TSTP Solution File: COL041-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COL041-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Sun May 5 04:45:37 EDT 2024
% Result : Unsatisfiable 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 53
% Syntax : Number of formulae : 173 ( 10 unt; 0 def)
% Number of atoms : 453 ( 121 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 594 ( 314 ~; 231 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 51 ( 49 usr; 50 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 210 ( 210 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f992,plain,
$false,
inference(avatar_sat_refutation,[],[f8,f12,f16,f20,f33,f37,f53,f57,f70,f74,f133,f137,f220,f240,f259,f263,f267,f271,f314,f330,f334,f338,f382,f395,f399,f403,f407,f411,f415,f419,f423,f493,f680,f684,f688,f692,f801,f806,f810,f850,f855,f860,f864,f868,f872,f964,f968,f972,f976,f987]) ).
fof(f987,plain,
~ spl0_42,
inference(avatar_contradiction_clause,[],[f986]) ).
fof(f986,plain,
( $false
| ~ spl0_42 ),
inference(equality_resolution,[],[f859]) ).
fof(f859,plain,
( ! [X0] : apply(X0,apply(apply(b,f(apply(apply(b,X0),apply(apply(c,b),X0)))),X0)) != apply(m,apply(apply(b,f(apply(apply(b,X0),apply(apply(c,b),X0)))),X0))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f858,plain,
( spl0_42
<=> ! [X0] : apply(X0,apply(apply(b,f(apply(apply(b,X0),apply(apply(c,b),X0)))),X0)) != apply(m,apply(apply(b,f(apply(apply(b,X0),apply(apply(c,b),X0)))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f976,plain,
( spl0_49
| ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f128,f72,f18,f10,f974]) ).
fof(f974,plain,
( spl0_49
<=> ! [X0,X1] : apply(apply(X0,X1),apply(m,c)) = apply(apply(apply(m,apply(m,c)),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f10,plain,
( spl0_2
<=> ! [X0] : apply(m,X0) = apply(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f18,plain,
( spl0_4
<=> ! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f72,plain,
( spl0_10
<=> ! [X0,X1] : apply(apply(X0,X1),apply(c,X0)) = apply(apply(m,apply(c,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f128,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(m,c)) = apply(apply(apply(m,apply(m,c)),X0),X1)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f121,f11]) ).
fof(f11,plain,
( ! [X0] : apply(m,X0) = apply(X0,X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f121,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(c,c)) = apply(apply(apply(m,apply(c,c)),X0),X1)
| ~ spl0_4
| ~ spl0_10 ),
inference(superposition,[],[f19,f73]) ).
fof(f73,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(c,X0)) = apply(apply(m,apply(c,X0)),X1)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f19,plain,
( ! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f972,plain,
( spl0_48
| ~ spl0_3
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f119,f72,f14,f970]) ).
fof(f970,plain,
( spl0_48
<=> ! [X0,X1] : apply(X0,apply(apply(c,b),X1)) = apply(apply(apply(m,apply(c,b)),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f14,plain,
( spl0_3
<=> ! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f119,plain,
( ! [X0,X1] : apply(X0,apply(apply(c,b),X1)) = apply(apply(apply(m,apply(c,b)),X0),X1)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f15,f73]) ).
fof(f15,plain,
( ! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f968,plain,
( spl0_47
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f75,f68,f10,f966]) ).
fof(f966,plain,
( spl0_47
<=> ! [X0] : apply(apply(m,apply(b,X0)),apply(b,X0)) = apply(X0,apply(m,apply(b,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f68,plain,
( spl0_9
<=> ! [X0,X1] : apply(X0,apply(apply(b,X0),X1)) = apply(apply(m,apply(b,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f75,plain,
( ! [X0] : apply(apply(m,apply(b,X0)),apply(b,X0)) = apply(X0,apply(m,apply(b,X0)))
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f69,f11]) ).
fof(f69,plain,
( ! [X0,X1] : apply(X0,apply(apply(b,X0),X1)) = apply(apply(m,apply(b,X0)),X1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f964,plain,
( spl0_46
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f59,f55,f10,f962]) ).
fof(f962,plain,
( spl0_46
<=> ! [X0] : apply(m,apply(apply(m,c),X0)) = apply(apply(c,apply(apply(m,c),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f55,plain,
( spl0_8
<=> ! [X0,X1] : apply(apply(c,X1),X0) = apply(apply(apply(m,c),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f59,plain,
( ! [X0] : apply(m,apply(apply(m,c),X0)) = apply(apply(c,apply(apply(m,c),X0)),X0)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f56,f11]) ).
