TSTP Solution File: SWW678_1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWW678_1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 19:09:29 EDT 2022
% Result : Theorem 1.53s 0.57s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 41
% Syntax : Number of formulae : 159 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 722 ( 203 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 850 ( 271 ~; 323 |; 165 &)
% ( 31 <=>; 57 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 178 ( 96 atm; 0 fun; 0 num; 82 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 22 ( 16 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 178 ( 132 !; 46 ?; 178 :)
% 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_9,type,
sK2: 'Tree' > $int ).
tff(func_def_10,type,
sK3: 'Tree' > $int ).
tff(func_def_11,type,
sK4: ( 'Tree' * $int ) > 'Tree' ).
tff(func_def_12,type,
sK5: ( 'Tree' * $int ) > 'Tree' ).
tff(func_def_13,type,
sK6: 'Tree' ).
tff(func_def_14,type,
sK7: $int ).
tff(pred_def_1,type,
searchtree: 'Tree' > $o ).
tff(pred_def_2,type,
in: ( $int * 'Tree' ) > $o ).
tff(pred_def_6,type,
sP0: 'Tree' > $o ).
tff(pred_def_7,type,
sP1: ( 'Tree' * $int ) > $o ).
tff(f575,plain,
$false,
inference(avatar_sat_refutation,[],[f124,f125,f136,f152,f162,f167,f260,f265,f289,f303,f315,f321,f346,f354,f370,f371,f372,f391,f573,f574]) ).
tff(f574,plain,
( spl8_4
| ~ spl8_24
| spl8_23
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f389,f300,f291,f295,f133]) ).
tff(f133,plain,
( spl8_4
<=> ( 'empty:Tree' = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
tff(f295,plain,
( spl8_24
<=> sP0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
tff(f291,plain,
( spl8_23
<=> $less('val:(Tree)>Int'(sK6),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
tff(f300,plain,
( spl8_25
<=> in(sK7,'right:(Tree)>Tree'(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f389,plain,
( $less('val:(Tree)>Int'(sK6),sK7)
| ~ sP0(sK6)
| ( 'empty:Tree' = sK6 )
| ~ spl8_25 ),
inference(resolution,[],[f302,f73]) ).
tff(f73,plain,
! [X3: $int,X0: 'Tree'] :
( ~ in(X3,'right:(Tree)>Tree'(X0))
| ~ sP0(X0)
| ( 'empty:Tree' = X0 )
| $less('val:(Tree)>Int'(X0),X3) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( 'empty:Tree' != X0 )
& ( ~ searchtree('right:(Tree)>Tree'(X0))
| ( in(sK2(X0),'right:(Tree)>Tree'(X0))
& ~ $less('val:(Tree)>Int'(X0),sK2(X0)) )
| ( $less('val:(Tree)>Int'(X0),sK3(X0))
& in(sK3(X0),'left:(Tree)>Tree'(X0)) )
| ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
& ( ( 'empty:Tree' = X0 )
| ( searchtree('right:(Tree)>Tree'(X0))
& ! [X3: $int] :
( ~ in(X3,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X3) )
& ! [X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0)) )
& searchtree('left:(Tree)>Tree'(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f48,f50,f49]) ).
tff(f49,plain,
! [X0: 'Tree'] :
( ? [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
& ~ $less('val:(Tree)>Int'(X0),X1) )
=> ( in(sK2(X0),'right:(Tree)>Tree'(X0))
& ~ $less('val:(Tree)>Int'(X0),sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f50,plain,
! [X0: 'Tree'] :
( ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
=> ( $less('val:(Tree)>Int'(X0),sK3(X0))
& in(sK3(X0),'left:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f48,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( 'empty:Tree' != X0 )
& ( ~ searchtree('right:(Tree)>Tree'(X0))
| ? [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
& ~ $less('val:(Tree)>Int'(X0),X1) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
& ( ( 'empty:Tree' = X0 )
| ( searchtree('right:(Tree)>Tree'(X0))
& ! [X3: $int] :
( ~ in(X3,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X3) )
& ! [X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0)) )
& searchtree('left:(Tree)>Tree'(X0)) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f47]) ).
