TSTP Solution File: ITP130^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP130^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 04:02:21 EDT 2023
% Result : Theorem 0.20s 0.74s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_nat,type,
nat: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_ya,type,
ya: int ).
thf(ty_power_power_int,type,
power_power_int: int > nat > int ).
thf(ty_power_power_real,type,
power_power_real: real > nat > real ).
thf(ty_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(ty_pm,type,
pm: nat ).
thf(ty_na,type,
na: int ).
thf(ty_ring_1_of_int_real,type,
ring_1_of_int_real: int > real ).
thf(ty_zero_zero_int,type,
zero_zero_int: int ).
thf(ty_p,type,
p: nat ).
thf(sP1,plain,
( sP1
<=> ( ord_less_int @ na @ ( power_power_int @ ya @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( power_power_real @ ( ring_1_of_int_real @ ya ) @ p )
= ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ p ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( p
= ( suc @ pm ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ X1 ) )
= ( ord_less_int @ na @ ( power_power_int @ ya @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ya = zero_zero_int ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> $false ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: int,X2: int,X3: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ X1 ) @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ X3 ) )
= ( ord_less_int @ X1 @ ( power_power_int @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: int,X2: nat] :
( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ X1 ) @ X2 ) )
= ( ord_less_int @ na @ ( power_power_int @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP4 = sP1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(conj_0,conjecture,
sP3 ).
thf(h0,negated_conjecture,
~ sP3,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ ( ord_less_int @ ya @ zero_zero_int ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ord_less_int @ na @ zero_zero_int ),
introduced(assumption,[]) ).
thf(h3,assumption,
ord_less_int @ zero_zero_int @ ya,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP3
| ~ sP2
| sP8 ),
inference(mating_rule,[status(thm)],]) ).
thf(2,plain,
( sP2
| ~ sP5
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP4
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
~ sP8,
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_86_p,axiom,
sP5 ).
thf(fact_81_yyn,axiom,
sP1 ).
thf(fact_3_of__int__power__less__of__int__cancel__iff,axiom,
sP9 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h1,h2,h1,h2,h0])],[1,2,3,4,5,6,7,h0,fact_86_p,fact_81_yyn,fact_3_of__int__power__less__of__int__cancel__iff]) ).
thf(fact_19_y00,axiom,
~ sP7 ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h4,h1,h2,h1,h2,h0])],[h4,fact_19_y00]) ).
thf(fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062,axiom,
( ~ ( ord_less_int @ zero_zero_int @ ya )
=> sP7 ) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062,8,9,h3,h4]) ).
thf(fact_25_not_I2_J,axiom,
~ ( ~ ( ord_less_int @ ya @ zero_zero_int )
=> ( ord_less_int @ na @ zero_zero_int ) ) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h1,h2])],[fact_25_not_I2_J,10,h1,h2]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_25_not_I2_J,11,h1,h2]) ).
thf(0,theorem,
sP3,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP130^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 11:29:38 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.74 % SZS status Theorem
% 0.20/0.74 % Mode: cade22sinegrackle2x6978
% 0.20/0.74 % Steps: 7538
% 0.20/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------