fof(f56,plain,
( ! [X0,X1] : apply(apply(c,X1),X0) = apply(apply(apply(m,c),X0),X1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f872,plain,
( spl0_45
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f102,f72,f10,f870]) ).
fof(f870,plain,
( spl0_45
<=> ! [X0] : apply(apply(m,apply(c,X0)),X0) = apply(apply(m,X0),apply(c,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f102,plain,
( ! [X0] : apply(apply(m,apply(c,X0)),X0) = apply(apply(m,X0),apply(c,X0))
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f73,f11]) ).
fof(f868,plain,
( spl0_44
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f101,f72,f10,f866]) ).
fof(f866,plain,
( spl0_44
<=> ! [X0] : apply(apply(m,apply(c,m)),X0) = apply(apply(X0,X0),apply(c,m)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f101,plain,
( ! [X0] : apply(apply(m,apply(c,m)),X0) = apply(apply(X0,X0),apply(c,m))
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f73,f11]) ).
fof(f864,plain,
( spl0_43
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f58,f55,f10,f862]) ).
fof(f862,plain,
( spl0_43
<=> ! [X0] : apply(apply(c,X0),apply(m,c)) = apply(apply(m,apply(m,c)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f58,plain,
( ! [X0] : apply(apply(c,X0),apply(m,c)) = apply(apply(m,apply(m,c)),X0)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f56,f11]) ).
fof(f860,plain,
( spl0_42
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f477,f397,f131,f858]) ).
fof(f131,plain,
( spl0_11
<=> ! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f397,plain,
( spl0_25
<=> ! [X2,X0,X1] : apply(X2,apply(apply(X0,f(apply(apply(b,X2),apply(apply(c,X0),X1)))),X1)) != apply(f(apply(apply(b,X2),apply(apply(c,X0),X1))),apply(X2,apply(apply(X0,f(apply(apply(b,X2),apply(apply(c,X0),X1)))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f477,plain,
( ! [X0] : apply(X0,apply(apply(b,f(apply(apply(b,X0),apply(apply(c,b),X0)))),X0)) != apply(m,apply(apply(b,f(apply(apply(b,X0),apply(apply(c,b),X0)))),X0))
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[],[f398,f132]) ).
fof(f132,plain,
( ! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f398,plain,
( ! [X2,X0,X1] : apply(X2,apply(apply(X0,f(apply(apply(b,X2),apply(apply(c,X0),X1)))),X1)) != apply(f(apply(apply(b,X2),apply(apply(c,X0),X1))),apply(X2,apply(apply(X0,f(apply(apply(b,X2),apply(apply(c,X0),X1)))),X1)))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f855,plain,
( spl0_41
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f162,f131,f35,f853]) ).
fof(f853,plain,
( spl0_41
<=> ! [X0,X1] : apply(apply(X0,f(apply(m,apply(apply(b,apply(c,X0)),X1)))),apply(X1,apply(apply(b,apply(c,X0)),X1))) != apply(f(apply(m,apply(apply(b,apply(c,X0)),X1))),apply(apply(X0,f(apply(m,apply(apply(b,apply(c,X0)),X1)))),apply(X1,apply(apply(b,apply(c,X0)),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f35,plain,
( spl0_6
<=> ! [X0,X1] : apply(apply(X0,f(apply(apply(c,X0),X1))),X1) != apply(f(apply(apply(c,X0),X1)),apply(apply(X0,f(apply(apply(c,X0),X1))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f162,plain,
( ! [X0,X1] : apply(apply(X0,f(apply(m,apply(apply(b,apply(c,X0)),X1)))),apply(X1,apply(apply(b,apply(c,X0)),X1))) != apply(f(apply(m,apply(apply(b,apply(c,X0)),X1))),apply(apply(X0,f(apply(m,apply(apply(b,apply(c,X0)),X1)))),apply(X1,apply(apply(b,apply(c,X0)),X1))))
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f36,f132]) ).
fof(f36,plain,
( ! [X0,X1] : apply(apply(X0,f(apply(apply(c,X0),X1))),X1) != apply(f(apply(apply(c,X0),X1)),apply(apply(X0,f(apply(apply(c,X0),X1))),X1))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f850,plain,
( spl0_40
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f160,f131,f31,f848]) ).
