TSTP Solution File: SET621+3 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n014.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 : Wed Aug 31 18:21:38 EDT 2022
% Result : Theorem 1.32s 0.53s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 130 ( 14 unt; 0 def)
% Number of atoms : 327 ( 23 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 345 ( 148 ~; 152 |; 23 &)
% ( 20 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 84 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f374,plain,
$false,
inference(avatar_sat_refutation,[],[f92,f123,f148,f161,f217,f219,f236,f239,f259,f260,f261,f285,f290,f311,f320,f324,f328,f333,f334,f337,f344,f345,f348,f350,f353,f354,f359,f370,f373]) ).
fof(f373,plain,
( spl6_10
| ~ spl6_11
| spl6_15 ),
inference(avatar_split_clause,[],[f371,f189,f145,f141]) ).
fof(f141,plain,
( spl6_10
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f145,plain,
( spl6_11
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f189,plain,
( spl6_15
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f371,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| spl6_15 ),
inference(resolution,[],[f190,f59]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) )
& ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X1,X0,X2] :
( ( ( ~ member(X1,X0)
& member(X1,X2) )
| ~ member(X1,difference(X2,X0)) )
& ( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X1,X0,X2] :
( ( ( ~ member(X1,X0)
& member(X1,X2) )
| ~ member(X1,difference(X2,X0)) )
& ( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X2] :
( ( ~ member(X1,X0)
& member(X1,X2) )
<=> member(X1,difference(X2,X0)) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X0] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f190,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
| spl6_15 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f370,plain,
( ~ spl6_10
| spl6_14 ),
inference(avatar_split_clause,[],[f367,f182,f141]) ).
fof(f182,plain,
( spl6_14
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f367,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| spl6_14 ),
inference(resolution,[],[f183,f49]) ).
fof(f49,plain,
! [X2,X0,X1] :
( member(X1,union(X2,X0))
| ~ member(X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( member(X1,union(X2,X0))
| ( ~ member(X1,X0)
& ~ member(X1,X2) ) )
& ( member(X1,X0)
| member(X1,X2)
| ~ member(X1,union(X2,X0)) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X1,union(X2,X0))
| ( ~ member(X1,X0)
& ~ member(X1,X2) ) )
& ( member(X1,X0)
| member(X1,X2)
| ~ member(X1,union(X2,X0)) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( member(X1,union(X2,X0))
<=> ( member(X1,X0)
| member(X1,X2) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X0] :
( ( member(X2,X1)
| member(X2,X0) )
<=> member(X2,union(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f183,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
| spl6_14 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f359,plain,
( ~ spl6_15
| spl6_8 ),
inference(avatar_split_clause,[],[f356,f127,f189]) ).
fof(f127,plain,
( spl6_8
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f356,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
| spl6_8 ),
inference(resolution,[],[f129,f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( member(X1,union(X2,X0))
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f129,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
| spl6_8 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f354,plain,
( ~ spl6_14
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f352,f155,f182]) ).
fof(f155,plain,
( spl6_13
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f352,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
| ~ spl6_13 ),
inference(resolution,[],[f157,f61]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f157,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
| ~ spl6_13 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f353,plain,
( spl6_11
| ~ spl6_13 ),
inference(avatar_split_clause,[],[f351,f155,f145]) ).
fof(f351,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| ~ spl6_13 ),
inference(resolution,[],[f157,f60]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f350,plain,
( spl6_12
| spl6_13
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f349,f85,f155,f151]) ).
fof(f151,plain,
( spl6_12
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f85,plain,
( spl6_1
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f349,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
| member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
| ~ spl6_1 ),
inference(resolution,[],[f86,f48]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ member(X1,union(X2,X0))
| member(X1,X0)
| member(X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f86,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f348,plain,
( ~ spl6_8
| spl6_9
| spl6_2 ),
inference(avatar_split_clause,[],[f346,f89,f131,f127]) ).
