TSTP Solution File: ITP167^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP167^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 : Sun Jul 17 00:29:21 EDT 2022
% Result : Theorem 75.90s 75.51s
% Output : Proof 75.90s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_com,type,
com: $tType ).
thf(ty_list_char,type,
list_char: $tType ).
thf(ty_int,type,
int: $tType ).
thf(ty_p,type,
p: ( list_char > int ) > ( list_char > int ) > $o ).
thf(ty_c2,type,
c2: com ).
thf(ty_q,type,
q: ( list_char > int ) > ( list_char > int ) > $o ).
thf(ty_relati1310524937decomp,type,
relati1310524937decomp: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( list_char > int ) > ( list_char > int ) > $o ).
thf(ty_skip,type,
skip: com ).
thf(ty_relati2102071307_hoare,type,
relati2102071307_hoare: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
thf(ty_c,type,
c: com ).
thf(ty_relati775585786_valid,type,
relati775585786_valid: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o,X2: com,X3: com,X4: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ X1 @ X2 @ X3 @ X4 )
=> ( relati2102071307_hoare @ X1 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: com,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ p @ X1 @ X2 @ X3 )
=> ( relati775585786_valid @ p @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ X1 @ X2 )
=> ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: com,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ X1 @ X2 @ X3 )
=> ( relati2102071307_hoare @ p @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ p @ c @ c2 @ X1 )
=> ( relati775585786_valid @ p @ c @ c2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: com,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ X1 @ X2 @ X3 )
=> ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o,X4: com,X5: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( ( relati775585786_valid @ X1 @ X2 @ skip @ X3 )
=> ~ ( relati775585786_valid @ X3 @ skip @ X4 @ X5 ) )
=> ( relati775585786_valid @ X1 @ X2 @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ c @ skip @ X1 )
=> ( relati2102071307_hoare @ p @ c @ skip @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( relati2102071307_hoare @ p @ c @ c2 @ q ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( relati775585786_valid @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( relati775585786_valid @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
=> ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: com,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ X1 @ X2 @ X3 )
=> ~ ( ( relati775585786_valid @ p @ X1 @ skip @ ( relati1310524937decomp @ p @ X1 @ X2 @ X3 ) )
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ p @ X1 @ X2 @ X3 ) @ skip @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( relati775585786_valid @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ X1 )
=> ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o,X3: com,X4: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( ( relati775585786_valid @ p @ X1 @ skip @ X2 )
=> ~ ( relati775585786_valid @ X2 @ skip @ X3 @ X4 ) )
=> ( relati775585786_valid @ p @ X1 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ X1 )
=> ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( relati775585786_valid @ p @ c @ c2 @ q ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ p @ c @ X1 @ X2 )
=> ( relati775585786_valid @ p @ c @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ c @ c2 @ X1 )
=> ~ ( ( relati775585786_valid @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ X1 ) )
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ X1 ) @ skip @ c2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ c @ X1 @ X2 )
=> ( relati2102071307_hoare @ p @ c @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ c @ X1 @ X2 )
=> ~ ( ( relati775585786_valid @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ X1 @ X2 ) )
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ X1 @ X2 ) @ skip @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP10
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o,X2: com,X3: com,X4: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ X1 @ X2 @ X3 @ X4 )
=> ~ ( ( relati775585786_valid @ X1 @ X2 @ skip @ ( relati1310524937decomp @ X1 @ X2 @ X3 @ X4 ) )
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ X1 @ X2 @ X3 @ X4 ) @ skip @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ p @ c @ c2 @ X1 )
=> ( relati2102071307_hoare @ p @ c @ c2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP23
=> ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ p @ c @ skip @ X1 )
=> ( relati775585786_valid @ p @ c @ skip @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP29
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP18
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o,X2: com,X3: com,X4: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ X1 @ X2 @ X3 @ X4 )
=> ( relati775585786_valid @ X1 @ X2 @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: com,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ X1 @ X2 @ X3 )
=> ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ X1 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( sP13
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ X1 @ X2 ) )
=> ( relati775585786_valid @ p @ c @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP9
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( sP13
=> ~ ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ X1 ) )
=> ( relati775585786_valid @ p @ c @ c2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: ( list_char > int ) > ( list_char > int ) > $o,X2: com,X3: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( ( relati775585786_valid @ p @ c @ skip @ X1 )
=> ~ ( relati775585786_valid @ X1 @ skip @ X2 @ X3 ) )
=> ( relati775585786_valid @ p @ c @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: com,X2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ X1 @ X2 )
=> ( relati775585786_valid @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP18
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(conj_0,conjecture,
( sP9
= ( ~ ( sP22
=> ~ sP23 ) ) ) ).
thf(h0,negated_conjecture,
sP9
!= ( ~ ( sP22
=> ~ sP23 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h1,assumption,
sP9,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP22
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h4,assumption,
( sP22
=> ~ sP23 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ sP22,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(1,plain,
( sP10
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP24
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP20
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP40
| ~ sP18
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP36
| ~ sP9
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP21
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP8
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP11
| ~ sP13
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP26
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_8_ir__valid__decomp1,axiom,
sP26 ).
thf(fact_1_completeness,axiom,
sP1 ).
thf(fact_0_soundness,axiom,
sP33 ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h1,h5,fact_8_ir__valid__decomp1,fact_1_completeness,fact_0_soundness]) ).
thf(18,plain,
( sP10
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP3
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP31
| ~ sP29
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP12
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP24
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP20
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP40
| ~ sP18
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP26
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP34
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP1
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP5
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP36
| ~ sP9
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h1,h2,h0])],[18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,h1,h6,fact_8_ir__valid__decomp1,fact_1_completeness,fact_0_soundness]) ).
thf(35,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h2,17,34,h5,h6]) ).
thf(h7,assumption,
sP22,
introduced(assumption,[]) ).
thf(h8,assumption,
sP23,
introduced(assumption,[]) ).
thf(36,plain,
( ~ sP35
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP37
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP25
| sP10
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP10
| ~ sP13
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP15
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP38
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP39
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP16
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP28
| ~ sP23
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP7
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP21
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP27
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP32
| ~ sP18
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP33
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP6
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP19
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP30
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP17
| ~ sP22
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(fact_9_ir__valid__decomp2,axiom,
sP7 ).
thf(58,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h3,h4,h0])],[36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,h3,h7,h8,fact_9_ir__valid__decomp2,fact_1_completeness,fact_0_soundness]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h0]),tab_negimp(discharge,[h7,h8])],[h4,58,h7,h8]) ).
thf(60,plain,
$false,
inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,35,59,h1,h2,h3,h4]) ).
thf(0,theorem,
( sP9
= ( ~ ( sP22
=> ~ sP23 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[60,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP167^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.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 : Sat Jun 4 01:50:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 75.90/75.51 % SZS status Theorem
% 75.90/75.51 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 75.90/75.51 % Inferences: 1231
% 75.90/75.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------