fof(f848,plain,
( spl0_40
<=> ! [X0,X1] : apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),f(apply(m,apply(apply(b,apply(b,X0)),X1))))) != apply(f(apply(m,apply(apply(b,apply(b,X0)),X1))),apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),f(apply(m,apply(apply(b,apply(b,X0)),X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f31,plain,
( spl0_5
<=> ! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f160,plain,
( ! [X0,X1] : apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),f(apply(m,apply(apply(b,apply(b,X0)),X1))))) != apply(f(apply(m,apply(apply(b,apply(b,X0)),X1))),apply(X0,apply(apply(X1,apply(apply(b,apply(b,X0)),X1)),f(apply(m,apply(apply(b,apply(b,X0)),X1))))))
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f32,f132]) ).
fof(f32,plain,
( ! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1)))))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f810,plain,
( spl0_39
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f169,f131,f35,f808]) ).
fof(f808,plain,
( spl0_39
<=> ! [X0,X1] : apply(apply(apply(X0,apply(apply(b,c),X0)),f(apply(apply(m,apply(apply(b,c),X0)),X1))),X1) != apply(f(apply(apply(m,apply(apply(b,c),X0)),X1)),apply(apply(apply(X0,apply(apply(b,c),X0)),f(apply(apply(m,apply(apply(b,c),X0)),X1))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f169,plain,
( ! [X0,X1] : apply(apply(apply(X0,apply(apply(b,c),X0)),f(apply(apply(m,apply(apply(b,c),X0)),X1))),X1) != apply(f(apply(apply(m,apply(apply(b,c),X0)),X1)),apply(apply(apply(X0,apply(apply(b,c),X0)),f(apply(apply(m,apply(apply(b,c),X0)),X1))),X1))
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f36,f132]) ).
fof(f806,plain,
( spl0_38
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f156,f131,f31,f804]) ).
fof(f804,plain,
( spl0_38
<=> ! [X0,X1] : apply(apply(X0,apply(apply(b,b),X0)),apply(X1,f(apply(apply(m,apply(apply(b,b),X0)),X1)))) != apply(f(apply(apply(m,apply(apply(b,b),X0)),X1)),apply(apply(X0,apply(apply(b,b),X0)),apply(X1,f(apply(apply(m,apply(apply(b,b),X0)),X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f156,plain,
( ! [X0,X1] : apply(apply(X0,apply(apply(b,b),X0)),apply(X1,f(apply(apply(m,apply(apply(b,b),X0)),X1)))) != apply(f(apply(apply(m,apply(apply(b,b),X0)),X1)),apply(apply(X0,apply(apply(b,b),X0)),apply(X1,f(apply(apply(m,apply(apply(b,b),X0)),X1)))))
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f32,f132]) ).
fof(f801,plain,
( spl0_37
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f86,f68,f35,f799]) ).
fof(f799,plain,
( spl0_37
<=> ! [X0,X1] : apply(apply(X0,f(apply(apply(m,apply(b,apply(c,X0))),X1))),apply(apply(b,apply(c,X0)),X1)) != apply(f(apply(apply(m,apply(b,apply(c,X0))),X1)),apply(apply(X0,f(apply(apply(m,apply(b,apply(c,X0))),X1))),apply(apply(b,apply(c,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f86,plain,
( ! [X0,X1] : apply(apply(X0,f(apply(apply(m,apply(b,apply(c,X0))),X1))),apply(apply(b,apply(c,X0)),X1)) != apply(f(apply(apply(m,apply(b,apply(c,X0))),X1)),apply(apply(X0,f(apply(apply(m,apply(b,apply(c,X0))),X1))),apply(apply(b,apply(c,X0)),X1)))
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f36,f69]) ).
fof(f692,plain,
( spl0_36
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f99,f68,f31,f14,f690]) ).
fof(f690,plain,
( spl0_36
<=> ! [X0,X1] : apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(m,apply(b,apply(b,X0))),X1))))) != apply(f(apply(apply(m,apply(b,apply(b,X0))),X1)),apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(m,apply(b,apply(b,X0))),X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f99,plain,
( ! [X0,X1] : apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(m,apply(b,apply(b,X0))),X1))))) != apply(f(apply(apply(m,apply(b,apply(b,X0))),X1)),apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(m,apply(b,apply(b,X0))),X1))))))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f84,f15]) ).
fof(f84,plain,
( ! [X0,X1] : apply(X0,apply(apply(apply(b,apply(b,X0)),X1),f(apply(apply(m,apply(b,apply(b,X0))),X1)))) != apply(f(apply(apply(m,apply(b,apply(b,X0))),X1)),apply(X0,apply(apply(apply(b,apply(b,X0)),X1),f(apply(apply(m,apply(b,apply(b,X0))),X1)))))
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f32,f69]) ).
fof(f688,plain,
( spl0_35
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f97,f68,f31,f686]) ).