fof(f131,plain,
( spl6_9
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f89,plain,
( spl6_2
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f346,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
| ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
| spl6_2 ),
inference(resolution,[],[f91,f59]) ).
fof(f91,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
| spl6_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f345,plain,
( spl6_10
| ~ spl6_16 ),
inference(avatar_split_clause,[],[f338,f193,f141]) ).
fof(f193,plain,
( spl6_16
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f338,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| ~ spl6_16 ),
inference(resolution,[],[f195,f60]) ).
fof(f195,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3))
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f344,plain,
( spl6_9
| spl6_11
| ~ spl6_18 ),
inference(avatar_split_clause,[],[f343,f294,f145,f131]) ).
fof(f294,plain,
( spl6_18
<=> member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f343,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
| ~ spl6_18 ),
inference(resolution,[],[f296,f48]) ).
fof(f296,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
| ~ spl6_18 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f337,plain,
( spl6_18
| ~ spl6_10
| spl6_12 ),
inference(avatar_split_clause,[],[f335,f151,f141,f294]) ).
fof(f335,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
| spl6_12 ),
inference(resolution,[],[f152,f59]) ).
fof(f152,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
| spl6_12 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f334,plain,
( ~ spl6_13
| spl6_1 ),
inference(avatar_split_clause,[],[f331,f85,f155]) ).
fof(f331,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
| spl6_1 ),
inference(resolution,[],[f87,f50]) ).
fof(f87,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
| spl6_1 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f333,plain,
( ~ spl6_12
| spl6_1 ),
inference(avatar_split_clause,[],[f330,f85,f151]) ).
fof(f330,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
| spl6_1 ),
inference(resolution,[],[f87,f49]) ).
fof(f328,plain,
( spl6_8
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f326,f89,f127]) ).
fof(f326,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
| ~ spl6_2 ),
inference(resolution,[],[f90,f60]) ).
fof(f90,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f324,plain,
( ~ spl6_11
| spl6_18 ),
inference(avatar_split_clause,[],[f321,f294,f145]) ).
fof(f321,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| spl6_18 ),
inference(resolution,[],[f295,f49]) ).
fof(f295,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
| spl6_18 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f320,plain,
( ~ spl6_18
| ~ spl6_12 ),
inference(avatar_split_clause,[],[f319,f151,f294]) ).
fof(f319,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
| ~ spl6_12 ),
inference(resolution,[],[f153,f61]) ).
fof(f153,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,union(sK3,sK2)))
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f311,plain,
( ~ spl6_9
| spl6_14 ),
inference(avatar_split_clause,[],[f308,f182,f131]) ).
fof(f308,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
| spl6_14 ),
inference(resolution,[],[f183,f50]) ).
fof(f290,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(avatar_split_clause,[],[f288,f151,f131]) ).
fof(f288,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
| ~ spl6_12 ),
inference(resolution,[],[f267,f50]) ).
fof(f267,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK3,sK2))
| ~ spl6_12 ),
inference(resolution,[],[f153,f61]) ).
fof(f285,plain,
( ~ spl6_11
| ~ spl6_16 ),
inference(avatar_split_clause,[],[f284,f193,f145]) ).
fof(f284,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| ~ spl6_16 ),
inference(resolution,[],[f195,f61]) ).
fof(f261,plain,
( spl6_15
| spl6_16
| ~ spl6_8 ),
inference(avatar_split_clause,[],[f241,f127,f193,f189]) ).
fof(f241,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3))
| member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
| ~ spl6_8 ),
inference(resolution,[],[f128,f48]) ).
fof(f128,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,sK3),difference(sK3,sK1)))
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f260,plain,
( ~ spl6_10
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f235,f189,f141]) ).
fof(f235,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| ~ spl6_15 ),
inference(resolution,[],[f191,f61]) ).
fof(f191,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,sK1))
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f259,plain,
( spl6_9
| spl6_10
| ~ spl6_14 ),
inference(avatar_split_clause,[],[f258,f182,f141,f131]) ).
fof(f258,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
| ~ spl6_14 ),
inference(resolution,[],[f184,f48]) ).
