TSTP Solution File: SWW678_1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW678_1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Fri Sep 1 01:05:47 EDT 2023
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 58
% Syntax : Number of formulae : 296 ( 13 unt; 17 typ; 0 def)
% Number of atoms : 1327 ( 298 equ)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 1605 ( 557 ~; 781 |; 163 &)
% ( 45 <=>; 57 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 185 ( 110 atm; 0 fun; 0 num; 75 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 11 ( 8 >; 3 *; 0 +; 0 <<)
% Number of predicates : 37 ( 31 usr; 31 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 158 (; 112 !; 46 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Tree': $tType ).
tff(func_def_0,type,
'empty:Tree': 'Tree' ).
tff(func_def_1,type,
'left:(Tree)>Tree': 'Tree' > 'Tree' ).
tff(func_def_2,type,
'val:(Tree)>Int': 'Tree' > $int ).
tff(func_def_3,type,
'node:(Int*Tree*Tree)>Tree': ( $int * 'Tree' * 'Tree' ) > 'Tree' ).
tff(func_def_4,type,
'right:(Tree)>Tree': 'Tree' > 'Tree' ).
tff(func_def_5,type,
sK0: 'Tree' ).
tff(func_def_6,type,
sK1: $int ).
tff(func_def_7,type,
sK2: 'Tree' ).
tff(func_def_8,type,
sK3: 'Tree' ).
tff(func_def_9,type,
sK4: 'Tree' > $int ).
tff(func_def_10,type,
sK5: 'Tree' > $int ).
tff(func_def_11,type,
sF6: 'Tree' ).
tff(func_def_12,type,
sF7: 'Tree' ).
tff(func_def_13,type,
sF8: $int ).
tff(pred_def_1,type,
searchtree: 'Tree' > $o ).
tff(pred_def_2,type,
in: ( $int * 'Tree' ) > $o ).
tff(f695,plain,
$false,
inference(avatar_smt_refutation,[],[f99,f104,f109,f114,f119,f128,f151,f162,f170,f175,f180,f200,f212,f261,f289,f295,f304,f306,f308,f324,f333,f339,f365,f369,f393,f394,f413,f432,f434,f478,f516,f552,f591,f595,f597,f599,f601,f603,f624,f636,f646,f648,f650,f652,f655,f657,f660,f662,f688,f692,f694]) ).
tff(f694,plain,
( spl9_6
| ~ spl9_7
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f693]) ).
tff(f693,plain,
( $false
| spl9_6
| ~ spl9_7
| ~ spl9_8 ),
inference(global_subsumption,[],[f689,f142]) ).
tff(f142,plain,
( ( sK1 = sF8 )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f140]) ).
tff(f140,plain,
( spl9_8
<=> ( sK1 = sF8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
tff(f689,plain,
( ( sK1 != sF8 )
| spl9_6
| ~ spl9_7 ),
inference(global_subsumption,[],[f127,f123,f90]) ).
tff(f90,plain,
( ~ in(sK1,sK0)
| ( sK1 != sF8 )
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f50,f86]) ).
tff(f86,plain,
'val:(Tree)>Int'(sK0) = sF8,
introduced(function_definition,[]) ).
tff(f50,plain,
( ~ in(sK1,sK0)
| ( sK1 != 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
( ( ~ in(sK1,sK0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(sK1,X2)
| ( 'right:(Tree)>Tree'(sK0) != X2 ) )
& ~ $less(sK1,'val:(Tree)>Int'(sK0)) )
| ( ! [X3: 'Tree'] :
( ~ in(sK1,X3)
| ( 'left:(Tree)>Tree'(sK0) != X3 ) )
& $less(sK1,'val:(Tree)>Int'(sK0)) ) )
& ( sK1 != 'val:(Tree)>Int'(sK0) )
& ( 'empty:Tree' != sK0 ) )
| ( 'empty:Tree' = sK0 ) )
& ( in(sK1,sK0)
| ( ( ( ( ( in(sK1,sK2)
& ( 'right:(Tree)>Tree'(sK0) = sK2 ) )
| $less(sK1,'val:(Tree)>Int'(sK0)) )
& ( ( in(sK1,sK3)
& ( 'left:(Tree)>Tree'(sK0) = sK3 ) )
| ~ $less(sK1,'val:(Tree)>Int'(sK0)) ) )
| ( sK1 = 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) )
& ( 'empty:Tree' != sK0 ) ) )
& searchtree(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f33,f32,f31]) ).
tff(f31,plain,
( ? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'right:(Tree)>Tree'(X0) != X2 ) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ~ in(X1,X3)
| ( 'left:(Tree)>Tree'(X0) != X3 ) )
& $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( in(X1,X0)
| ( ( ( ( ? [X4: 'Tree'] :
( in(X1,X4)
& ( 'right:(Tree)>Tree'(X0) = X4 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X5: 'Tree'] :
( in(X1,X5)
& ( 'left:(Tree)>Tree'(X0) = X5 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) ) )
& searchtree(X0) )
=> ( ( ~ in(sK1,sK0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(sK1,X2)
| ( 'right:(Tree)>Tree'(sK0) != X2 ) )
& ~ $less(sK1,'val:(Tree)>Int'(sK0)) )
| ( ! [X3: 'Tree'] :
( ~ in(sK1,X3)
| ( 'left:(Tree)>Tree'(sK0) != X3 ) )
& $less(sK1,'val:(Tree)>Int'(sK0)) ) )
& ( sK1 != 'val:(Tree)>Int'(sK0) )
& ( 'empty:Tree' != sK0 ) )
| ( 'empty:Tree' = sK0 ) )
& ( in(sK1,sK0)
| ( ( ( ( ? [X4: 'Tree'] :
( in(sK1,X4)
& ( 'right:(Tree)>Tree'(sK0) = X4 ) )
| $less(sK1,'val:(Tree)>Int'(sK0)) )
& ( ? [X5: 'Tree'] :
( in(sK1,X5)
& ( 'left:(Tree)>Tree'(sK0) = X5 ) )
| ~ $less(sK1,'val:(Tree)>Int'(sK0)) ) )
| ( sK1 = 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) )
& ( 'empty:Tree' != sK0 ) ) )
& searchtree(sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f32,plain,
( ? [X4: 'Tree'] :
( in(sK1,X4)
& ( 'right:(Tree)>Tree'(sK0) = X4 ) )
=> ( in(sK1,sK2)
& ( 'right:(Tree)>Tree'(sK0) = sK2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f33,plain,
( ? [X5: 'Tree'] :
( in(sK1,X5)
& ( 'left:(Tree)>Tree'(sK0) = X5 ) )
=> ( in(sK1,sK3)
& ( 'left:(Tree)>Tree'(sK0) = sK3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'right:(Tree)>Tree'(X0) != X2 ) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ~ in(X1,X3)
| ( 'left:(Tree)>Tree'(X0) != X3 ) )
& $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( in(X1,X0)
| ( ( ( ( ? [X4: 'Tree'] :
( in(X1,X4)
& ( 'right:(Tree)>Tree'(X0) = X4 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X5: 'Tree'] :
( in(X1,X5)
& ( 'left:(Tree)>Tree'(X0) = X5 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) ) )
& searchtree(X0) ),
inference(rectify,[],[f29]) ).