fof(f686,plain,
( spl0_35
<=> ! [X0,X1] : apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(b,apply(m,apply(b,X0))),X1))))) != apply(f(apply(apply(b,apply(m,apply(b,X0))),X1)),apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(b,apply(m,apply(b,X0))),X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f97,plain,
( ! [X0,X1] : apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(b,apply(m,apply(b,X0))),X1))))) != apply(f(apply(apply(b,apply(m,apply(b,X0))),X1)),apply(X0,apply(apply(b,X0),apply(X1,f(apply(apply(b,apply(m,apply(b,X0))),X1))))))
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f32,f69]) ).
fof(f684,plain,
( spl0_34
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f95,f68,f35,f682]) ).
fof(f682,plain,
( spl0_34
<=> ! [X0,X1] : apply(apply(X0,apply(apply(b,X0),f(apply(apply(c,apply(m,apply(b,X0))),X1)))),X1) != apply(f(apply(apply(c,apply(m,apply(b,X0))),X1)),apply(apply(X0,apply(apply(b,X0),f(apply(apply(c,apply(m,apply(b,X0))),X1)))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f95,plain,
( ! [X0,X1] : apply(apply(X0,apply(apply(b,X0),f(apply(apply(c,apply(m,apply(b,X0))),X1)))),X1) != apply(f(apply(apply(c,apply(m,apply(b,X0))),X1)),apply(apply(X0,apply(apply(b,X0),f(apply(apply(c,apply(m,apply(b,X0))),X1)))),X1))
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f36,f69]) ).
fof(f680,plain,
( spl0_33
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f94,f68,f31,f678]) ).
fof(f678,plain,
( spl0_33
<=> ! [X0,X1] : apply(X1,apply(X0,apply(apply(b,X0),f(apply(apply(b,X1),apply(m,apply(b,X0))))))) != apply(f(apply(apply(b,X1),apply(m,apply(b,X0)))),apply(X1,apply(X0,apply(apply(b,X0),f(apply(apply(b,X1),apply(m,apply(b,X0)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f94,plain,
( ! [X0,X1] : apply(X1,apply(X0,apply(apply(b,X0),f(apply(apply(b,X1),apply(m,apply(b,X0))))))) != apply(f(apply(apply(b,X1),apply(m,apply(b,X0)))),apply(X1,apply(X0,apply(apply(b,X0),f(apply(apply(b,X1),apply(m,apply(b,X0))))))))
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f32,f69]) ).
fof(f493,plain,
( ~ spl0_32
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f224,f218,f72,f490]) ).
fof(f490,plain,
( spl0_32
<=> apply(apply(m,apply(c,m)),apply(b,f(apply(apply(c,b),apply(c,m))))) = apply(apply(b,f(apply(apply(c,b),apply(c,m)))),apply(c,m)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f218,plain,
( spl0_13
<=> ! [X0] : apply(apply(b,f(apply(apply(c,b),X0))),X0) != apply(apply(m,apply(b,f(apply(apply(c,b),X0)))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f224,plain,
( apply(apply(m,apply(c,m)),apply(b,f(apply(apply(c,b),apply(c,m))))) != apply(apply(b,f(apply(apply(c,b),apply(c,m)))),apply(c,m))
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f219,f73]) ).
fof(f219,plain,
( ! [X0] : apply(apply(b,f(apply(apply(c,b),X0))),X0) != apply(apply(m,apply(b,f(apply(apply(c,b),X0)))),X0)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f423,plain,
( spl0_31
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f65,f55,f31,f421]) ).
fof(f421,plain,
( spl0_31
<=> ! [X0,X1] : apply(apply(c,apply(X1,f(apply(apply(b,apply(apply(m,c),X0)),X1)))),X0) != apply(f(apply(apply(b,apply(apply(m,c),X0)),X1)),apply(apply(c,apply(X1,f(apply(apply(b,apply(apply(m,c),X0)),X1)))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f65,plain,
( ! [X0,X1] : apply(apply(c,apply(X1,f(apply(apply(b,apply(apply(m,c),X0)),X1)))),X0) != apply(f(apply(apply(b,apply(apply(m,c),X0)),X1)),apply(apply(c,apply(X1,f(apply(apply(b,apply(apply(m,c),X0)),X1)))),X0))
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f32,f56]) ).
fof(f419,plain,
( spl0_30
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f62,f55,f31,f417]) ).