fof(f184,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f239,plain,
( ~ spl6_11
| spl6_14
| spl6_13 ),
inference(avatar_split_clause,[],[f237,f155,f182,f145]) ).
fof(f237,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(sK1,sK2))
| ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| spl6_13 ),
inference(resolution,[],[f156,f59]) ).
fof(f156,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK3,union(sK1,sK2)))
| spl6_13 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f236,plain,
( spl6_11
| ~ spl6_15 ),
inference(avatar_split_clause,[],[f234,f189,f145]) ).
fof(f234,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| ~ spl6_15 ),
inference(resolution,[],[f191,f60]) ).
fof(f219,plain,
~ spl6_7,
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f218,plain,
( $false
| ~ spl6_7 ),
inference(resolution,[],[f122,f72]) ).
fof(f72,plain,
~ sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),
inference(equality_proxy_replacement,[],[f64,f70]) ).
fof(f70,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).
fof(f64,plain,
difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))),
inference(definition_unfolding,[],[f47,f51]) ).
fof(f51,plain,
! [X0,X1] : symmetric_difference(X1,X0) = union(difference(X1,X0),difference(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] : symmetric_difference(X1,X0) = union(difference(X1,X0),difference(X0,X1)),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f47,plain,
difference(symmetric_difference(sK1,sK3),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
difference(symmetric_difference(sK1,sK3),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f27,f28]) ).
fof(f28,plain,
( ? [X0,X1,X2] : union(difference(X0,union(X2,X1)),difference(X2,union(X0,X1))) != difference(symmetric_difference(X0,X2),X1)
=> difference(symmetric_difference(sK1,sK3),sK2) != union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1,X2] : union(difference(X0,union(X2,X1)),difference(X2,union(X0,X1))) != difference(symmetric_difference(X0,X2),X1),
inference(rectify,[],[f20]) ).
fof(f20,plain,
? [X1,X0,X2] : difference(symmetric_difference(X1,X2),X0) != union(difference(X1,union(X2,X0)),difference(X2,union(X1,X0))),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X0,X1,X2] : difference(symmetric_difference(X1,X2),X0) = union(difference(X1,union(X2,X0)),difference(X2,union(X1,X0))),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X2,X0,X1] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X2,X0,X1] : difference(symmetric_difference(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th97) ).
fof(f122,plain,
( sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f120,plain,
( spl6_7
<=> sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f217,plain,
( spl6_10
| ~ spl6_12 ),
inference(avatar_split_clause,[],[f215,f151,f141]) ).
fof(f215,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| ~ spl6_12 ),
inference(resolution,[],[f153,f60]) ).
fof(f161,plain,
( ~ spl6_9
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f160,f89,f131]) ).
fof(f160,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK2)
| ~ spl6_2 ),
inference(resolution,[],[f90,f61]) ).
fof(f148,plain,
( ~ spl6_10
| spl6_11
| spl6_8 ),
inference(avatar_split_clause,[],[f138,f127,f145,f141]) ).
fof(f138,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK3)
| ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),sK1)
| spl6_8 ),
inference(resolution,[],[f135,f59]) ).
fof(f135,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(sK1,sK3))
| spl6_8 ),
inference(resolution,[],[f129,f49]) ).
fof(f123,plain,
( spl6_7
| spl6_2
| spl6_1 ),
inference(avatar_split_clause,[],[f115,f85,f89,f120]) ).
fof(f115,plain,
( member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
| sQ5_eqProxy(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2))))
| spl6_1 ),
inference(resolution,[],[f87,f75]) ).
fof(f75,plain,
! [X0,X1] :
( member(sK4(X0,X1),X1)
| sQ5_eqProxy(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f55,f70]) ).
fof(f55,plain,
! [X0,X1] :
( X0 = X1
| member(sK4(X0,X1),X0)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1) )
& ( member(sK4(X0,X1),X0)
| member(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f34,f35]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) )
=> ( ( ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1) )
& ( member(sK4(X0,X1),X0)
| member(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) ) )
& ( ! [X3] :
( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| X0 != X1 ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X1,X0] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f92,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f83,f89,f85]) ).
