TSTP Solution File: SET949+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 : Tue Apr 30 15:14:05 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 49
% Syntax : Number of formulae : 166 ( 35 unt; 0 def)
% Number of atoms : 524 ( 83 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 633 ( 275 ~; 266 |; 46 &)
% ( 39 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 35 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 393 ( 360 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f266,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f67,f72,f77,f81,f85,f91,f95,f99,f108,f114,f119,f123,f129,f133,f141,f146,f151,f155,f161,f166,f176,f182,f186,f190,f196,f200,f204,f208,f212,f221,f234,f240,f245,f259]) ).
fof(f259,plain,
( ~ spl11_25
| ~ spl11_34 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| ~ spl11_25
| ~ spl11_34 ),
inference(trivial_inequality_removal,[],[f247]) ).
fof(f247,plain,
( sK1 != sK1
| ~ spl11_25
| ~ spl11_34 ),
inference(superposition,[],[f189,f244]) ).
fof(f244,plain,
( sK1 = unordered_pair(singleton(sK7(sK3,sK2,sK1)),unordered_pair(sK8(sK3,sK2,sK1),sK7(sK3,sK2,sK1)))
| ~ spl11_34 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f242,plain,
( spl11_34
<=> sK1 = unordered_pair(singleton(sK7(sK3,sK2,sK1)),unordered_pair(sK8(sK3,sK2,sK1),sK7(sK3,sK2,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_34])]) ).
fof(f189,plain,
( ! [X0,X1] : sK1 != unordered_pair(singleton(X1),unordered_pair(X0,X1))
| ~ spl11_25 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f188,plain,
( spl11_25
<=> ! [X0,X1] : sK1 != unordered_pair(singleton(X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_25])]) ).
fof(f245,plain,
( spl11_34
| ~ spl11_1
| ~ spl11_31 ),
inference(avatar_split_clause,[],[f223,f219,f60,f242]) ).
fof(f60,plain,
( spl11_1
<=> in(sK1,cartesian_product2(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f219,plain,
( spl11_31
<=> ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK7(X2,X1,X0)),unordered_pair(sK8(X2,X1,X0),sK7(X2,X1,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).
fof(f223,plain,
( sK1 = unordered_pair(singleton(sK7(sK3,sK2,sK1)),unordered_pair(sK8(sK3,sK2,sK1),sK7(sK3,sK2,sK1)))
| ~ spl11_1
| ~ spl11_31 ),
inference(resolution,[],[f220,f62]) ).
fof(f62,plain,
( in(sK1,cartesian_product2(sK2,sK3))
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f220,plain,
( ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK7(X2,X1,X0)),unordered_pair(sK8(X2,X1,X0),sK7(X2,X1,X0))) = X0 )
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f240,plain,
( spl11_33
| ~ spl11_5
| ~ spl11_20 ),
inference(avatar_split_clause,[],[f162,f159,f79,f238]) ).
fof(f238,plain,
( spl11_33
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK4(X0,X1,X2) = unordered_pair(singleton(sK5(X0,X1,X2)),unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)))
| ~ in(X2,sK4(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_33])]) ).
fof(f79,plain,
( spl11_5
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
fof(f159,plain,
( spl11_20
<=> ! [X2,X0,X1] :
( sK4(X0,X1,X2) = unordered_pair(singleton(sK5(X0,X1,X2)),unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)))
| sP0(X0,X1,X2)
| in(sK4(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_20])]) ).
fof(f162,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK4(X0,X1,X2) = unordered_pair(singleton(sK5(X0,X1,X2)),unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)))
| ~ in(X2,sK4(X0,X1,X2)) )
| ~ spl11_5
| ~ spl11_20 ),
inference(resolution,[],[f160,f80]) ).
fof(f80,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f160,plain,
( ! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| sK4(X0,X1,X2) = unordered_pair(singleton(sK5(X0,X1,X2)),unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2))) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f234,plain,
( spl11_32
| ~ spl11_8
| ~ spl11_18 ),
inference(avatar_split_clause,[],[f156,f149,f93,f232]) ).
fof(f232,plain,
( spl11_32
<=> ! [X4,X0,X3,X2,X1] :
( unordered_pair(singleton(X0),unordered_pair(X1,X0)) != sK4(X2,X3,X4)
| sP0(X2,X3,X4)
| ~ in(X1,X2)
| ~ in(X0,X3)
| ~ in(sK4(X2,X3,X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).