tff(f47,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( 'empty:Tree' != X0 )
& ( ~ searchtree('right:(Tree)>Tree'(X0))
| ? [X2: $int] :
( in(X2,'right:(Tree)>Tree'(X0))
& ~ $less('val:(Tree)>Int'(X0),X2) )
| ? [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
& in(X1,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
& ( ( 'empty:Tree' = X0 )
| ( searchtree('right:(Tree)>Tree'(X0))
& ! [X2: $int] :
( ~ in(X2,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X2) )
& ! [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'left:(Tree)>Tree'(X0)) )
& searchtree('left:(Tree)>Tree'(X0)) )
| ~ sP0(X0) ) ),
inference(flattening,[],[f46]) ).
tff(f46,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( 'empty:Tree' != X0 )
& ( ~ searchtree('right:(Tree)>Tree'(X0))
| ? [X2: $int] :
( in(X2,'right:(Tree)>Tree'(X0))
& ~ $less('val:(Tree)>Int'(X0),X2) )
| ? [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
& in(X1,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('left:(Tree)>Tree'(X0)) ) ) )
& ( ( 'empty:Tree' = X0 )
| ( searchtree('right:(Tree)>Tree'(X0))
& ! [X2: $int] :
( ~ in(X2,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X2) )
& ! [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'left:(Tree)>Tree'(X0)) )
& searchtree('left:(Tree)>Tree'(X0)) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: 'Tree'] :
( sP0(X0)
<=> ( ( 'empty:Tree' = X0 )
| ( searchtree('right:(Tree)>Tree'(X0))
& ! [X2: $int] :
( ~ in(X2,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X2) )
& ! [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'left:(Tree)>Tree'(X0)) )
& searchtree('left:(Tree)>Tree'(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f302,plain,
( in(sK7,'right:(Tree)>Tree'(sK6))
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f300]) ).
tff(f573,plain,
( ~ spl8_6
| ~ spl8_23 ),
inference(avatar_contradiction_clause,[],[f570]) ).
tff(f570,plain,
( $false
| ~ spl8_6
| ~ spl8_23 ),
inference(resolution,[],[f538,f16]) ).
tff(f16,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_147,[]) ).
tff(f538,plain,
( $less(sK7,sK7)
| ~ spl8_6
| ~ spl8_23 ),
inference(resolution,[],[f401,f292]) ).
tff(f292,plain,
( $less('val:(Tree)>Int'(sK6),sK7)
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f291]) ).
tff(f401,plain,
( ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(sK6),X2)
| $less(sK7,X2) )
| ~ spl8_6 ),
inference(resolution,[],[f146,f17]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,X2)
| ~ $less(X1,X2) ),
introduced(theory_axiom_148,[]) ).
tff(f146,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f144]) ).
tff(f144,plain,
( spl8_6
<=> $less(sK7,'val:(Tree)>Int'(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
tff(f391,plain,
( spl8_6
| spl8_2
| spl8_4
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f388,f300,f133,f121,f144]) ).
tff(f121,plain,
( spl8_2
<=> sP1(sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
tff(f388,plain,
( ( 'empty:Tree' = sK6 )
| sP1(sK6,sK7)
| $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl8_25 ),
inference(resolution,[],[f302,f110]) ).
tff(f110,plain,
! [X0: 'Tree',X1: $int] :
( ~ in(X1,'right:(Tree)>Tree'(X0))
| sP1(X0,X1)
| $less(X1,'val:(Tree)>Int'(X0))
| ( 'empty:Tree' = X0 ) ),
inference(equality_resolution,[],[f91]) ).
tff(f91,plain,
! [X3: 'Tree',X0: 'Tree',X1: $int] :
( sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| $less(X1,'val:(Tree)>Int'(X0))
| ( 'right:(Tree)>Tree'(X0) != X3 )
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f59]) ).
tff(f59,plain,
! [X0: 'Tree',X1: $int] :
( ( sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| ( ( 'val:(Tree)>Int'(X0) != X1 )
& ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'left:(Tree)>Tree'(X0) != X2 ) )
& $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X0) != X3 )
| ~ in(X1,X3) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ( 'empty:Tree' != X0 )
& ( ( 'val:(Tree)>Int'(X0) = X1 )
| ( ( ( in(X1,sK4(X0,X1))
& ( 'left:(Tree)>Tree'(X0) = sK4(X0,X1) ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) )
& ( ( ( 'right:(Tree)>Tree'(X0) = sK5(X0,X1) )
& in(X1,sK5(X0,X1)) )
| $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'empty:Tree' = X0 ) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f56,f58,f57]) ).