tff(f29,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'right:(Tree)>Tree'(X0) != X2 ) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ~ in(X1,X3)
| ( 'left:(Tree)>Tree'(X0) != X3 ) )
& $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( in(X1,X0)
| ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) ) )
& searchtree(X0) ),
inference(flattening,[],[f28]) ).
tff(f28,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'right:(Tree)>Tree'(X0) != X2 ) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ~ in(X1,X3)
| ( 'left:(Tree)>Tree'(X0) != X3 ) )
& $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( in(X1,X0)
| ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) ) )
& searchtree(X0) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
? [X0: 'Tree',X1: $int] :
( ( ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
<~> in(X1,X0) )
& searchtree(X0) ),
inference(flattening,[],[f23]) ).
tff(f23,plain,
? [X0: 'Tree',X1: $int] :
( ( ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
<~> in(X1,X0) )
& searchtree(X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,plain,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( ( 'empty:Tree' != X0 )
=> ( ( 'val:(Tree)>Int'(X0) != X1 )
=> ( ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) ) )
& ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) ) ) ) ) )
& ( 'empty:Tree' != X0 ) )
<=> in(X1,X0) ) ),
inference(flattening,[],[f12]) ).
tff(f12,plain,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( ( 'empty:Tree' != X0 )
=> ( ( 'val:(Tree)>Int'(X0) != X1 )
=> ( ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) ) )
& ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) ) ) ) ) )
& ( ~ 'empty:Tree' = X0 ) )
<=> in(X1,X0) ) ),
inference(true_and_false_elimination,[],[f11]) ).
tff(f11,plain,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( ( 'empty:Tree' != X0 )
=> ( ( ( 'val:(Tree)>Int'(X0) != X1 )
=> ( ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) ) )
& ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) ) ) ) )
& ( ( 'val:(Tree)>Int'(X0) = X1 )
=> $true ) ) )
& ( ( 'empty:Tree' = X0 )
=> $false ) )
<=> in(X1,X0) ) ),
inference(rectify,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X5: 'Tree',X4: $int] :
( searchtree(X5)
=> ( ( ( ( 'empty:Tree' != X5 )
=> ( ( ( 'val:(Tree)>Int'(X5) != X4 )
=> ( ( ~ $less(X4,'val:(Tree)>Int'(X5))
=> ? [X7: 'Tree'] :
( in(X4,X7)
& ( 'right:(Tree)>Tree'(X5) = X7 ) ) )
& ( $less(X4,'val:(Tree)>Int'(X5))
=> ? [X6: 'Tree'] :
( in(X4,X6)
& ( 'left:(Tree)>Tree'(X5) = X6 ) ) ) ) )
& ( ( 'val:(Tree)>Int'(X5) = X4 )
=> $true ) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) )
<=> in(X4,X5) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X5: 'Tree',X4: $int] :
( searchtree(X5)
=> ( ( ( ( 'empty:Tree' != X5 )
=> ( ( ( 'val:(Tree)>Int'(X5) != X4 )
=> ( ( ~ $less(X4,'val:(Tree)>Int'(X5))
=> ? [X7: 'Tree'] :
( in(X4,X7)
& ( 'right:(Tree)>Tree'(X5) = X7 ) ) )
& ( $less(X4,'val:(Tree)>Int'(X5))
=> ? [X6: 'Tree'] :
( in(X4,X6)
& ( 'left:(Tree)>Tree'(X5) = X6 ) ) ) ) )
& ( ( 'val:(Tree)>Int'(X5) = X4 )
=> $true ) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) )
<=> in(X4,X5) ) ),
file('/export/starexec/sandbox/tmp/tmp.en3yXdOSM5/Vampire---4.8_9125',formula_007) ).
tff(f123,plain,
( ( 'empty:Tree' != sK0 )
| spl9_6 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f121,plain,
( spl9_6
<=> ( 'empty:Tree' = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
tff(f127,plain,
( in(sK1,sK0)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f125,plain,
( spl9_7
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
tff(f692,plain,
( ~ spl9_5
| spl9_6
| ~ spl9_7
| ~ spl9_17 ),
inference(avatar_contradiction_clause,[],[f691]) ).
tff(f691,plain,
( $false
| ~ spl9_5
| spl9_6
| ~ spl9_7
| ~ spl9_17 ),
inference(global_subsumption,[],[f689,f690]) ).
tff(f690,plain,
( ( sK1 = sF8 )
| ~ spl9_5
| ~ spl9_17 ),
inference(backward_demodulation,[],[f118,f287]) ).
tff(f287,plain,
( ( sK1 = 'val:(Tree)>Int'(sK0) )
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f286]) ).
tff(f286,plain,
( spl9_17
<=> ( sK1 = 'val:(Tree)>Int'(sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
tff(f118,plain,
( ( 'val:(Tree)>Int'(sK0) = sF8 )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f116,plain,
( spl9_5
<=> ( 'val:(Tree)>Int'(sK0) = sF8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
tff(f688,plain,
( ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_22
| ~ spl9_28 ),
inference(avatar_contradiction_clause,[],[f687]) ).
tff(f687,plain,
( $false
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_22
| ~ spl9_28 ),
inference(global_subsumption,[],[f391,f686]) ).
tff(f686,plain,
( ~ in(sK1,sF7)
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_28 ),
inference(resolution,[],[f437,f590]) ).
tff(f590,plain,
( $less(sF8,sK1)
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f588]) ).
tff(f588,plain,
( spl9_28
<=> $less(sF8,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
tff(f437,plain,
( ! [X0: $int] :
( ~ $less(sF8,X0)
| ~ in(X0,sF7) )
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f372]) ).
tff(f372,plain,
( ! [X0: $int] :
( ~ $less(sF8,X0)
| ~ in(X0,sF7) )
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f43,f123,f236]) ).
tff(f236,plain,
( ! [X0: $int] :
( ~ in(X0,sF7)
| ~ $less(sF8,X0)
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0) )
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_demodulation,[],[f234,f113]) ).
tff(f113,plain,
( ( 'left:(Tree)>Tree'(sK0) = sF7 )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f111]) ).
tff(f111,plain,
( spl9_4
<=> ( 'left:(Tree)>Tree'(sK0) = sF7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
tff(f234,plain,
( ! [X0: $int] :
( ~ $less(sF8,X0)
| ~ in(X0,'left:(Tree)>Tree'(sK0))
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0) )
| ~ spl9_5 ),
inference(superposition,[],[f58,f118]) ).