fof(f417,plain,
( spl0_30
<=> ! [X0,X1] : apply(X1,apply(apply(c,f(apply(apply(b,X1),apply(apply(m,c),X0)))),X0)) != apply(f(apply(apply(b,X1),apply(apply(m,c),X0))),apply(X1,apply(apply(c,f(apply(apply(b,X1),apply(apply(m,c),X0)))),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f62,plain,
( ! [X0,X1] : apply(X1,apply(apply(c,f(apply(apply(b,X1),apply(apply(m,c),X0)))),X0)) != apply(f(apply(apply(b,X1),apply(apply(m,c),X0))),apply(X1,apply(apply(c,f(apply(apply(b,X1),apply(apply(m,c),X0)))),X0)))
| ~ spl0_5
| ~ spl0_8 ),
inference(superposition,[],[f32,f56]) ).
fof(f415,plain,
( spl0_29
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f46,f35,f18,f413]) ).
fof(f413,plain,
( spl0_29
<=> ! [X2,X0,X1] : apply(apply(apply(X0,f(apply(apply(c,apply(apply(c,X0),X1)),X2))),X1),X2) != apply(f(apply(apply(c,apply(apply(c,X0),X1)),X2)),apply(apply(apply(X0,f(apply(apply(c,apply(apply(c,X0),X1)),X2))),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f46,plain,
( ! [X2,X0,X1] : apply(apply(apply(X0,f(apply(apply(c,apply(apply(c,X0),X1)),X2))),X1),X2) != apply(f(apply(apply(c,apply(apply(c,X0),X1)),X2)),apply(apply(apply(X0,f(apply(apply(c,apply(apply(c,X0),X1)),X2))),X1),X2))
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f36,f19]) ).
fof(f411,plain,
( spl0_28
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f45,f35,f14,f409]) ).
fof(f409,plain,
( spl0_28
<=> ! [X2,X0,X1] : apply(apply(X0,apply(X1,f(apply(apply(c,apply(apply(b,X0),X1)),X2)))),X2) != apply(f(apply(apply(c,apply(apply(b,X0),X1)),X2)),apply(apply(X0,apply(X1,f(apply(apply(c,apply(apply(b,X0),X1)),X2)))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f45,plain,
( ! [X2,X0,X1] : apply(apply(X0,apply(X1,f(apply(apply(c,apply(apply(b,X0),X1)),X2)))),X2) != apply(f(apply(apply(c,apply(apply(b,X0),X1)),X2)),apply(apply(X0,apply(X1,f(apply(apply(c,apply(apply(b,X0),X1)),X2)))),X2))
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f36,f15]) ).
fof(f407,plain,
( spl0_27
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f42,f31,f18,f405]) ).
fof(f405,plain,
( spl0_27
<=> ! [X2,X0,X1] : apply(apply(X0,apply(X2,f(apply(apply(b,apply(apply(c,X0),X1)),X2)))),X1) != apply(f(apply(apply(b,apply(apply(c,X0),X1)),X2)),apply(apply(X0,apply(X2,f(apply(apply(b,apply(apply(c,X0),X1)),X2)))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f42,plain,
( ! [X2,X0,X1] : apply(apply(X0,apply(X2,f(apply(apply(b,apply(apply(c,X0),X1)),X2)))),X1) != apply(f(apply(apply(b,apply(apply(c,X0),X1)),X2)),apply(apply(X0,apply(X2,f(apply(apply(b,apply(apply(c,X0),X1)),X2)))),X1))
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f32,f19]) ).
fof(f403,plain,
( spl0_26
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f41,f31,f14,f401]) ).
fof(f401,plain,
( spl0_26
<=> ! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),X2)),apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f41,plain,
( ! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))) != apply(f(apply(apply(b,apply(apply(b,X0),X1)),X2)),apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f32,f15]) ).
fof(f399,plain,
( spl0_25
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f40,f31,f18,f397]) ).
fof(f40,plain,
( ! [X2,X0,X1] : apply(X2,apply(apply(X0,f(apply(apply(b,X2),apply(apply(c,X0),X1)))),X1)) != apply(f(apply(apply(b,X2),apply(apply(c,X0),X1))),apply(X2,apply(apply(X0,f(apply(apply(b,X2),apply(apply(c,X0),X1)))),X1)))
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f32,f19]) ).
fof(f395,plain,
( spl0_24
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f39,f31,f14,f393]) ).
fof(f393,plain,
( spl0_24
<=> ! [X2,X0,X1] : apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))) != apply(f(apply(apply(b,X2),apply(apply(b,X0),X1))),apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f39,plain,
( ! [X2,X0,X1] : apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))) != apply(f(apply(apply(b,X2),apply(apply(b,X0),X1))),apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))))
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f32,f15]) ).
fof(f382,plain,
( spl0_23
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f66,f55,f35,f18,f380]) ).