fof(f93,plain,
( spl11_8
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
fof(f149,plain,
( spl11_18
<=> ! [X4,X0,X5,X2,X1] :
( sK4(X0,X1,X2) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| sP0(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK4(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
fof(f156,plain,
( ! [X2,X3,X0,X1,X4] :
( unordered_pair(singleton(X0),unordered_pair(X1,X0)) != sK4(X2,X3,X4)
| sP0(X2,X3,X4)
| ~ in(X1,X2)
| ~ in(X0,X3)
| ~ in(sK4(X2,X3,X4),X4) )
| ~ spl11_8
| ~ spl11_18 ),
inference(superposition,[],[f150,f94]) ).
fof(f94,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f150,plain,
( ! [X2,X0,X1,X4,X5] :
( sK4(X0,X1,X2) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| sP0(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK4(X0,X1,X2),X2) )
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f221,plain,
( spl11_31
| ~ spl11_6
| ~ spl11_17 ),
inference(avatar_split_clause,[],[f147,f144,f83,f219]) ).
fof(f83,plain,
( spl11_6
<=> ! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
fof(f144,plain,
( spl11_17
<=> ! [X0,X8,X2,X1] :
( unordered_pair(singleton(sK7(X0,X1,X8)),unordered_pair(sK8(X0,X1,X8),sK7(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
fof(f147,plain,
( ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK7(X2,X1,X0)),unordered_pair(sK8(X2,X1,X0),sK7(X2,X1,X0))) = X0 )
| ~ spl11_6
| ~ spl11_17 ),
inference(resolution,[],[f145,f84]) ).
fof(f84,plain,
( ! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1))
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f145,plain,
( ! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| unordered_pair(singleton(sK7(X0,X1,X8)),unordered_pair(sK8(X0,X1,X8),sK7(X0,X1,X8))) = X8 )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f212,plain,
( spl11_30
| ~ spl11_6
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f142,f139,f83,f210]) ).
fof(f210,plain,
( spl11_30
<=> ! [X0,X3,X2,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_30])]) ).
fof(f139,plain,
( spl11_16
<=> ! [X10,X0,X9,X2,X1] :
( in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
fof(f142,plain,
( ! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) )
| ~ spl11_6
| ~ spl11_16 ),
inference(resolution,[],[f140,f84]) ).
fof(f140,plain,
( ! [X2,X10,X0,X1,X9] :
( ~ sP0(X0,X1,X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),X2) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f208,plain,
( spl11_29
| ~ spl11_5
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f137,f131,f79,f206]) ).
fof(f206,plain,
( spl11_29
<=> ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK4(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_29])]) ).
fof(f131,plain,
( spl11_15
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
fof(f137,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK4(X0,X1,X2)) )
| ~ spl11_5
| ~ spl11_15 ),
inference(resolution,[],[f132,f80]) ).
fof(f132,plain,
( ! [X2,X0,X1] :
( in(sK6(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f204,plain,
( spl11_28
| ~ spl11_5
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f136,f131,f79,f202]) ).
fof(f202,plain,
( spl11_28
<=> ! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_28])]) ).
fof(f136,plain,
( ! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X0,sK6(X0,X1,X2)) )
| ~ spl11_5
| ~ spl11_15 ),
inference(resolution,[],[f132,f80]) ).
fof(f200,plain,
( spl11_27
| ~ spl11_5
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f135,f127,f79,f198]) ).
fof(f198,plain,
( spl11_27
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK4(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_27])]) ).
fof(f127,plain,
( spl11_14
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
fof(f135,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X2,sK4(X0,X1,X2)) )
| ~ spl11_5
| ~ spl11_14 ),
inference(resolution,[],[f128,f80]) ).
fof(f128,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f196,plain,
( spl11_26
| ~ spl11_5
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f134,f127,f79,f194]) ).
fof(f194,plain,
( spl11_26
<=> ! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_26])]) ).
fof(f134,plain,
( ! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X2)
| sP0(X0,X1,X2)
| ~ in(X1,sK5(X0,X1,X2)) )
| ~ spl11_5
| ~ spl11_14 ),
inference(resolution,[],[f128,f80]) ).
fof(f190,plain,
( spl11_25
| ~ spl11_8
| ~ spl11_19 ),
inference(avatar_split_clause,[],[f169,f153,f93,f188]) ).
fof(f153,plain,
( spl11_19
<=> ! [X0,X1] : sK1 != unordered_pair(unordered_pair(X1,X0),singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_19])]) ).
fof(f169,plain,
( ! [X0,X1] : sK1 != unordered_pair(singleton(X1),unordered_pair(X0,X1))
| ~ spl11_8
| ~ spl11_19 ),
inference(superposition,[],[f154,f94]) ).
fof(f154,plain,
( ! [X0,X1] : sK1 != unordered_pair(unordered_pair(X1,X0),singleton(X0))
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f186,plain,
( spl11_24
| ~ spl11_6
| ~ spl11_13 ),
inference(avatar_split_clause,[],[f125,f121,f83,f184]) ).
