TSTP Solution File: ITP032^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP032^1 : 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 04:01:38 EDT 2023
% Result : Theorem 0.20s 0.74s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_a,type,
a: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_binary1439146945Tree_a,type,
binary1439146945Tree_a: $tType ).
thf(ty_x,type,
x: a ).
thf(ty_h,type,
h: a > int ).
thf(ty_w,type,
w: a ).
thf(ty_binary504661350_eqs_a,type,
binary504661350_eqs_a: ( a > int ) > a > set_a ).
thf(ty_t2,type,
t2: binary1439146945Tree_a ).
thf(ty_member_a,type,
member_a: a > set_a > $o ).
thf(ty_binary717961607le_T_a,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(ty_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(ty_e,type,
e: a ).
thf(ty_binary476621312_Tip_a,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(ty_t1,type,
t1: binary1439146945Tree_a ).
thf(ty_insert_a,type,
insert_a: a > set_a > set_a ).
thf(ty_binary1721989714Tree_a,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(ty_binary1226383794sert_a,type,
binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(ty_bot_bot_set_a,type,
bot_bot_set_a: set_a ).
thf(ty_sup_sup_set_a,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(ty_binary945792244etOf_a,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(ty_minus_minus_set_a,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(sP1,plain,
( sP1
<=> ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( binary1721989714Tree_a @ h @ binary476621312_Tip_a ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ X1 ) )
= ( ~ ( ~ ( ~ ( ( binary1721989714Tree_a @ h @ t1 )
=> ~ ! [X2: a] :
( ( member_a @ X2 @ ( binary945792244etOf_a @ t1 ) )
=> ( ord_less_int @ ( h @ X2 ) @ ( h @ x ) ) ) )
=> ~ ! [X2: a] :
( ( member_a @ X2 @ ( binary945792244etOf_a @ X1 ) )
=> ( ord_less_int @ ( h @ x ) @ ( h @ X2 ) ) ) )
=> ~ ( binary1721989714Tree_a @ h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
= ( ~ ( ~ ( ~ ( ( binary1721989714Tree_a @ h @ t1 )
=> ~ ! [X1: a] :
( ( member_a @ X1 @ ( binary945792244etOf_a @ t1 ) )
=> ( ord_less_int @ ( h @ X1 ) @ ( h @ x ) ) ) )
=> ~ ! [X1: a] :
( ( member_a @ X1 @ ( binary945792244etOf_a @ t2 ) )
=> ( ord_less_int @ ( h @ x ) @ ( h @ X1 ) ) ) )
=> ~ ( binary1721989714Tree_a @ h @ t2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > int] : ( binary1721989714Tree_a @ X1 @ binary476621312_Tip_a ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( binary1721989714Tree_a @ h @ t1 )
=> ~ ! [X1: a] :
( ( member_a @ X1 @ ( binary945792244etOf_a @ t1 ) )
=> ( ord_less_int @ ( h @ X1 ) @ ( h @ x ) ) ) )
=> ~ ! [X1: a] :
( ( member_a @ X1 @ ( binary945792244etOf_a @ t2 ) )
=> ( ord_less_int @ ( h @ x ) @ ( h @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( member_a @ X1 @ ( binary945792244etOf_a @ t1 ) )
=> ( ord_less_int @ ( h @ X1 ) @ ( h @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( member_a @ w @ ( binary945792244etOf_a @ t1 ) )
=> ( ord_less_int @ ( h @ w ) @ ( h @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( binary1721989714Tree_a @ h @ t1 )
=> ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ord_less_int @ ( h @ w ) @ ( h @ x ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( binary1721989714Tree_a @ h @ t2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP6
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: binary1439146945Tree_a,X2: a,X3: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ X1 @ X2 @ X3 ) )
= ( ~ ( ~ ( ~ ( ( binary1721989714Tree_a @ h @ X1 )
=> ~ ! [X4: a] :
( ( member_a @ X4 @ ( binary945792244etOf_a @ X1 ) )
=> ( ord_less_int @ ( h @ X4 ) @ ( h @ X2 ) ) ) )
=> ~ ! [X4: a] :
( ( member_a @ X4 @ ( binary945792244etOf_a @ X3 ) )
=> ( ord_less_int @ ( h @ X2 ) @ ( h @ X4 ) ) ) )
=> ~ ( binary1721989714Tree_a @ h @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( member_a @ w @ ( binary945792244etOf_a @ t1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a,X2: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ X1 @ X2 ) )
= ( ~ ( ~ ( ~ ( ( binary1721989714Tree_a @ h @ t1 )
=> ~ ! [X3: a] :
( ( member_a @ X3 @ ( binary945792244etOf_a @ t1 ) )
=> ( ord_less_int @ ( h @ X3 ) @ ( h @ X1 ) ) ) )
=> ~ ! [X3: a] :
( ( member_a @ X3 @ ( binary945792244etOf_a @ X2 ) )