fof(f83,plain,
( ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2))
| ~ member(sK4(difference(union(difference(sK1,sK3),difference(sK3,sK1)),sK2),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))),union(difference(sK1,union(sK3,sK2)),difference(sK3,union(sK1,sK2)))) ),
inference(resolution,[],[f72,f74]) ).
fof(f74,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
| ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1) ),
inference(equality_proxy_replacement,[],[f56,f70]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK4(X0,X1),X0)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n014.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 : Tue Aug 30 14:05:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.47 % (32206)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.49 % (32206)Instruction limit reached!
% 0.21/0.49 % (32206)------------------------------
% 0.21/0.49 % (32206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (32198)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.49 % (32206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (32206)Termination reason: Unknown
% 0.21/0.49 % (32206)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (32206)Memory used [KB]: 5884
% 0.21/0.49 % (32206)Time elapsed: 0.004 s
% 0.21/0.49 % (32206)Instructions burned: 3 (million)
% 0.21/0.49 % (32206)------------------------------
% 0.21/0.49 % (32206)------------------------------
% 0.21/0.50 % (32215)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.50 % (32195)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (32220)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.21/0.52 % (32203)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.52 % (32212)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.21/0.52 % (32195)Refutation not found, incomplete strategy% (32195)------------------------------
% 0.21/0.52 % (32195)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (32195)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (32195)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52
% 0.21/0.52 % (32195)Memory used [KB]: 5884
% 0.21/0.52 % (32195)Time elapsed: 0.105 s
% 0.21/0.52 % (32195)Instructions burned: 3 (million)
% 0.21/0.52 % (32195)------------------------------
% 0.21/0.52 % (32195)------------------------------
% 0.21/0.52 % (32214)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.53 % (32220)Instruction limit reached!
% 0.21/0.53 % (32220)------------------------------
% 0.21/0.53 % (32220)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (32205)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53 % (32203)Instruction limit reached!
% 0.21/0.53 % (32203)------------------------------
% 0.21/0.53 % (32203)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (32203)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (32203)Termination reason: Unknown
% 0.21/0.53 % (32203)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (32203)Memory used [KB]: 6012
% 0.21/0.53 % (32203)Time elapsed: 0.122 s
% 0.21/0.53 % (32203)Instructions burned: 7 (million)
% 0.21/0.53 % (32198)Instruction limit reached!
% 0.21/0.53 % (32198)------------------------------
% 0.21/0.53 % (32198)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53 % (32198)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (32198)Termination reason: Unknown
% 0.21/0.53 % (32198)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (32198)Memory used [KB]: 6396
% 0.21/0.53 % (32198)Time elapsed: 0.113 s
% 0.21/0.53 % (32198)Instructions burned: 39 (million)
% 0.21/0.53 % (32198)------------------------------
% 0.21/0.53 % (32198)------------------------------
% 0.21/0.53 % (32203)------------------------------
% 0.21/0.53 % (32203)------------------------------
% 0.21/0.53 % (32212)First to succeed.
% 1.32/0.53 % (32212)Refutation found. Thanks to Tanya!
% 1.32/0.53 % SZS status Theorem for theBenchmark
% 1.32/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.32/0.54 % (32212)------------------------------
% 1.32/0.54 % (32212)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.32/0.54 % (32212)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.32/0.54 % (32212)Termination reason: Refutation
% 1.32/0.54
% 1.32/0.54 % (32212)Memory used [KB]: 6012
% 1.32/0.54 % (32212)Time elapsed: 0.120 s
% 1.32/0.54 % (32212)Instructions burned: 8 (million)
% 1.32/0.54 % (32212)------------------------------
% 1.32/0.54 % (32212)------------------------------
% 1.32/0.54 % (32191)Success in time 0.171 s
%------------------------------------------------------------------------------