fof(f380,plain,
( spl0_23
<=> ! [X0,X1] : apply(apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),X1),X0) != apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),apply(apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f66,plain,
( ! [X0,X1] : apply(apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),X1),X0) != apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),apply(apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),X1),X0))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f63,f19]) ).
fof(f63,plain,
( ! [X0,X1] : apply(apply(apply(c,f(apply(apply(c,apply(apply(m,c),X0)),X1))),X0),X1) != apply(f(apply(apply(c,apply(apply(m,c),X0)),X1)),apply(apply(apply(c,f(apply(apply(c,apply(apply(m,c),X0)),X1))),X0),X1))
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f36,f56]) ).
fof(f338,plain,
( spl0_22
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f208,f135,f31,f18,f336]) ).
fof(f336,plain,
( spl0_22
<=> ! [X0] : apply(apply(b,apply(X0,f(apply(m,apply(apply(c,b),X0))))),X0) != apply(f(apply(m,apply(apply(c,b),X0))),apply(apply(b,apply(X0,f(apply(m,apply(apply(c,b),X0))))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f135,plain,
( spl0_12
<=> ! [X0,X1] : apply(m,apply(apply(c,X0),X1)) = apply(apply(X0,apply(apply(c,X0),X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f208,plain,
( ! [X0] : apply(apply(b,apply(X0,f(apply(m,apply(apply(c,b),X0))))),X0) != apply(f(apply(m,apply(apply(c,b),X0))),apply(apply(b,apply(X0,f(apply(m,apply(apply(c,b),X0))))),X0))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f192,f19]) ).
fof(f192,plain,
( ! [X0] : apply(apply(apply(c,b),X0),apply(X0,f(apply(m,apply(apply(c,b),X0))))) != apply(f(apply(m,apply(apply(c,b),X0))),apply(apply(apply(c,b),X0),apply(X0,f(apply(m,apply(apply(c,b),X0))))))
| ~ spl0_5
| ~ spl0_12 ),
inference(superposition,[],[f32,f136]) ).
fof(f136,plain,
( ! [X0,X1] : apply(m,apply(apply(c,X0),X1)) = apply(apply(X0,apply(apply(c,X0),X1)),X1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f334,plain,
( spl0_21
| ~ spl0_2
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f127,f72,f35,f10,f332]) ).
fof(f332,plain,
( spl0_21
<=> ! [X0] : apply(apply(X0,f(apply(apply(m,apply(m,c)),X0))),apply(m,c)) != apply(f(apply(apply(m,apply(m,c)),X0)),apply(apply(X0,f(apply(apply(m,apply(m,c)),X0))),apply(m,c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f127,plain,
( ! [X0] : apply(apply(X0,f(apply(apply(m,apply(m,c)),X0))),apply(m,c)) != apply(f(apply(apply(m,apply(m,c)),X0)),apply(apply(X0,f(apply(apply(m,apply(m,c)),X0))),apply(m,c)))
| ~ spl0_2
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f120,f11]) ).
fof(f120,plain,
( ! [X0] : apply(apply(X0,f(apply(apply(m,apply(c,c)),X0))),apply(c,c)) != apply(f(apply(apply(m,apply(c,c)),X0)),apply(apply(X0,f(apply(apply(m,apply(c,c)),X0))),apply(c,c)))
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f36,f73]) ).
fof(f330,plain,
( spl0_20
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f118,f72,f31,f328]) ).
fof(f328,plain,
( spl0_20
<=> ! [X0] : apply(X0,apply(apply(c,b),f(apply(apply(m,apply(c,b)),X0)))) != apply(f(apply(apply(m,apply(c,b)),X0)),apply(X0,apply(apply(c,b),f(apply(apply(m,apply(c,b)),X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f118,plain,
( ! [X0] : apply(X0,apply(apply(c,b),f(apply(apply(m,apply(c,b)),X0)))) != apply(f(apply(apply(m,apply(c,b)),X0)),apply(X0,apply(apply(c,b),f(apply(apply(m,apply(c,b)),X0)))))
| ~ spl0_5
| ~ spl0_10 ),
inference(superposition,[],[f32,f73]) ).
fof(f314,plain,
( ~ spl0_19
| ~ spl0_2
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f225,f218,f72,f10,f311]) ).
fof(f311,plain,
( spl0_19
<=> apply(apply(m,apply(b,f(apply(m,apply(c,b))))),apply(c,b)) = apply(apply(m,apply(c,b)),f(apply(m,apply(c,b)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f225,plain,
( apply(apply(m,apply(b,f(apply(m,apply(c,b))))),apply(c,b)) != apply(apply(m,apply(c,b)),f(apply(m,apply(c,b))))
| ~ spl0_2
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f221,f73]) ).