tff(f57,plain,
! [X0: 'Tree',X1: $int] :
( ? [X4: 'Tree'] :
( in(X1,X4)
& ( 'left:(Tree)>Tree'(X0) = X4 ) )
=> ( in(X1,sK4(X0,X1))
& ( 'left:(Tree)>Tree'(X0) = sK4(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f58,plain,
! [X0: 'Tree',X1: $int] :
( ? [X5: 'Tree'] :
( ( 'right:(Tree)>Tree'(X0) = X5 )
& in(X1,X5) )
=> ( ( 'right:(Tree)>Tree'(X0) = sK5(X0,X1) )
& in(X1,sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f56,plain,
! [X0: 'Tree',X1: $int] :
( ( sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| ( ( 'val:(Tree)>Int'(X0) != X1 )
& ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'left:(Tree)>Tree'(X0) != X2 ) )
& $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X0) != X3 )
| ~ in(X1,X3) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ( 'empty:Tree' != X0 )
& ( ( 'val:(Tree)>Int'(X0) = X1 )
| ( ( ? [X4: 'Tree'] :
( in(X1,X4)
& ( 'left:(Tree)>Tree'(X0) = X4 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X5: 'Tree'] :
( ( 'right:(Tree)>Tree'(X0) = X5 )
& in(X1,X5) )
| $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'empty:Tree' = X0 ) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f55]) ).
tff(f55,plain,
! [X1: 'Tree',X0: $int] :
( ( sP1(X1,X0)
| ( 'empty:Tree' = X1 )
| ( ( 'val:(Tree)>Int'(X1) != X0 )
& ( ( ! [X2: 'Tree'] :
( ~ in(X0,X2)
| ( 'left:(Tree)>Tree'(X1) != X2 ) )
& $less(X0,'val:(Tree)>Int'(X1)) )
| ( ! [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) != X3 )
| ~ in(X0,X3) )
& ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
& ( 'empty:Tree' != X1 ) ) )
& ( ( ( 'empty:Tree' != X1 )
& ( ( 'val:(Tree)>Int'(X1) = X0 )
| ( ( ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) )
| $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'empty:Tree' = X1 ) ) )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f54]) ).
tff(f54,plain,
! [X1: 'Tree',X0: $int] :
( ( sP1(X1,X0)
| ( 'empty:Tree' = X1 )
| ( ( 'val:(Tree)>Int'(X1) != X0 )
& ( ( ! [X2: 'Tree'] :
( ~ in(X0,X2)
| ( 'left:(Tree)>Tree'(X1) != X2 ) )
& $less(X0,'val:(Tree)>Int'(X1)) )
| ( ! [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) != X3 )
| ~ in(X0,X3) )
& ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
& ( 'empty:Tree' != X1 ) ) )
& ( ( ( 'empty:Tree' != X1 )
& ( ( 'val:(Tree)>Int'(X1) = X0 )
| ( ( ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) )
| $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'empty:Tree' = X1 ) ) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X1: 'Tree',X0: $int] :
( sP1(X1,X0)
<=> ( ( 'empty:Tree' != X1 )
& ( ( 'val:(Tree)>Int'(X1) = X0 )
| ( ( ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) )
| $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'empty:Tree' = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f372,plain,
( ~ spl8_3
| spl8_4
| spl8_2 ),
inference(avatar_split_clause,[],[f344,f121,f133,f129]) ).
tff(f129,plain,
( spl8_3
<=> ( sK7 = 'val:(Tree)>Int'(sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f344,plain,
( ( 'empty:Tree' = sK6 )
| ( sK7 != 'val:(Tree)>Int'(sK6) )
| spl8_2 ),
inference(constrained_resolution,[],[f122,f106]) ).
tff(f106,plain,
! [X0: 'Tree'] :
( sP1(X0,'val:(Tree)>Int'(X0))
| ( 'empty:Tree' = X0 ) ),
inference(equality_resolution,[],[f94]) ).
tff(f94,plain,
! [X0: 'Tree',X1: $int] :
( sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| ( 'val:(Tree)>Int'(X0) != X1 ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f122,plain,
( ~ sP1(sK6,sK7)
| spl8_2 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f371,plain,
( ~ spl8_23
| ~ spl8_24
| spl8_4
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f366,f351,f133,f295,f291]) ).