tff(f58,plain,
! [X0: 'Tree',X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ( ( ( ~ $less('val:(Tree)>Int'(X0),sK4(X0))
& in(sK4(X0),'right:(Tree)>Tree'(X0)) )
| ( $less('val:(Tree)>Int'(X0),sK5(X0))
& in(sK5(X0),'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X3: $int] :
( $less('val:(Tree)>Int'(X0),X3)
| ~ in(X3,'right:(Tree)>Tree'(X0)) )
& ! [X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f37,f39,f38]) ).
tff(f38,plain,
! [X0: 'Tree'] :
( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
=> ( ~ $less('val:(Tree)>Int'(X0),sK4(X0))
& in(sK4(X0),'right:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f39,plain,
! [X0: 'Tree'] :
( ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
=> ( $less('val:(Tree)>Int'(X0),sK5(X0))
& in(sK5(X0),'left:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f37,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ( ( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X3: $int] :
( $less('val:(Tree)>Int'(X0),X3)
| ~ in(X3,'right:(Tree)>Tree'(X0)) )
& ! [X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ) ),
inference(rectify,[],[f36]) ).
tff(f36,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ( ( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ) ),
inference(flattening,[],[f35]) ).
tff(f35,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ( ( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 ) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( 'empty:Tree' != X0 )
=> ( ! [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X1) )
& ! [X2: $int] :
( in(X2,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X2) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) ) ) ),
inference(true_and_false_elimination,[],[f14]) ).
tff(f14,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ( 'empty:Tree' != X0 )
=> ( ! [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X1) )
& ! [X2: $int] :
( in(X2,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X2) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) ) )
& ( ( 'empty:Tree' = X0 )
=> $true ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,plain,
! [X5: 'Tree'] :
( searchtree(X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( ! [X4: $int] :
( in(X4,'right:(Tree)>Tree'(X5))
=> $less('val:(Tree)>Int'(X5),X4) )
& ! [X4: $int] :
( in(X4,'left:(Tree)>Tree'(X5))
=> ~ $less('val:(Tree)>Int'(X5),X4) )
& searchtree('right:(Tree)>Tree'(X5))
& searchtree('left:(Tree)>Tree'(X5)) ) )
& ( ( 'empty:Tree' = X5 )
=> $true ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,axiom,
! [X5: 'Tree'] :
( searchtree(X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( ! [X4: $int] :
( in(X4,'right:(Tree)>Tree'(X5))
=> $greater(X4,'val:(Tree)>Int'(X5)) )
& ! [X4: $int] :
( in(X4,'left:(Tree)>Tree'(X5))
=> $lesseq(X4,'val:(Tree)>Int'(X5)) )
& searchtree('right:(Tree)>Tree'(X5))
& searchtree('left:(Tree)>Tree'(X5)) ) )
& ( ( 'empty:Tree' = X5 )
=> $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.en3yXdOSM5/Vampire---4.8_9125',formula_006) ).
tff(f43,plain,
searchtree(sK0),
inference(cnf_transformation,[],[f34]) ).
tff(f391,plain,
( in(sK1,sF7)
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f390]) ).
tff(f390,plain,
( spl9_22
<=> in(sK1,sF7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
tff(f662,plain,
( spl9_6
| ~ spl9_7
| spl9_9
| spl9_19
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f661]) ).
tff(f661,plain,
( $false
| spl9_6
| ~ spl9_7
| spl9_9
| spl9_19
| ~ spl9_27 ),
inference(global_subsumption,[],[f127,f123,f145,f87,f551]) ).
tff(f551,plain,
( in(sK1,sF6)
| ~ spl9_27 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f549,plain,
( spl9_27
<=> in(sK1,sF6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
tff(f87,plain,
( ~ in(sK1,sK0)
| ~ in(sK1,sF6)
| $less(sK1,sF8)
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f77,f86,f83]) ).
tff(f83,plain,
'right:(Tree)>Tree'(sK0) = sF6,
introduced(function_definition,[]) ).
tff(f77,plain,
( ~ in(sK1,sK0)
| ~ in(sK1,'right:(Tree)>Tree'(sK0))
| $less(sK1,'val:(Tree)>Int'(sK0))
| ( 'empty:Tree' = sK0 ) ),
inference(equality_resolution,[],[f53]) ).
tff(f53,plain,
! [X2: 'Tree'] :
( ~ in(sK1,sK0)
| ~ in(sK1,X2)
| ( 'right:(Tree)>Tree'(sK0) != X2 )
| $less(sK1,'val:(Tree)>Int'(sK0))
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f145,plain,
( ~ $less(sK1,sF8)
| spl9_9 ),
inference(avatar_component_clause,[],[f144]) ).
tff(f144,plain,
( spl9_9
<=> $less(sK1,sF8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
tff(f660,plain,
( spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| spl9_22
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f659]) ).
tff(f659,plain,
( $false
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| spl9_22
| ~ spl9_27 ),
inference(global_subsumption,[],[f127,f123,f145,f87,f551]) ).
tff(f657,plain,
( spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f656]) ).
tff(f656,plain,
( $false
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_27 ),
inference(global_subsumption,[],[f127,f123,f145,f87,f551]) ).
tff(f655,plain,
( spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f654]) ).
tff(f654,plain,
( $false
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| ~ spl9_27 ),
inference(global_subsumption,[],[f127,f123,f551,f145,f87]) ).
tff(f652,plain,
( spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f651]) ).
tff(f651,plain,
( $false
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_27 ),
inference(global_subsumption,[],[f127,f123,f551,f145,f87]) ).
tff(f650,plain,
( ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| ~ spl9_27 ),
inference(avatar_contradiction_clause,[],[f649]) ).
tff(f649,plain,
( $false
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| ~ spl9_27 ),
inference(global_subsumption,[],[f87,f127,f123,f551,f145]) ).
tff(f648,plain,
( ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| ~ spl9_27
| ~ spl9_28 ),
inference(avatar_contradiction_clause,[],[f647]) ).
tff(f647,plain,
( $false
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| spl9_9
| ~ spl9_11
| ~ spl9_27
| ~ spl9_28 ),
inference(global_subsumption,[],[f87,f127,f123,f551,f145]) ).
tff(f646,plain,
( ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_11
| ~ spl9_19
| ~ spl9_28 ),
inference(avatar_contradiction_clause,[],[f645]) ).
tff(f645,plain,
( $false
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_11
| ~ spl9_19
| ~ spl9_28 ),
inference(global_subsumption,[],[f332,f644]) ).
tff(f644,plain,
( ~ in(sK1,sK3)
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_11
| ~ spl9_28 ),
inference(resolution,[],[f607,f590]) ).
tff(f607,plain,
( ! [X0: $int] :
( ~ $less(sF8,X0)
| ~ in(X0,sK3) )
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_11 ),
inference(backward_demodulation,[],[f437,f161]) ).