fof(f221,plain,
( apply(apply(b,f(apply(m,apply(c,b)))),apply(c,b)) != apply(apply(m,apply(b,f(apply(m,apply(c,b))))),apply(c,b))
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f219,f11]) ).
fof(f271,plain,
( spl0_18
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f211,f135,f35,f18,f10,f269]) ).
fof(f269,plain,
( spl0_18
<=> ! [X0] : apply(apply(f(apply(m,apply(apply(m,c),X0))),X0),X0) != apply(f(apply(m,apply(apply(m,c),X0))),apply(apply(f(apply(m,apply(apply(m,c),X0))),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f211,plain,
( ! [X0] : apply(apply(f(apply(m,apply(apply(m,c),X0))),X0),X0) != apply(f(apply(m,apply(apply(m,c),X0))),apply(apply(f(apply(m,apply(apply(m,c),X0))),X0),X0))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f210,f11]) ).
fof(f210,plain,
( ! [X0] : apply(apply(f(apply(m,apply(apply(c,c),X0))),X0),X0) != apply(f(apply(m,apply(apply(c,c),X0))),apply(apply(f(apply(m,apply(apply(c,c),X0))),X0),X0))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f209,f19]) ).
fof(f209,plain,
( ! [X0] : apply(apply(apply(c,f(apply(m,apply(apply(c,c),X0)))),X0),X0) != apply(f(apply(m,apply(apply(c,c),X0))),apply(apply(apply(c,f(apply(m,apply(apply(c,c),X0)))),X0),X0))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f194,f19]) ).
fof(f194,plain,
( ! [X0] : apply(apply(apply(apply(c,c),X0),f(apply(m,apply(apply(c,c),X0)))),X0) != apply(f(apply(m,apply(apply(c,c),X0))),apply(apply(apply(apply(c,c),X0),f(apply(m,apply(apply(c,c),X0)))),X0))
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f36,f136]) ).
fof(f267,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f60,f55,f35,f265]) ).
fof(f265,plain,
( spl0_17
<=> ! [X0] : apply(apply(c,X0),f(apply(apply(c,apply(m,c)),X0))) != apply(f(apply(apply(c,apply(m,c)),X0)),apply(apply(c,X0),f(apply(apply(c,apply(m,c)),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f60,plain,
( ! [X0] : apply(apply(c,X0),f(apply(apply(c,apply(m,c)),X0))) != apply(f(apply(apply(c,apply(m,c)),X0)),apply(apply(c,X0),f(apply(apply(c,apply(m,c)),X0))))
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f36,f56]) ).
fof(f263,plain,
( spl0_16
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f48,f35,f18,f261]) ).
fof(f261,plain,
( spl0_16
<=> ! [X0,X1] : apply(apply(X0,X1),f(apply(apply(c,apply(c,X0)),X1))) != apply(f(apply(apply(c,apply(c,X0)),X1)),apply(apply(X0,X1),f(apply(apply(c,apply(c,X0)),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f48,plain,
( ! [X0,X1] : apply(apply(X0,X1),f(apply(apply(c,apply(c,X0)),X1))) != apply(f(apply(apply(c,apply(c,X0)),X1)),apply(apply(X0,X1),f(apply(apply(c,apply(c,X0)),X1))))
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f36,f19]) ).
fof(f259,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f47,f35,f14,f257]) ).
fof(f257,plain,
( spl0_15
<=> ! [X0,X1] : apply(X0,apply(f(apply(apply(c,apply(b,X0)),X1)),X1)) != apply(f(apply(apply(c,apply(b,X0)),X1)),apply(X0,apply(f(apply(apply(c,apply(b,X0)),X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f47,plain,
( ! [X0,X1] : apply(X0,apply(f(apply(apply(c,apply(b,X0)),X1)),X1)) != apply(f(apply(apply(c,apply(b,X0)),X1)),apply(X0,apply(f(apply(apply(c,apply(b,X0)),X1)),X1)))
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f36,f15]) ).
fof(f240,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f38,f31,f10,f238]) ).
fof(f238,plain,
( spl0_14
<=> ! [X0] : apply(X0,apply(apply(b,X0),f(apply(m,apply(b,X0))))) != apply(f(apply(m,apply(b,X0))),apply(X0,apply(apply(b,X0),f(apply(m,apply(b,X0)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f38,plain,
( ! [X0] : apply(X0,apply(apply(b,X0),f(apply(m,apply(b,X0))))) != apply(f(apply(m,apply(b,X0))),apply(X0,apply(apply(b,X0),f(apply(m,apply(b,X0))))))
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f32,f11]) ).