tff(f351,plain,
( spl8_29
<=> in(sK7,'left:(Tree)>Tree'(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
tff(f366,plain,
( ( 'empty:Tree' = sK6 )
| ~ sP0(sK6)
| ~ $less('val:(Tree)>Int'(sK6),sK7)
| ~ spl8_29 ),
inference(resolution,[],[f353,f72]) ).
tff(f72,plain,
! [X0: 'Tree',X4: $int] :
( ~ in(X4,'left:(Tree)>Tree'(X0))
| ~ sP0(X0)
| ~ $less('val:(Tree)>Int'(X0),X4)
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f51]) ).
tff(f353,plain,
( in(sK7,'left:(Tree)>Tree'(sK6))
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f351]) ).
tff(f370,plain,
( spl8_2
| ~ spl8_6
| spl8_4
| ~ spl8_29 ),
inference(avatar_split_clause,[],[f367,f351,f133,f144,f121]) ).
tff(f367,plain,
( ( 'empty:Tree' = sK6 )
| ~ $less(sK7,'val:(Tree)>Int'(sK6))
| sP1(sK6,sK7)
| ~ spl8_29 ),
inference(resolution,[],[f353,f109]) ).
tff(f109,plain,
! [X0: 'Tree',X1: $int] :
( ~ in(X1,'left:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ $less(X1,'val:(Tree)>Int'(X0))
| sP1(X0,X1) ),
inference(equality_resolution,[],[f92]) ).
tff(f92,plain,
! [X2: 'Tree',X0: 'Tree',X1: $int] :
( sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| ~ in(X1,X2)
| ( 'left:(Tree)>Tree'(X0) != X2 )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ),
inference(cnf_transformation,[],[f59]) ).
tff(f354,plain,
( spl8_3
| spl8_29
| spl8_25
| spl8_4
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f340,f117,f133,f300,f351,f129]) ).
tff(f117,plain,
( spl8_1
<=> in(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
tff(f340,plain,
( ( 'empty:Tree' = sK6 )
| in(sK7,'right:(Tree)>Tree'(sK6))
| in(sK7,'left:(Tree)>Tree'(sK6))
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ~ spl8_1 ),
inference(resolution,[],[f119,f102]) ).
tff(f102,plain,
! [X0: 'Tree',X1: $int] :
( ~ in(X1,X0)
| in(X1,'right:(Tree)>Tree'(X0))
| in(X1,'left:(Tree)>Tree'(X0))
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f67]) ).
tff(f67,plain,
! [X0: 'Tree',X1: $int] :
( ( ( ( 'empty:Tree' != X0 )
& ( ( 'empty:Tree' = X0 )
| in(X1,'right:(Tree)>Tree'(X0))
| in(X1,'left:(Tree)>Tree'(X0))
| ( 'val:(Tree)>Int'(X0) = X1 ) ) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( 'empty:Tree' = X0 )
| ( ( 'empty:Tree' != X0 )
& ~ in(X1,'right:(Tree)>Tree'(X0))
& ~ in(X1,'left:(Tree)>Tree'(X0))
& ( 'val:(Tree)>Int'(X0) != X1 ) ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,plain,
! [X1: 'Tree',X0: $int] :
( ( ( ( 'empty:Tree' != X1 )
& ( ( 'empty:Tree' = X1 )
| in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( 'empty:Tree' = X1 )
| ( ( 'empty:Tree' != X1 )
& ~ in(X0,'right:(Tree)>Tree'(X1))
& ~ in(X0,'left:(Tree)>Tree'(X1))
& ( 'val:(Tree)>Int'(X1) != X0 ) ) ) ),
inference(flattening,[],[f65]) ).
tff(f65,plain,
! [X1: 'Tree',X0: $int] :
( ( ( ( 'empty:Tree' != X1 )
& ( ( 'empty:Tree' = X1 )
| in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( 'empty:Tree' = X1 )
| ( ( 'empty:Tree' != X1 )
& ~ in(X0,'right:(Tree)>Tree'(X1))
& ~ in(X0,'left:(Tree)>Tree'(X1))
& ( 'val:(Tree)>Int'(X1) != X0 ) ) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X1: 'Tree',X0: $int] :
( ( ( 'empty:Tree' != X1 )
& ( ( 'empty:Tree' = X1 )
| in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
<=> in(X0,X1) ),
inference(flattening,[],[f38]) ).