tff(f161,plain,
( ( sK3 = sF7 )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f159]) ).
tff(f159,plain,
( spl9_11
<=> ( sK3 = sF7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
tff(f332,plain,
( in(sK1,sK3)
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f330]) ).
tff(f330,plain,
( spl9_19
<=> in(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
tff(f636,plain,
( spl9_29
| ~ spl9_11
| ~ spl9_23 ),
inference(avatar_split_clause,[],[f606,f410,f159,f633]) ).
tff(f633,plain,
( spl9_29
<=> ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sK3,sF6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
tff(f410,plain,
( spl9_23
<=> ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
tff(f606,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sK3,sF6) )
| ~ spl9_11
| ~ spl9_23 ),
inference(backward_demodulation,[],[f412,f161]) ).
tff(f412,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) )
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f410]) ).
tff(f624,plain,
( spl9_20
| ~ spl9_4
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f604,f159,f111,f336]) ).
tff(f336,plain,
( spl9_20
<=> ( 'left:(Tree)>Tree'(sK0) = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
tff(f604,plain,
( ( 'left:(Tree)>Tree'(sK0) = sK3 )
| ~ spl9_4
| ~ spl9_11 ),
inference(backward_demodulation,[],[f113,f161]) ).
tff(f603,plain,
( spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_11
| ~ spl9_22 ),
inference(avatar_contradiction_clause,[],[f602]) ).
tff(f602,plain,
( $false
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_11
| ~ spl9_22 ),
inference(global_subsumption,[],[f593,f391]) ).
tff(f593,plain,
( ~ in(sK1,sF7)
| spl9_6
| ~ spl9_7
| ~ spl9_9 ),
inference(global_subsumption,[],[f146,f127,f123,f88]) ).
tff(f88,plain,
( ~ in(sK1,sK0)
| ~ $less(sK1,sF8)
| ~ in(sK1,sF7)
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f78,f84,f86]) ).
tff(f84,plain,
'left:(Tree)>Tree'(sK0) = sF7,
introduced(function_definition,[]) ).
tff(f78,plain,
( ~ in(sK1,sK0)
| ~ $less(sK1,'val:(Tree)>Int'(sK0))
| ~ in(sK1,'left:(Tree)>Tree'(sK0))
| ( 'empty:Tree' = sK0 ) ),
inference(equality_resolution,[],[f52]) ).
tff(f52,plain,
! [X3: 'Tree'] :
( ~ in(sK1,sK0)
| ~ $less(sK1,'val:(Tree)>Int'(sK0))
| ~ in(sK1,X3)
| ( 'left:(Tree)>Tree'(sK0) != X3 )
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f146,plain,
( $less(sK1,sF8)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f144]) ).
tff(f601,plain,
( spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_19
| ~ spl9_22 ),
inference(avatar_contradiction_clause,[],[f600]) ).
tff(f600,plain,
( $false
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_19
| ~ spl9_22 ),
inference(global_subsumption,[],[f593,f391]) ).
tff(f599,plain,
( spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_20
| ~ spl9_22 ),
inference(avatar_contradiction_clause,[],[f598]) ).
tff(f598,plain,
( $false
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_20
| ~ spl9_22 ),
inference(global_subsumption,[],[f593,f391]) ).
tff(f597,plain,
( spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_22 ),
inference(avatar_contradiction_clause,[],[f596]) ).
tff(f596,plain,
( $false
| spl9_6
| ~ spl9_7
| ~ spl9_9
| ~ spl9_22 ),
inference(global_subsumption,[],[f593,f391]) ).
tff(f595,plain,
( ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| ~ spl9_9
| spl9_27 ),
inference(avatar_contradiction_clause,[],[f594]) ).
tff(f594,plain,
( $false
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| ~ spl9_9
| spl9_27 ),
inference(global_subsumption,[],[f592,f550]) ).
tff(f550,plain,
( ~ in(sK1,sF6)
| spl9_27 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f592,plain,
( in(sK1,sF6)
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| ~ spl9_9 ),
inference(global_subsumption,[],[f90,f146,f88,f127,f123,f525]) ).
tff(f525,plain,
( in(sK1,sF7)
| in(sK1,sF6)
| ( sK1 = sF8 )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7 ),
inference(resolution,[],[f438,f127]) ).
tff(f438,plain,
( ! [X0: $int] :
( ~ in(X0,sK0)
| in(X0,sF7)
| in(X0,sF6)
| ( sF8 = X0 ) )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f387]) ).
tff(f387,plain,
( ! [X0: $int] :
( ( sF8 = X0 )
| in(X0,sF7)
| in(X0,sF6)
| ~ in(X0,sK0) )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f123,f386]) ).
tff(f386,plain,
( ! [X0: $int] :
( ( sF8 = X0 )
| in(X0,sF7)
| in(X0,sF6)
| ( 'empty:Tree' = sK0 )
| ~ in(X0,sK0) )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_demodulation,[],[f385,f118]) ).
tff(f385,plain,
( ! [X0: $int] :
( in(X0,sF7)
| in(X0,sF6)
| ( 'val:(Tree)>Int'(sK0) = X0 )
| ( 'empty:Tree' = sK0 )
| ~ in(X0,sK0) )
| ~ spl9_3
| ~ spl9_4 ),
inference(forward_demodulation,[],[f347,f113]) ).
tff(f347,plain,
( ! [X0: $int] :
( in(X0,sF6)
| in(X0,'left:(Tree)>Tree'(sK0))
| ( 'val:(Tree)>Int'(sK0) = X0 )
| ( 'empty:Tree' = sK0 )
| ~ in(X0,sK0) )
| ~ spl9_3 ),
inference(superposition,[],[f66,f108]) ).
tff(f108,plain,
( ( 'right:(Tree)>Tree'(sK0) = sF6 )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f106]) ).
tff(f106,plain,
( spl9_3
<=> ( 'right:(Tree)>Tree'(sK0) = sF6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
tff(f66,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: $int,X1: 'Tree'] :
( ( in(X0,X1)
| ( ~ in(X0,'right:(Tree)>Tree'(X1))
& ~ in(X0,'left:(Tree)>Tree'(X1))
& ( 'val:(Tree)>Int'(X1) != X0 )
& ( 'empty:Tree' != X1 ) )
| ( 'empty:Tree' = X1 ) )
& ( ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f41]) ).
tff(f41,plain,
! [X0: $int,X1: 'Tree'] :
( ( in(X0,X1)
| ( ~ in(X0,'right:(Tree)>Tree'(X1))
& ~ in(X0,'left:(Tree)>Tree'(X1))
& ( 'val:(Tree)>Int'(X1) != X0 )
& ( 'empty:Tree' != X1 ) )
| ( 'empty:Tree' = X1 ) )
& ( ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(flattening,[],[f26]) ).
tff(f26,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(ennf_transformation,[],[f18]) ).
tff(f18,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(flattening,[],[f17]) ).