=> ( ord_less_int @ ( h @ X1 ) @ ( h @ X3 ) ) ) )
=> ~ ( binary1721989714Tree_a @ h @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a > int,X2: binary1439146945Tree_a,X3: a,X4: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ X1 @ ( binary717961607le_T_a @ X2 @ X3 @ X4 ) )
= ( ~ ( ~ ( ~ ( ( binary1721989714Tree_a @ X1 @ X2 )
=> ~ ! [X5: a] :
( ( member_a @ X5 @ ( binary945792244etOf_a @ X2 ) )
=> ( ord_less_int @ ( X1 @ X5 ) @ ( X1 @ X3 ) ) ) )
=> ~ ! [X5: a] :
( ( member_a @ X5 @ ( binary945792244etOf_a @ X4 ) )
=> ( ord_less_int @ ( X1 @ X3 ) @ ( X1 @ X5 ) ) ) )
=> ~ ( binary1721989714Tree_a @ X1 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( binary1721989714Tree_a @ h @ t1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(conj_0,conjecture,
sP10 ).
thf(h0,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h2,assumption,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ binary476621312_Tip_a ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ binary476621312_Tip_a ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h4,assumption,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h6,assumption,
( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ),
introduced(assumption,[]) ).
thf(fact_2_s2,axiom,
sP11 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h3,h1,h0])],[fact_2_s2,h5]) ).
thf(fact_3_s1,axiom,
sP17 ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h1,h0])],[fact_3_s1,h3]) ).
thf(fact_306_h2,axiom,
( sP11
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
thf(3,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_306_h2,1,2,h5,h6]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h4,h1,h0])],[fact_2_s2,h5]) ).
thf(5,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_155_sortedTree_Osimps_I1_J,axiom,
sP5 ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h1,h0])],[5,h1,fact_155_sortedTree_Osimps_I1_J]) ).
thf(7,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_306_h2,4,6,h5,h6]) ).
thf(fact_307_h1,axiom,
( sP17
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
thf(8,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_307_h1,3,7,h3,h4]) ).
thf(9,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h3,h2,h0])],[fact_2_s2,h5]) ).
thf(10,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h6,h3,h2,h0])],[fact_3_s1,h3]) ).
thf(11,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h3,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_306_h2,9,10,h5,h6]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h4,h2,h0])],[fact_2_s2,h5]) ).
thf(13,plain,
( ~ sP8
| ~ sP14
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP6
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( sP12
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP4
| ~ sP1
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP15
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP13
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP16
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_19_sortedTree_Osimps_I2_J,axiom,
sP16 ).
thf(fact_1_s,axiom,
sP1 ).
thf(fact_0_whSet,axiom,
sP14 ).
thf(23,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h2,h0])],[13,14,15,16,17,18,19,20,21,22,h0,fact_19_sortedTree_Osimps_I2_J,fact_1_s,fact_0_whSet]) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h4,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[fact_306_h2,12,23,h5,h6]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_307_h1,11,24,h3,h4]) ).
thf(fact_308__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062,axiom,
( sP2
=> ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ binary476621312_Tip_a ) )
= ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ binary476621312_Tip_a ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
thf(26,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_308__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062,8,25,h1,h2]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP032^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n015.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 : Sun Aug 27 17:01:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.74 % SZS status Theorem
% 0.20/0.74 % Mode: cade22sinegrackle2x6978
% 0.20/0.74 % Steps: 4136
% 0.20/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------