tff(f38,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| in(X0,'right:(Tree)>Tree'(X1))
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(ennf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| in(X0,'right:(Tree)>Tree'(X1)) ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(flattening,[],[f26]) ).
tff(f26,plain,
! [X0: $int,X1: 'Tree'] :
( ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| in(X0,'right:(Tree)>Tree'(X1)) ) )
& ( ( ~ 'empty:Tree' )
= X1 ) )
<=> in(X0,X1) ),
inference(true_and_false_elimination,[],[f25]) ).
tff(f25,plain,
! [X0: $int,X1: 'Tree'] :
( ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| in(X0,'right:(Tree)>Tree'(X1)) ) )
& ( ( 'empty:Tree' = X1 )
=> $false ) )
<=> in(X0,X1) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X4: $int,X5: 'Tree'] :
( ( ( ( 'empty:Tree' != X5 )
=> ( ( 'val:(Tree)>Int'(X5) = X4 )
| in(X4,'right:(Tree)>Tree'(X5))
| in(X4,'left:(Tree)>Tree'(X5)) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) )
<=> in(X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_005) ).
tff(f119,plain,
( in(sK7,sK6)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f346,plain,
spl8_24,
inference(avatar_contradiction_clause,[],[f345]) ).
tff(f345,plain,
( $false
| spl8_24 ),
inference(resolution,[],[f297,f126]) ).
tff(f126,plain,
sP0(sK6),
inference(resolution,[],[f95,f81]) ).
tff(f81,plain,
! [X0: 'Tree'] :
( ~ searchtree(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ~ searchtree(X0) )
& ( searchtree(X0)
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: 'Tree'] :
( sP0(X0)
<=> searchtree(X0) ),
inference(definition_folding,[],[f35,f40]) ).
tff(f35,plain,
! [X0: 'Tree'] :
( ( ( 'empty:Tree' = X0 )
| ( searchtree('right:(Tree)>Tree'(X0))
& ! [X2: $int] :
( ~ in(X2,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X2) )
& ! [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'left:(Tree)>Tree'(X0)) )
& searchtree('left:(Tree)>Tree'(X0)) ) )
<=> searchtree(X0) ),
inference(ennf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( 'empty:Tree' != X0 )
=> ( searchtree('left:(Tree)>Tree'(X0))
& searchtree('right:(Tree)>Tree'(X0))
& ! [X1: $int] :
( in(X1,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X1) )
& ! [X2: $int] :
( in(X2,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X2) ) ) ) ),
inference(true_and_false_elimination,[],[f30]) ).
tff(f30,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ( 'empty:Tree' != X0 )
=> ( searchtree('left:(Tree)>Tree'(X0))
& searchtree('right:(Tree)>Tree'(X0))
& ! [X1: $int] :
( in(X1,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X1) )
& ! [X2: $int] :
( in(X2,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X2) ) ) )
& ( ( 'empty:Tree' = X0 )
=> $true ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,plain,
! [X5: 'Tree'] :
( searchtree(X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( searchtree('right:(Tree)>Tree'(X5))
& ! [X4: $int] :
( in(X4,'left:(Tree)>Tree'(X5))
=> ~ $less('val:(Tree)>Int'(X5),X4) )
& searchtree('left:(Tree)>Tree'(X5))
& ! [X4: $int] :
( in(X4,'right:(Tree)>Tree'(X5))
=> $less('val:(Tree)>Int'(X5),X4) ) ) )
& ( ( 'empty:Tree' = X5 )
=> $true ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,axiom,
! [X5: 'Tree'] :
( searchtree(X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( searchtree('right:(Tree)>Tree'(X5))
& ! [X4: $int] :
( in(X4,'left:(Tree)>Tree'(X5))
=> $lesseq(X4,'val:(Tree)>Int'(X5)) )
& searchtree('left:(Tree)>Tree'(X5))
& ! [X4: $int] :
( in(X4,'right:(Tree)>Tree'(X5))
=> $greater(X4,'val:(Tree)>Int'(X5)) ) ) )
& ( ( 'empty:Tree' = X5 )
=> $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_006) ).
tff(f95,plain,
searchtree(sK6),
inference(cnf_transformation,[],[f64]) ).