tff(f17,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
& ( ~ 'empty:Tree' = X1 ) ) ),
inference(true_and_false_elimination,[],[f16]) ).
tff(f16,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
& ( ( 'empty:Tree' = X1 )
=> $false ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X4: $int,X5: 'Tree'] :
( in(X4,X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( in(X4,'right:(Tree)>Tree'(X5))
| in(X4,'left:(Tree)>Tree'(X5))
| ( 'val:(Tree)>Int'(X5) = X4 ) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) ) ),
file('/export/starexec/sandbox/tmp/tmp.en3yXdOSM5/Vampire---4.8_9125',formula_005) ).
tff(f591,plain,
( spl9_28
| ~ spl9_3
| ~ spl9_5
| spl9_6
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f568,f549,f121,f116,f106,f588]) ).
tff(f568,plain,
( $less(sF8,sK1)
| ~ spl9_3
| ~ spl9_5
| spl9_6
| ~ spl9_27 ),
inference(resolution,[],[f551,f436]) ).
tff(f436,plain,
( ! [X1: $int] :
( ~ in(X1,sF6)
| $less(sF8,X1) )
| ~ spl9_3
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f371]) ).
tff(f371,plain,
( ! [X1: $int] :
( ~ in(X1,sF6)
| $less(sF8,X1) )
| ~ spl9_3
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f43,f123,f355]) ).
tff(f355,plain,
( ! [X1: $int] :
( $less(sF8,X1)
| ~ in(X1,sF6)
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0) )
| ~ spl9_3
| ~ spl9_5 ),
inference(forward_demodulation,[],[f348,f118]) ).
tff(f348,plain,
( ! [X1: $int] :
( ~ in(X1,sF6)
| $less('val:(Tree)>Int'(sK0),X1)
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0) )
| ~ spl9_3 ),
inference(superposition,[],[f59,f108]) ).
tff(f59,plain,
! [X3: $int,X0: 'Tree'] :
( ~ in(X3,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X3)
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f552,plain,
( spl9_27
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| spl9_22 ),
inference(avatar_split_clause,[],[f535,f390,f125,f121,f116,f111,f106,f549]) ).
tff(f535,plain,
( in(sK1,sF6)
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6
| ~ spl9_7
| spl9_22 ),
inference(global_subsumption,[],[f90,f392,f127,f123,f525]) ).
tff(f392,plain,
( ~ in(sK1,sF7)
| spl9_22 ),
inference(avatar_component_clause,[],[f390]) ).
tff(f516,plain,
( spl9_25
| spl9_26
| ~ spl9_3
| spl9_6 ),
inference(avatar_split_clause,[],[f473,f121,f106,f513,f509]) ).
tff(f509,plain,
( spl9_25
<=> ( 'empty:Tree' = sF6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
tff(f513,plain,
( spl9_26
<=> in('val:(Tree)>Int'(sF6),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
tff(f473,plain,
( in('val:(Tree)>Int'(sF6),sK0)
| ( 'empty:Tree' = sF6 )
| ~ spl9_3
| spl9_6 ),
inference(resolution,[],[f435,f80]) ).
tff(f80,plain,
! [X1: 'Tree'] :
( in('val:(Tree)>Int'(X1),X1)
| ( 'empty:Tree' = X1 ) ),
inference(equality_resolution,[],[f68]) ).
tff(f68,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
| ( 'val:(Tree)>Int'(X1) != X0 )
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f435,plain,
( ! [X2: $int] :
( ~ in(X2,sF6)
| in(X2,sK0) )
| ~ spl9_3
| spl9_6 ),
inference(global_subsumption,[],[f370]) ).
tff(f370,plain,
( ! [X2: $int] :
( ~ in(X2,sF6)
| in(X2,sK0) )
| ~ spl9_3
| spl9_6 ),
inference(global_subsumption,[],[f123,f350]) ).
tff(f350,plain,
( ! [X2: $int] :
( ~ in(X2,sF6)
| in(X2,sK0)
| ( 'empty:Tree' = sK0 ) )
| ~ spl9_3 ),
inference(superposition,[],[f70,f108]) ).
tff(f70,plain,
! [X0: $int,X1: 'Tree'] :
( ~ in(X0,'right:(Tree)>Tree'(X1))
| in(X0,X1)
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f478,plain,
( spl9_23
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f440,f121,f116,f111,f106,f410]) ).
tff(f440,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f379]) ).
tff(f379,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(global_subsumption,[],[f123,f378]) ).
tff(f378,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) )
| ( 'empty:Tree' = sK0 )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_demodulation,[],[f377,f118]) ).
tff(f377,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'('val:(Tree)>Int'(sK0),sF7,sF6) )
| ( 'empty:Tree' = sK0 )
| ~ spl9_3
| ~ spl9_4 ),
inference(forward_demodulation,[],[f219,f108]) ).
tff(f219,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'('val:(Tree)>Int'(sK0),sF7,'right:(Tree)>Tree'(sK0)) )
| ( 'empty:Tree' = sK0 )
| ~ spl9_4 ),
inference(superposition,[],[f55,f113]) ).
tff(f55,plain,
! [X0: 'Tree'] :
( ( 'node:(Int*Tree*Tree)>Tree'('val:(Tree)>Int'(X0),'left:(Tree)>Tree'(X0),'right:(Tree)>Tree'(X0)) = X0 )
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: 'Tree'] :
( ( 'node:(Int*Tree*Tree)>Tree'('val:(Tree)>Int'(X0),'left:(Tree)>Tree'(X0),'right:(Tree)>Tree'(X0)) = X0 )
| ( 'empty:Tree' = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.en3yXdOSM5/Vampire---4.8_9125',formula) ).
tff(f434,plain,
~ spl9_24,
inference(avatar_contradiction_clause,[],[f433]) ).
tff(f433,plain,
( $false
| ~ spl9_24 ),
inference(resolution,[],[f431,f82]) ).
tff(f82,plain,
! [X0: $int] : ~ in(X0,'empty:Tree'),
inference(equality_resolution,[],[f65]) ).
tff(f65,plain,
! [X0: $int,X1: 'Tree'] :
( ( 'empty:Tree' != X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tff(f431,plain,
( in(sK1,'empty:Tree')
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f429]) ).
tff(f429,plain,
( spl9_24
<=> in(sK1,'empty:Tree') ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
tff(f432,plain,
( spl9_24
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| ~ spl9_7
| spl9_23 ),
inference(avatar_split_clause,[],[f422,f410,f125,f116,f111,f106,f429]) ).
tff(f422,plain,
( in(sK1,'empty:Tree')
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| ~ spl9_7
| spl9_23 ),
inference(backward_demodulation,[],[f127,f417]) ).
tff(f417,plain,
( ( 'empty:Tree' = sK0 )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_23 ),
inference(subsumption_resolution,[],[f402,f411]) ).