fof(f184,plain,
( spl11_24
<=> ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK8(X2,X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_24])]) ).
fof(f121,plain,
( spl11_13
<=> ! [X0,X8,X2,X1] :
( in(sK8(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
fof(f125,plain,
( ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK8(X2,X1,X0),X2) )
| ~ spl11_6
| ~ spl11_13 ),
inference(resolution,[],[f122,f84]) ).
fof(f122,plain,
( ! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK8(X0,X1,X8),X0) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f182,plain,
( spl11_23
| ~ spl11_6
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f124,f117,f83,f180]) ).
fof(f180,plain,
( spl11_23
<=> ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK7(X2,X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_23])]) ).
fof(f117,plain,
( spl11_12
<=> ! [X0,X8,X2,X1] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).
fof(f124,plain,
( ! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK7(X2,X1,X0),X1) )
| ~ spl11_6
| ~ spl11_12 ),
inference(resolution,[],[f118,f84]) ).
fof(f118,plain,
( ! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK7(X0,X1,X8),X1) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f176,plain,
( spl11_22
| ~ spl11_8
| ~ spl11_10 ),
inference(avatar_split_clause,[],[f109,f106,f93,f174]) ).
fof(f174,plain,
( spl11_22
<=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_22])]) ).
fof(f106,plain,
( spl11_10
<=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
fof(f109,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ spl11_8
| ~ spl11_10 ),
inference(superposition,[],[f107,f94]) ).
fof(f107,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f166,plain,
( spl11_21
| ~ spl11_2
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f102,f93,f65,f164]) ).
fof(f164,plain,
( spl11_21
<=> ! [X0,X1] : sK1 != unordered_pair(singleton(X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_21])]) ).
fof(f65,plain,
( spl11_2
<=> ! [X4,X3] : sK1 != unordered_pair(unordered_pair(X3,X4),singleton(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f102,plain,
( ! [X0,X1] : sK1 != unordered_pair(singleton(X0),unordered_pair(X0,X1))
| ~ spl11_2
| ~ spl11_8 ),
inference(superposition,[],[f66,f94]) ).
fof(f66,plain,
( ! [X3,X4] : sK1 != unordered_pair(unordered_pair(X3,X4),singleton(X3))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f161,plain,
spl11_20,
inference(avatar_split_clause,[],[f55,f159]) ).
fof(f55,plain,
! [X2,X0,X1] :
( sK4(X0,X1,X2) = unordered_pair(singleton(sK5(X0,X1,X2)),unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)))
| sP0(X0,X1,X2)
| in(sK4(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f54,f30]) ).
fof(f30,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f54,plain,
! [X2,X0,X1] :
( sK4(X0,X1,X2) = unordered_pair(singleton(sK5(X0,X1,X2)),unordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)))
| sP0(X0,X1,X2)
| in(sK4(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f48,f30]) ).
fof(f48,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK4(X0,X1,X2) = unordered_pair(unordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)),singleton(sK5(X0,X1,X2)))
| in(sK4(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f39,f31]) ).
fof(f31,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f39,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| sK4(X0,X1,X2) = ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2))
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK4(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( sK4(X0,X1,X2) = ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2))
& in(sK6(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
& in(sK8(X0,X1,X8),X0)
& in(sK7(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f17,f20,f19,f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK4(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK4(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK4(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK4(X0,X1,X2) = ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2))
& in(sK6(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
& in(sK8(X0,X1,X8),X0)
& in(sK7(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f155,plain,
( spl11_19
| ~ spl11_2
| ~ spl11_8 ),
inference(avatar_split_clause,[],[f101,f93,f65,f153]) ).
fof(f101,plain,
( ! [X0,X1] : sK1 != unordered_pair(unordered_pair(X1,X0),singleton(X0))
| ~ spl11_2
| ~ spl11_8 ),
inference(superposition,[],[f66,f94]) ).
fof(f151,plain,
spl11_18,
inference(avatar_split_clause,[],[f53,f149]) ).
fof(f53,plain,
! [X2,X0,X1,X4,X5] :
( sK4(X0,X1,X2) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
| sP0(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK4(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f47,f30]) ).
fof(f47,plain,
! [X2,X0,X1,X4,X5] :
( sP0(X0,X1,X2)
| sK4(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK4(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f40,f31]) ).
fof(f40,plain,
! [X2,X0,X1,X4,X5] :
( sP0(X0,X1,X2)
| ordered_pair(X4,X5) != sK4(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f146,plain,
spl11_17,
inference(avatar_split_clause,[],[f58,f144]) ).