tff(f64,plain,
( ( ~ sP1(sK6,sK7)
| ~ in(sK7,sK6) )
& ( sP1(sK6,sK7)
| in(sK7,sK6) )
& searchtree(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f62,f63]) ).
tff(f63,plain,
( ? [X0: 'Tree',X1: $int] :
( ( ~ sP1(X0,X1)
| ~ in(X1,X0) )
& ( sP1(X0,X1)
| in(X1,X0) )
& searchtree(X0) )
=> ( ( ~ sP1(sK6,sK7)
| ~ in(sK7,sK6) )
& ( sP1(sK6,sK7)
| in(sK7,sK6) )
& searchtree(sK6) ) ),
introduced(choice_axiom,[]) ).
tff(f62,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ sP1(X0,X1)
| ~ in(X1,X0) )
& ( sP1(X0,X1)
| in(X1,X0) )
& searchtree(X0) ),
inference(rectify,[],[f61]) ).
tff(f61,plain,
? [X1: 'Tree',X0: $int] :
( ( ~ sP1(X1,X0)
| ~ in(X0,X1) )
& ( sP1(X1,X0)
| in(X0,X1) )
& searchtree(X1) ),
inference(flattening,[],[f60]) ).
tff(f60,plain,
? [X1: 'Tree',X0: $int] :
( ( ~ sP1(X1,X0)
| ~ in(X0,X1) )
& ( sP1(X1,X0)
| in(X0,X1) )
& searchtree(X1) ),
inference(nnf_transformation,[],[f43]) ).
tff(f43,plain,
? [X1: 'Tree',X0: $int] :
( ( in(X0,X1)
<~> sP1(X1,X0) )
& searchtree(X1) ),
inference(definition_folding,[],[f37,f42]) ).
tff(f37,plain,
? [X1: 'Tree',X0: $int] :
( ( in(X0,X1)
<~> ( ( 'empty:Tree' != X1 )
& ( ( 'val:(Tree)>Int'(X1) = X0 )
| ( ( ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) )
| $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'empty:Tree' = X1 ) ) ) )
& searchtree(X1) ),
inference(flattening,[],[f36]) ).
tff(f36,plain,
? [X1: 'Tree',X0: $int] :
( ( in(X0,X1)
<~> ( ( ( ( ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) )
| $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) )
& searchtree(X1) ),
inference(ennf_transformation,[],[f34]) ).
tff(f34,plain,
~ ! [X1: 'Tree',X0: $int] :
( searchtree(X1)
=> ( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( ( 'val:(Tree)>Int'(X1) != X0 )
=> ( ( $less(X0,'val:(Tree)>Int'(X1))
=> ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) ) )
& ( ~ $less(X0,'val:(Tree)>Int'(X1))
=> ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) ) ) ) ) )
& ( 'empty:Tree' != X1 ) ) ) ),
inference(flattening,[],[f33]) ).
tff(f33,plain,
~ ! [X0: $int,X1: 'Tree'] :
( searchtree(X1)
=> ( ( ( ( ~ 'empty:Tree' )
= X1 )
& ( ( 'empty:Tree' != X1 )
=> ( ( 'val:(Tree)>Int'(X1) != X0 )
=> ( ( $less(X0,'val:(Tree)>Int'(X1))
=> ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) ) )
& ( ~ $less(X0,'val:(Tree)>Int'(X1))
=> ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) ) ) ) ) ) )
<=> in(X0,X1) ) ),
inference(true_and_false_elimination,[],[f32]) ).
tff(f32,plain,
~ ! [X0: $int,X1: 'Tree'] :
( searchtree(X1)
=> ( ( ( ( 'empty:Tree' = X1 )
=> $false )
& ( ( 'empty:Tree' != X1 )
=> ( ( ( 'val:(Tree)>Int'(X1) = X0 )
=> $true )
& ( ( 'val:(Tree)>Int'(X1) != X0 )
=> ( ( $less(X0,'val:(Tree)>Int'(X1))
=> ? [X2: 'Tree'] :
( in(X0,X2)
& ( 'left:(Tree)>Tree'(X1) = X2 ) ) )
& ( ~ $less(X0,'val:(Tree)>Int'(X1))
=> ? [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = X3 )
& in(X0,X3) ) ) ) ) ) ) )
<=> in(X0,X1) ) ),
inference(rectify,[],[f9]) ).