tff(f411,plain,
( ( sK0 != 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) )
| spl9_23 ),
inference(avatar_component_clause,[],[f410]) ).
tff(f402,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'(sF8,sF7,sF6) )
| ( 'empty:Tree' = sK0 )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5 ),
inference(forward_demodulation,[],[f401,f118]) ).
tff(f401,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'('val:(Tree)>Int'(sK0),sF7,sF6) )
| ( 'empty:Tree' = sK0 )
| ~ spl9_3
| ~ spl9_4 ),
inference(forward_demodulation,[],[f398,f108]) ).
tff(f398,plain,
( ( sK0 = 'node:(Int*Tree*Tree)>Tree'('val:(Tree)>Int'(sK0),sF7,'right:(Tree)>Tree'(sK0)) )
| ( 'empty:Tree' = sK0 )
| ~ spl9_4 ),
inference(superposition,[],[f55,f113]) ).
tff(f413,plain,
( spl9_23
| ~ spl9_3
| ~ spl9_4
| ~ spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f379,f121,f116,f111,f106,f410]) ).
tff(f394,plain,
( spl9_7
| spl9_8
| ~ spl9_9
| spl9_11 ),
inference(avatar_split_clause,[],[f376,f159,f144,f140,f125]) ).
tff(f376,plain,
( in(sK1,sK0)
| spl9_8
| ~ spl9_9
| spl9_11 ),
inference(global_subsumption,[],[f44,f141,f160,f146,f94]) ).
tff(f94,plain,
( in(sK1,sK0)
| ( sK3 = sF7 )
| ~ $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f45,f86,f86,f84]) ).
tff(f45,plain,
( in(sK1,sK0)
| ( 'left:(Tree)>Tree'(sK0) = sK3 )
| ~ $less(sK1,'val:(Tree)>Int'(sK0))
| ( sK1 = 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f160,plain,
( ( sK3 != sF7 )
| spl9_11 ),
inference(avatar_component_clause,[],[f159]) ).
tff(f141,plain,
( ( sK1 != sF8 )
| spl9_8 ),
inference(avatar_component_clause,[],[f140]) ).
tff(f44,plain,
( in(sK1,sK0)
| ( 'empty:Tree' != sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f393,plain,
( ~ spl9_22
| spl9_6
| spl9_8
| ~ spl9_9
| spl9_11 ),
inference(avatar_split_clause,[],[f375,f159,f144,f140,f121,f390]) ).
tff(f375,plain,
( ~ in(sK1,sF7)
| spl9_6
| spl9_8
| ~ spl9_9
| spl9_11 ),
inference(global_subsumption,[],[f94,f123,f141,f160,f146,f88]) ).
tff(f369,plain,
( ~ spl9_4
| spl9_7
| ~ spl9_11
| ~ spl9_19 ),
inference(avatar_contradiction_clause,[],[f368]) ).
tff(f368,plain,
( $false
| ~ spl9_4
| spl9_7
| ~ spl9_11
| ~ spl9_19 ),
inference(global_subsumption,[],[f126,f367]) ).
tff(f367,plain,
( in(sK1,sK0)
| ~ spl9_4
| spl9_7
| ~ spl9_11
| ~ spl9_19 ),
inference(resolution,[],[f311,f332]) ).
tff(f311,plain,
( ! [X0: $int] :
( ~ in(X0,sK3)
| in(X0,sK0) )
| ~ spl9_4
| spl9_7
| ~ spl9_11 ),
inference(backward_demodulation,[],[f207,f161]) ).
tff(f207,plain,
( ! [X0: $int] :
( ~ in(X0,sF7)
| in(X0,sK0) )
| ~ spl9_4
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f205]) ).
tff(f205,plain,
( ! [X0: $int] :
( ~ in(X0,sF7)
| in(X0,sK0)
| ( 'empty:Tree' = sK0 ) )
| ~ spl9_4 ),
inference(superposition,[],[f69,f113]) ).
tff(f69,plain,
! [X0: $int,X1: 'Tree'] :
( ~ in(X0,'left:(Tree)>Tree'(X1))
| in(X0,X1)
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f42]) ).
tff(f126,plain,
( ~ in(sK1,sK0)
| spl9_7 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f365,plain,
( spl9_21
| ~ spl9_3
| spl9_7 ),
inference(avatar_split_clause,[],[f360,f125,f106,f362]) ).
tff(f362,plain,
( spl9_21
<=> searchtree(sF6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
tff(f360,plain,
( searchtree(sF6)
| ~ spl9_3
| spl9_7 ),
inference(global_subsumption,[],[f44,f43,f126,f351]) ).
tff(f351,plain,
( searchtree(sF6)
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0)
| ~ spl9_3 ),
inference(superposition,[],[f57,f108]) ).
tff(f57,plain,
! [X0: 'Tree'] :
( searchtree('right:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f339,plain,
( spl9_20
| ~ spl9_4
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f309,f159,f111,f336]) ).
tff(f309,plain,
( ( 'left:(Tree)>Tree'(sK0) = sK3 )
| ~ spl9_4
| ~ spl9_11 ),
inference(backward_demodulation,[],[f113,f161]) ).
tff(f333,plain,
( spl9_19
| spl9_7
| spl9_8
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f319,f144,f140,f125,f330]) ).
tff(f319,plain,
( in(sK1,sK3)
| spl9_7
| spl9_8
| ~ spl9_9 ),
inference(global_subsumption,[],[f155]) ).
tff(f155,plain,
( in(sK1,sK3)
| spl9_7
| spl9_8
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f153,f141]) ).
tff(f153,plain,
( in(sK1,sK3)
| ( sK1 = sF8 )
| spl9_7
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f135,f146]) ).
tff(f135,plain,
( in(sK1,sK3)
| ~ $less(sK1,sF8)
| ( sK1 = sF8 )
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f130]) ).
tff(f130,plain,
( in(sK1,sK3)
| ~ $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 )
| spl9_7 ),
inference(subsumption_resolution,[],[f93,f126]) ).
tff(f93,plain,
( in(sK1,sK0)
| in(sK1,sK3)
| ~ $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f46,f86,f86]) ).
tff(f46,plain,
( in(sK1,sK0)
| in(sK1,sK3)
| ~ $less(sK1,'val:(Tree)>Int'(sK0))
| ( sK1 = 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f324,plain,
( spl9_18
| ~ spl9_11
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f310,f197,f159,f321]) ).
tff(f321,plain,
( spl9_18
<=> searchtree(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
tff(f197,plain,
( spl9_14
<=> searchtree(sF7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
tff(f310,plain,
( searchtree(sK3)
| ~ spl9_11
| ~ spl9_14 ),
inference(backward_demodulation,[],[f199,f161]) ).
tff(f199,plain,
( searchtree(sF7)
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f197]) ).
