 21.08/21.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------