fof(f58,plain,
! [X2,X0,X1,X8] :
( unordered_pair(singleton(sK7(X0,X1,X8)),unordered_pair(sK8(X0,X1,X8),sK7(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f57,f30]) ).
fof(f57,plain,
! [X2,X0,X1,X8] :
( unordered_pair(singleton(sK7(X0,X1,X8)),unordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f50,f30]) ).
fof(f50,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)),singleton(sK7(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f35,f31]) ).
fof(f35,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f141,plain,
spl11_16,
inference(avatar_split_clause,[],[f56,f139]) ).
fof(f56,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ),
inference(forward_demodulation,[],[f51,f30]) ).
fof(f51,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f36,f31]) ).
fof(f36,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f133,plain,
spl11_15,
inference(avatar_split_clause,[],[f38,f131]) ).
fof(f38,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK6(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f129,plain,
spl11_14,
inference(avatar_split_clause,[],[f37,f127]) ).
fof(f37,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f123,plain,
spl11_13,
inference(avatar_split_clause,[],[f34,f121]) ).
fof(f34,plain,
! [X2,X0,X1,X8] :
( in(sK8(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f119,plain,
spl11_12,
inference(avatar_split_clause,[],[f33,f117]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f114,plain,
spl11_11,
inference(avatar_split_clause,[],[f42,f112]) ).
fof(f112,plain,
( spl11_11
<=> ! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).
fof(f42,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f12]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f108,plain,
( spl11_10
| ~ spl11_8
| ~ spl11_9 ),
inference(avatar_split_clause,[],[f100,f97,f93,f106]) ).
fof(f97,plain,
( spl11_9
<=> ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
fof(f100,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ spl11_8
| ~ spl11_9 ),
inference(forward_demodulation,[],[f98,f94]) ).
fof(f98,plain,
( ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0)))
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
spl11_9,
inference(avatar_split_clause,[],[f46,f97]) ).
fof(f46,plain,
! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(definition_unfolding,[],[f29,f31]) ).
fof(f29,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f95,plain,
spl11_8,
inference(avatar_split_clause,[],[f30,f93]) ).
fof(f91,plain,
( ~ spl11_7
| ~ spl11_1
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f86,f79,f60,f88]) ).
fof(f88,plain,
( spl11_7
<=> in(cartesian_product2(sK2,sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
fof(f86,plain,
( ~ in(cartesian_product2(sK2,sK3),sK1)
| ~ spl11_1
| ~ spl11_5 ),
inference(resolution,[],[f80,f62]) ).
fof(f85,plain,
spl11_6,
inference(avatar_split_clause,[],[f52,f83]) ).
fof(f52,plain,
! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f81,plain,
spl11_5,
inference(avatar_split_clause,[],[f32,f79]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f77,plain,
spl11_4,
inference(avatar_split_clause,[],[f44,f74]) ).
fof(f74,plain,
( spl11_4
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
fof(f44,plain,
empty(sK10),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f6,f25]) ).
fof(f25,plain,
( ? [X0] : empty(X0)
=> empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f6,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f72,plain,
~ spl11_3,
inference(avatar_split_clause,[],[f43,f69]) ).
fof(f69,plain,
( spl11_3
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
fof(f43,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
~ empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f7,f23]) ).
fof(f23,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f67,plain,
spl11_2,
inference(avatar_split_clause,[],[f45,f65]) ).
fof(f45,plain,
! [X3,X4] : sK1 != unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(definition_unfolding,[],[f28,f31]) ).
fof(f28,plain,
! [X3,X4] : ordered_pair(X3,X4) != sK1,
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ! [X3,X4] : ordered_pair(X3,X4) != sK1
& in(sK1,cartesian_product2(sK2,sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f10,f14]) ).
fof(f14,plain,
( ? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) )
=> ( ! [X4,X3] : ordered_pair(X3,X4) != sK1
& in(sK1,cartesian_product2(sK2,sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f63,plain,
spl11_1,
inference(avatar_split_clause,[],[f27,f60]) ).
fof(f27,plain,
in(sK1,cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 01:14:32 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (20499)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (20502)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (20503)WARNING: value z3 for option sas not known
% 0.14/0.38 % (20501)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (20506)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (20504)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (20507)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (20503)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (20508)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 % (20506)First to succeed.
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 % (20506)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (20506)------------------------------
% 0.21/0.39 % (20506)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.39 % (20506)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (20506)Memory used [KB]: 915
% 0.21/0.39 % (20506)Time elapsed: 0.012 s
% 0.21/0.39 % (20506)Instructions burned: 17 (million)
% 0.21/0.39 % (20506)------------------------------
% 0.21/0.39 % (20506)------------------------------
% 0.21/0.39 % (20499)Success in time 0.029 s
%------------------------------------------------------------------------------