tff(f308,plain,
( spl9_7
| spl9_8
| spl9_9
| ~ spl9_11
| spl9_12 ),
inference(avatar_contradiction_clause,[],[f307]) ).
tff(f307,plain,
( $false
| spl9_7
| spl9_8
| spl9_9
| ~ spl9_11
| spl9_12 ),
inference(global_subsumption,[],[f296,f173]) ).
tff(f173,plain,
( ( sK2 != sF6 )
| spl9_12 ),
inference(avatar_component_clause,[],[f172]) ).
tff(f172,plain,
( spl9_12
<=> ( sK2 = sF6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
tff(f296,plain,
( ( sK2 = sF6 )
| spl9_7
| spl9_8
| spl9_9 ),
inference(global_subsumption,[],[f145,f163]) ).
tff(f163,plain,
( ( sK2 = sF6 )
| $less(sK1,sF8)
| spl9_7
| spl9_8 ),
inference(global_subsumption,[],[f141,f134]) ).
tff(f134,plain,
( ( sK2 = sF6 )
| $less(sK1,sF8)
| ( sK1 = sF8 )
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f131]) ).
tff(f131,plain,
( ( sK2 = sF6 )
| $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 )
| spl9_7 ),
inference(subsumption_resolution,[],[f92,f126]) ).
tff(f92,plain,
( in(sK1,sK0)
| ( sK2 = sF6 )
| $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f47,f86,f86,f83]) ).
tff(f47,plain,
( in(sK1,sK0)
| ( 'right:(Tree)>Tree'(sK0) = sK2 )
| $less(sK1,'val:(Tree)>Int'(sK0))
| ( sK1 = 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f306,plain,
( spl9_7
| spl9_8
| spl9_9
| spl9_12 ),
inference(avatar_contradiction_clause,[],[f305]) ).
tff(f305,plain,
( $false
| spl9_7
| spl9_8
| spl9_9
| spl9_12 ),
inference(global_subsumption,[],[f296,f173]) ).
tff(f304,plain,
( ~ spl9_3
| spl9_7
| spl9_8
| spl9_9
| spl9_13 ),
inference(avatar_contradiction_clause,[],[f303]) ).
tff(f303,plain,
( $false
| ~ spl9_3
| spl9_7
| spl9_8
| spl9_9
| spl9_13 ),
inference(global_subsumption,[],[f297,f178]) ).
tff(f178,plain,
( ( 'right:(Tree)>Tree'(sK0) != sK2 )
| spl9_13 ),
inference(avatar_component_clause,[],[f177]) ).
tff(f177,plain,
( spl9_13
<=> ( 'right:(Tree)>Tree'(sK0) = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
tff(f297,plain,
( ( 'right:(Tree)>Tree'(sK0) = sK2 )
| ~ spl9_3
| spl9_7
| spl9_8
| spl9_9 ),
inference(backward_demodulation,[],[f108,f296]) ).
tff(f295,plain,
( spl9_7
| ~ spl9_10
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f294]) ).
tff(f294,plain,
( $false
| spl9_7
| ~ spl9_10
| ~ spl9_13 ),
inference(global_subsumption,[],[f126,f293]) ).
tff(f293,plain,
( in(sK1,sK0)
| spl9_7
| ~ spl9_10
| ~ spl9_13 ),
inference(resolution,[],[f216,f150]) ).
tff(f150,plain,
( in(sK1,sK2)
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f148]) ).
tff(f148,plain,
( spl9_10
<=> in(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
tff(f216,plain,
( ! [X0: $int] :
( ~ in(X0,sK2)
| in(X0,sK0) )
| spl9_7
| ~ spl9_13 ),
inference(global_subsumption,[],[f44,f126,f214]) ).
tff(f214,plain,
( ! [X0: $int] :
( ~ in(X0,sK2)
| in(X0,sK0)
| ( 'empty:Tree' = sK0 ) )
| ~ spl9_13 ),
inference(superposition,[],[f70,f179]) ).
tff(f179,plain,
( ( 'right:(Tree)>Tree'(sK0) = sK2 )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f177]) ).
tff(f289,plain,
( ~ spl9_17
| spl9_7 ),
inference(avatar_split_clause,[],[f190,f125,f286]) ).
tff(f190,plain,
( ( sK1 != 'val:(Tree)>Int'(sK0) )
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f186]) ).
tff(f186,plain,
( ( sK1 != 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 )
| spl9_7 ),
inference(constrained_resolution,[],[f80,f126]) ).
tff(f261,plain,
( spl9_16
| ~ spl9_5
| spl9_7 ),
inference(avatar_split_clause,[],[f191,f125,f116,f258]) ).
tff(f258,plain,
( spl9_16
<=> in(sF8,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
tff(f191,plain,
( in(sF8,sK0)
| ~ spl9_5
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f188]) ).
tff(f188,plain,
( in(sF8,sK0)
| ( 'empty:Tree' = sK0 )
| ~ spl9_5 ),
inference(superposition,[],[f80,f118]) ).
tff(f212,plain,
( spl9_15
| spl9_7
| ~ spl9_13 ),
inference(avatar_split_clause,[],[f203,f177,f125,f209]) ).
tff(f209,plain,
( spl9_15
<=> searchtree(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
tff(f203,plain,
( searchtree(sK2)
| spl9_7
| ~ spl9_13 ),
inference(global_subsumption,[],[f44,f43,f126,f201]) ).
tff(f201,plain,
( searchtree(sK2)
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0)
| ~ spl9_13 ),
inference(superposition,[],[f57,f179]) ).
tff(f200,plain,
( spl9_14
| ~ spl9_4
| spl9_7 ),
inference(avatar_split_clause,[],[f195,f125,f111,f197]) ).
tff(f195,plain,
( searchtree(sF7)
| ~ spl9_4
| spl9_7 ),
inference(global_subsumption,[],[f44,f43,f126,f193]) ).
tff(f193,plain,
( searchtree(sF7)
| ( 'empty:Tree' = sK0 )
| ~ searchtree(sK0)
| ~ spl9_4 ),
inference(superposition,[],[f56,f113]) ).
tff(f56,plain,
! [X0: 'Tree'] :
( searchtree('left:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f180,plain,
( spl9_13
| ~ spl9_3
| spl9_7
| spl9_8
| spl9_11 ),
inference(avatar_split_clause,[],[f168,f159,f140,f125,f106,f177]) ).
tff(f168,plain,
( ( 'right:(Tree)>Tree'(sK0) = sK2 )
| ~ spl9_3
| spl9_7
| spl9_8
| spl9_11 ),
inference(backward_demodulation,[],[f108,f167]) ).
tff(f167,plain,
( ( sK2 = sF6 )
| spl9_7
| spl9_8
| spl9_11 ),
inference(subsumption_resolution,[],[f163,f166]) ).
tff(f166,plain,
( ~ $less(sK1,sF8)
| spl9_7
| spl9_8
| spl9_11 ),
inference(subsumption_resolution,[],[f164,f160]) ).
