TSTP Solution File: ITP069^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP069^1 : 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 : n001.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 04:01:52 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_tree_a,type,
tree_a: $tType ).
thf(ty_t_a,type,
t_a: a > tree_a > tree_a > tree_a ).
thf(ty_l,type,
l: tree_a ).
thf(ty_is_heap_a,type,
is_heap_a: tree_a > $o ).
thf(ty_r,type,
r: tree_a ).
thf(ty_heapIm970322378pify_a,type,
heapIm970322378pify_a: tree_a > tree_a ).
thf(ty_v,type,
v: a ).
thf(ty_heapIm1091024090Down_a,type,
heapIm1091024090Down_a: tree_a > tree_a ).
thf(sP1,plain,
( sP1
<=> ( is_heap_a @ ( heapIm970322378pify_a @ l ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) )
= ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: tree_a,X2: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ v @ X1 @ X2 ) )
= ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ X1 ) @ ( heapIm970322378pify_a @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ v @ l @ X1 ) )
= ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
= ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( is_heap_a @ ( heapIm970322378pify_a @ r ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a,X2: tree_a,X3: tree_a] :
( ( heapIm970322378pify_a @ ( t_a @ X1 @ X2 @ X3 ) )
= ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm970322378pify_a @ X2 ) @ ( heapIm970322378pify_a @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(conj_0,conjecture,
sP5 ).
thf(h0,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
( sP8
=> sP7 ),
introduced(assumption,[]) ).
thf(fact_1_T_Ohyps_I1_J,axiom,
sP1 ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h1,h0])],[fact_1_T_Ohyps_I1_J,h1]) ).
thf(h3,assumption,
~ sP8,
introduced(assumption,[]) ).
thf(h4,assumption,
sP7,
introduced(assumption,[]) ).
thf(fact_0_T_Ohyps_I2_J,axiom,
sP8 ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h3,h2,h0])],[fact_0_T_Ohyps_I2_J,h3]) ).
thf(3,plain,
( ~ sP7
| sP5
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP6 ),
inference(symeq,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_3_heapify_Osimps_I2_J,axiom,
sP9 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h2,h0])],[3,4,5,6,7,h0,fact_3_heapify_Osimps_I2_J,h4]) ).
thf(9,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,2,8,h3,h4]) ).
thf(fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,axiom,
( sP1
=> ( sP8
=> sP7 ) ) ).
thf(10,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,1,9,h1,h2]) ).
thf(0,theorem,
sP5,
inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP069^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 12:39:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % Mode: cade22sinegrackle2x6978
% 0.20/0.45 % Steps: 1038
% 0.20/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------