fof(f220,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f92,f68,f35,f218]) ).
fof(f92,plain,
( ! [X0] : apply(apply(b,f(apply(apply(c,b),X0))),X0) != apply(apply(m,apply(b,f(apply(apply(c,b),X0)))),X0)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f36,f69]) ).
fof(f137,plain,
( spl0_12
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f27,f18,f10,f135]) ).
fof(f27,plain,
( ! [X0,X1] : apply(m,apply(apply(c,X0),X1)) = apply(apply(X0,apply(apply(c,X0),X1)),X1)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f19,f11]) ).
fof(f133,plain,
( spl0_11
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f22,f14,f10,f131]) ).
fof(f22,plain,
( ! [X0,X1] : apply(m,apply(apply(b,X0),X1)) = apply(X0,apply(X1,apply(apply(b,X0),X1)))
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f15,f11]) ).
fof(f74,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f26,f18,f10,f72]) ).
fof(f26,plain,
( ! [X0,X1] : apply(apply(X0,X1),apply(c,X0)) = apply(apply(m,apply(c,X0)),X1)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f19,f11]) ).
fof(f70,plain,
( spl0_9
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f21,f14,f10,f68]) ).
fof(f21,plain,
( ! [X0,X1] : apply(X0,apply(apply(b,X0),X1)) = apply(apply(m,apply(b,X0)),X1)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f15,f11]) ).
fof(f57,plain,
( spl0_8
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f25,f18,f10,f55]) ).
fof(f25,plain,
( ! [X0,X1] : apply(apply(c,X1),X0) = apply(apply(apply(m,c),X0),X1)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f19,f11]) ).
fof(f53,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f43,f35,f10,f51]) ).
fof(f51,plain,
( spl0_7
<=> ! [X0] : apply(apply(c,f(apply(apply(m,c),X0))),X0) != apply(f(apply(apply(m,c),X0)),apply(apply(c,f(apply(apply(m,c),X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f43,plain,
( ! [X0] : apply(apply(c,f(apply(apply(m,c),X0))),X0) != apply(f(apply(apply(m,c),X0)),apply(apply(c,f(apply(apply(m,c),X0))),X0))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f36,f11]) ).
fof(f37,plain,
( spl0_6
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f28,f18,f6,f35]) ).
fof(f6,plain,
( spl0_1
<=> ! [X1] : apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f28,plain,
( ! [X0,X1] : apply(apply(X0,f(apply(apply(c,X0),X1))),X1) != apply(f(apply(apply(c,X0),X1)),apply(apply(X0,f(apply(apply(c,X0),X1))),X1))
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f7,f19]) ).
fof(f7,plain,
( ! [X1] : apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f6]) ).
fof(f33,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f23,f14,f6,f31]) ).
fof(f23,plain,
( ! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1)))))
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f7,f15]) ).
fof(f20,plain,
spl0_4,
inference(avatar_split_clause,[],[f3,f18]) ).
fof(f3,axiom,
! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_definition) ).
fof(f16,plain,
spl0_3,
inference(avatar_split_clause,[],[f1,f14]) ).
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f12,plain,
spl0_2,
inference(avatar_split_clause,[],[f2,f10]) ).
fof(f2,axiom,
! [X0] : apply(m,X0) = apply(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).
fof(f8,plain,
spl0_1,
inference(avatar_split_clause,[],[f4,f6]) ).
fof(f4,axiom,
! [X1] : apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL041-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 18:29:53 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (28896)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (28899)WARNING: value z3 for option sas not known
% 0.15/0.37 % (28900)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (28898)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (28897)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (28899)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)
% 0.15/0.37 % (28901)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)
% 0.15/0.37 % (28902)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)
% 0.15/0.37 % (28903)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)
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [4]
% 0.21/0.42 TRYING [5]
% 0.21/0.42 TRYING [5]
% 0.21/0.44 % (28901)First to succeed.
% 0.21/0.44 % (28901)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28896"
% 0.21/0.44 % (28901)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45 % (28901)------------------------------
% 0.21/0.45 % (28901)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.45 % (28901)Termination reason: Refutation
% 0.21/0.45
% 0.21/0.45 % (28901)Memory used [KB]: 2013
% 0.21/0.45 % (28901)Time elapsed: 0.070 s
% 0.21/0.45 % (28901)Instructions burned: 119 (million)
% 0.21/0.45 % (28896)Success in time 0.075 s
%------------------------------------------------------------------------------