tff(f164,plain,
( ( sK3 = sF7 )
| ~ $less(sK1,sF8)
| spl9_7
| spl9_8 ),
inference(global_subsumption,[],[f141,f136]) ).
tff(f136,plain,
( ( sK3 = sF7 )
| ~ $less(sK1,sF8)
| ( sK1 = sF8 )
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f129]) ).
tff(f129,plain,
( ( sK3 = sF7 )
| ~ $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 )
| spl9_7 ),
inference(subsumption_resolution,[],[f94,f126]) ).
tff(f175,plain,
( spl9_12
| spl9_7
| spl9_8
| spl9_11 ),
inference(avatar_split_clause,[],[f167,f159,f140,f125,f172]) ).
tff(f170,plain,
( ~ spl9_9
| spl9_7
| spl9_8
| spl9_11 ),
inference(avatar_split_clause,[],[f166,f159,f140,f125,f144]) ).
tff(f162,plain,
( spl9_11
| spl9_7
| spl9_8
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f154,f144,f140,f125,f159]) ).
tff(f154,plain,
( ( sK3 = sF7 )
| spl9_7
| spl9_8
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f152,f141]) ).
tff(f152,plain,
( ( sK3 = sF7 )
| ( sK1 = sF8 )
| spl9_7
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f136,f146]) ).
tff(f151,plain,
( spl9_8
| spl9_9
| spl9_10
| spl9_7 ),
inference(avatar_split_clause,[],[f133,f125,f148,f144,f140]) ).
tff(f133,plain,
( in(sK1,sK2)
| $less(sK1,sF8)
| ( sK1 = sF8 )
| spl9_7 ),
inference(global_subsumption,[],[f44,f126,f132]) ).
tff(f132,plain,
( in(sK1,sK2)
| $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 )
| spl9_7 ),
inference(subsumption_resolution,[],[f91,f126]) ).
tff(f91,plain,
( in(sK1,sK0)
| in(sK1,sK2)
| $less(sK1,sF8)
| ( sK1 = sF8 )
| ( 'empty:Tree' = sK0 ) ),
inference(definition_folding,[],[f48,f86,f86]) ).
tff(f48,plain,
( in(sK1,sK0)
| in(sK1,sK2)
| $less(sK1,'val:(Tree)>Int'(sK0))
| ( sK1 = 'val:(Tree)>Int'(sK0) )
| ( 'empty:Tree' = sK0 ) ),
inference(cnf_transformation,[],[f34]) ).
tff(f128,plain,
( ~ spl9_6
| spl9_7 ),
inference(avatar_split_clause,[],[f44,f125,f121]) ).
tff(f119,plain,
spl9_5,
inference(avatar_split_clause,[],[f86,f116]) ).
tff(f114,plain,
spl9_4,
inference(avatar_split_clause,[],[f84,f111]) ).
tff(f109,plain,
spl9_3,
inference(avatar_split_clause,[],[f83,f106]) ).
tff(f104,plain,
spl9_2,
inference(avatar_split_clause,[],[f79,f101]) ).
tff(f101,plain,
( spl9_2
<=> searchtree('empty:Tree') ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
tff(f79,plain,
searchtree('empty:Tree'),
inference(equality_resolution,[],[f60]) ).
tff(f60,plain,
! [X0: 'Tree'] :
( searchtree(X0)
| ( 'empty:Tree' != X0 ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f99,plain,
spl9_1,
inference(avatar_split_clause,[],[f43,f96]) ).
tff(f96,plain,
( spl9_1
<=> searchtree(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW678_1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 18:53:16 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TF0_THM_EQU_ARI problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.en3yXdOSM5/Vampire---4.8_9125
% 0.14/0.36 % (9285)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (9288)dis-1010_2:3_canc=force:fsd=off:fde=unused:gs=on:gsem=on:nm=0:nwc=1.3:sas=z3:tha=off:thf=on:uwa=ground_572 on Vampire---4 for (572ds/0Mi)
% 0.20/0.42 % (9289)dis-10_20_canc=force:fsd=off:gs=on:gsem=off:nm=0:sas=z3:sac=on:tha=off:thi=strong:tgt=ground_476 on Vampire---4 for (476ds/0Mi)
% 0.20/0.42 % (9292)ott+10_1024_av=off:bd=preordered:br=off:ep=RSTC:fsr=off:fde=none:nm=2:urr=on_318 on Vampire---4 for (318ds/0Mi)
% 0.20/0.42 % (9291)lrs+1010_2:1_amm=off:bs=on:bsr=on:canc=force:fsd=off:fsr=off:gs=on:gsaa=full_model:gsem=on:nm=0:nwc=1.3:sas=z3:sac=on:tha=off:thi=overlap:tgt=ground:uwa=ground:stl=60_408 on Vampire---4 for (408ds/0Mi)
% 0.20/0.42 % (9287)lrs+2_32_add=large:amm=off:bd=off:bs=unit_only:drc=off:flr=on:fsd=off:fde=none:nm=0:nwc=1.1:sos=theory:sp=reverse_arity:tgt=ground:stl=180_1034 on Vampire---4 for (1034ds/0Mi)
% 0.20/0.42 % (9290)dis-11_10:1_canc=force:fsd=off:nwc=1.5:sas=z3:tha=off:uwa=all_472 on Vampire---4 for (472ds/0Mi)
% 0.20/0.42 % (9293)lrs-1010_3_av=off:br=off:drc=off:er=known:fsd=off:fde=unused:nm=4:nwc=3.0:sp=scramble:urr=on:stl=180_280 on Vampire---4 for (280ds/0Mi)
% 0.20/0.53 % (9291)First to succeed.
% 0.20/0.54 % (9291)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for Vampire---4
% 0.20/0.54 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.54 % (9291)------------------------------
% 0.20/0.54 % (9291)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.54 % (9291)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.54 % (9291)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (9291)Memory used [KB]: 6268
% 0.20/0.54 % (9291)Time elapsed: 0.119 s
% 0.20/0.54 % (9291)------------------------------
% 0.20/0.54 % (9291)------------------------------
% 0.20/0.54 % (9285)Success in time 0.181 s
% 0.20/0.54 9289 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.en3yXdOSM5/Vampire---4.8_9125
% 0.20/0.54 % (9289)------------------------------
% 0.20/0.54 % (9289)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.54 % (9289)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.54 % (9289)Termination reason: Refutation not found, SMT solver inside AVATAR returned Unknown
% 0.20/0.54
% 0.20/0.54 % (9289)Memory used [KB]: 5884
% 0.20/0.54 % (9289)Time elapsed: 0.125 s
% 0.20/0.54 % (9289)------------------------------
% 0.20/0.54 % (9289)------------------------------
% 0.20/0.54 % Vampire---4.8 exiting
%------------------------------------------------------------------------------