TSTP Solution File: SYO041^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO041^2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : Thu Jul 21 19:29:46 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 70
% Syntax : Number of formulae : 106 ( 51 unt; 4 typ; 0 def)
% Number of atoms : 269 ( 35 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 177 ( 74 ~; 52 |; 0 &; 17 @)
% ( 19 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 3 ( 0 ^ 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_y,type,
y: $o ).
thf(ty_g,type,
g: $o > $o ).
thf(ty_f,type,
f: $o > $o ).
thf(ty_x,type,
x: $o ).
thf(sP1,plain,
( sP1
<=> ( ( f @ ( f @ x ) )
= x ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( f @ ( f @ ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> y ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( f @ x )
= ( f @ ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( g @ x ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( ( f @ x )
= x )
=> ( x
= ( f @ x ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( f @ x ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( f @ sP8 )
= sP8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( x
= ( f @ sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o] :
( ( sP8 = X1 )
=> ( X1 = sP8 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> x ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( g @ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP8 = sP12 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP8 = sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP12 = sP8 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP4 = sP8 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( g @ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( f @ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(3,conjecture,
( ~ ( ~ ( ( sP12 != sP4 )
=> ( sP6 != sP4 ) )
=> ( sP18 != sP12 ) )
=> ( sP2 != sP13 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ( ~ ( ( sP12 != sP4 )
=> ( sP6 != sP4 ) )
=> ( sP18 != sP12 ) )
=> ( sP2 != sP13 ) ),
inference(assume_negation,[status(cth)],[3]) ).
thf(h1,assumption,
~ ( ~ ( ( sP12 != sP4 )
=> ( sP6 != sP4 ) )
=> ( sP18 != sP12 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP2 = sP13,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( sP12 != sP4 )
=> ( sP6 != sP4 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP18 = sP12,
introduced(assumption,[]) ).
thf(h5,assumption,
sP12 != sP4,
introduced(assumption,[]) ).
thf(h6,assumption,
sP6 = sP4,
introduced(assumption,[]) ).
thf(h7,assumption,
sP12,
introduced(assumption,[]) ).
thf(h8,assumption,
sP4,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h11,assumption,
sP6,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h13,assumption,
sP18,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h15,assumption,
sP2,
introduced(assumption,[]) ).
thf(h16,assumption,
sP13,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h18,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h13,h7,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).
thf(2,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h13,h7,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).
thf('3_001',plain,
$false,
inference(tab_bq,[status(thm),assumptions([h13,h7,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,1,2,h15,h16,h17,h18]) ).
thf(4,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h9,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).
thf(5,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h14,h9,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h8,h8]) ).
thf(6,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h9,h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,4,5,h15,h16,h17,h18]) ).
thf(7,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h11,h8,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,3,6,h13,h7,h14,h9]) ).
thf(8,plain,
( sP9
| sP19
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP2
| sP19
| ~ sP9 ),
inference(mating_rule,[status(thm)],]) ).
thf(10,plain,
( sP1
| ~ sP19
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP8
| ~ sP1 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( sP14
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP13
| sP6
| ~ sP14 ),
inference(mating_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h13,h7,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[8,9,10,11,12,13,h12,h7,h15,h16]) ).
thf(15,plain,
( sP14
| ~ sP8
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP7
| ~ sP14
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP11
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP8
| sP19
| ~ sP16 ),
inference(mating_rule,[status(thm)],]) ).
thf(19,plain,
( sP10
| ~ sP12
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP8
| sP2
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(21,plain,
( sP17
| sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
sP3,
inference(eq_sym,[status(thm)],]) ).
thf(24,plain,
( ~ sP18
| sP13
| ~ sP17 ),
inference(mating_rule,[status(thm)],]) ).
thf(25,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h13,h7,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[15,16,17,18,19,20,21,22,23,24,h10,h13,h7,h17,h18]) ).
thf(26,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h13,h7,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,14,25,h15,h16,h17,h18]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h9,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).
thf(28,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h14,h9,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).
thf(29,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h9,h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,27,28,h15,h16,h17,h18]) ).
thf(30,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h12,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,26,29,h13,h7,h14,h9]) ).
thf(31,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h11,h8]),tab_bq(discharge,[h12,h10])],[h6,7,30,h11,h8,h12,h10]) ).
thf(32,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h13,h7,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).
thf(33,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h13,h7,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h7,h9]) ).
thf(34,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h13,h7,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,32,33,h15,h16,h17,h18]) ).
thf(35,plain,
( sP14
| sP8
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP19
| sP8
| ~ sP14 ),
inference(mating_rule,[status(thm)],]) ).
thf(37,plain,
( sP1
| sP19
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP2
| sP8
| ~ sP1 ),
inference(mating_rule,[status(thm)],]) ).
thf(39,plain,
( sP15
| ~ sP8
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP13
| sP18
| ~ sP15 ),
inference(mating_rule,[status(thm)],]) ).
thf(41,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h9,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[35,36,37,38,39,40,h8,h14,h9,h15,h16]) ).
thf(42,plain,
( sP5
| ~ sP8
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP19
| sP2
| ~ sP5 ),
inference(mating_rule,[status(thm)],]) ).
thf(44,plain,
( sP10
| sP12
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP8
| sP2
| ~ sP10 ),
inference(mating_rule,[status(thm)],]) ).
thf(46,plain,
( sP16
| sP12
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP6
| sP13
| ~ sP16 ),
inference(mating_rule,[status(thm)],]) ).
thf(48,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h17,h18,h14,h9,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[42,43,44,45,46,47,h11,h9,h17,h18]) ).
thf(49,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h9,h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,41,48,h15,h16,h17,h18]) ).
thf(50,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h11,h8,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,34,49,h13,h7,h14,h9]) ).
thf(51,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h13,h7,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).
thf(52,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h13,h7,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).
thf(53,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h13,h7,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,51,52,h15,h16,h17,h18]) ).
thf(54,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h15,h16,h14,h9,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).
thf(55,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h17,h18,h14,h9,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).
thf(56,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h9,h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h16]),tab_bq(discharge,[h17,h18])],[h2,54,55,h15,h16,h17,h18]) ).
thf(57,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h12,h10,h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h7]),tab_bq(discharge,[h14,h9])],[h4,53,56,h13,h7,h14,h9]) ).
thf(58,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h9,h10,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h11,h8]),tab_bq(discharge,[h12,h10])],[h6,50,57,h11,h8,h12,h10]) ).
thf(59,plain,
$false,
inference(tab_be,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h7,h8]),tab_be(discharge,[h9,h10])],[h5,31,58,h7,h8,h9,h10]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,59,h5,h6]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,60,h3,h4]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,61,h1,h2]) ).
thf(0,theorem,
( ~ ( ~ ( ( sP12 != sP4 )
=> ( sP6 != sP4 ) )
=> ( sP18 != sP12 ) )
=> ( sP2 != sP13 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[62,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO041^2 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 04:20:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % Mode: mode213
% 0.12/0.38 % Inferences: 123
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------