tff(f9,negated_conjecture,
~ ! [X4: $int,X5: 'Tree'] :
( searchtree(X5)
=> ( ( ( ( 'empty:Tree' = X5 )
=> $false )
& ( ( 'empty:Tree' != X5 )
=> ( ( ( 'val:(Tree)>Int'(X5) = X4 )
=> $true )
& ( ( 'val:(Tree)>Int'(X5) != X4 )
=> ( ( $less(X4,'val:(Tree)>Int'(X5))
=> ? [X6: 'Tree'] :
( ( 'left:(Tree)>Tree'(X5) = X6 )
& in(X4,X6) ) )
& ( ~ $less(X4,'val:(Tree)>Int'(X5))
=> ? [X7: 'Tree'] :
( ( 'right:(Tree)>Tree'(X5) = X7 )
& in(X4,X7) ) ) ) ) ) ) )
<=> in(X4,X5) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f8,conjecture,
! [X4: $int,X5: 'Tree'] :
( searchtree(X5)
=> ( ( ( ( 'empty:Tree' = X5 )
=> $false )
& ( ( 'empty:Tree' != X5 )
=> ( ( ( 'val:(Tree)>Int'(X5) = X4 )
=> $true )
& ( ( 'val:(Tree)>Int'(X5) != X4 )
=> ( ( $less(X4,'val:(Tree)>Int'(X5))
=> ? [X6: 'Tree'] :
( ( 'left:(Tree)>Tree'(X5) = X6 )
& in(X4,X6) ) )
& ( ~ $less(X4,'val:(Tree)>Int'(X5))
=> ? [X7: 'Tree'] :
( ( 'right:(Tree)>Tree'(X5) = X7 )
& in(X4,X7) ) ) ) ) ) ) )
<=> in(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_007) ).
tff(f297,plain,
( ~ sP0(sK6)
| spl8_24 ),
inference(avatar_component_clause,[],[f295]) ).
tff(f321,plain,
( spl8_4
| spl8_1
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f317,f300,f117,f133]) ).
tff(f317,plain,
( in(sK7,sK6)
| ( 'empty:Tree' = sK6 )
| ~ spl8_25 ),
inference(resolution,[],[f302,f100]) ).
tff(f100,plain,
! [X0: 'Tree',X1: $int] :
( ~ in(X1,'right:(Tree)>Tree'(X0))
| in(X1,X0)
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f67]) ).
tff(f315,plain,
( spl8_3
| spl8_23
| spl8_6 ),
inference(avatar_split_clause,[],[f311,f144,f291,f129]) ).
tff(f311,plain,
( $less('val:(Tree)>Int'(sK6),sK7)
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| spl8_6 ),
inference(resolution,[],[f145,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_149,[]) ).
tff(f145,plain,
( ~ $less(sK7,'val:(Tree)>Int'(sK6))
| spl8_6 ),
inference(avatar_component_clause,[],[f144]) ).
tff(f303,plain,
( spl8_3
| spl8_4
| spl8_25
| spl8_6
| ~ spl8_2
| ~ spl8_7 ),
inference(avatar_split_clause,[],[f186,f149,f121,f144,f300,f133,f129]) ).
tff(f149,plain,
( spl8_7
<=> ( 'right:(Tree)>Tree'(sK6) = sK5(sK6,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
tff(f186,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| in(sK7,'right:(Tree)>Tree'(sK6))
| ( 'empty:Tree' = sK6 )
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ~ spl8_2
| ~ spl8_7 ),
inference(forward_demodulation,[],[f185,f151]) ).
tff(f151,plain,
( ( 'right:(Tree)>Tree'(sK6) = sK5(sK6,sK7) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f149]) ).
tff(f185,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| in(sK7,sK5(sK6,sK7))
| ( 'empty:Tree' = sK6 )
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ~ spl8_2 ),
inference(resolution,[],[f123,f84]) ).
tff(f84,plain,
! [X0: 'Tree',X1: $int] :
( ~ sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| ( 'val:(Tree)>Int'(X0) = X1 )
| $less(X1,'val:(Tree)>Int'(X0))
| in(X1,sK5(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
tff(f123,plain,
( sP1(sK6,sK7)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f289,plain,
( spl8_4
| spl8_1
| ~ spl8_18
| ~ spl8_19 ),
inference(avatar_split_clause,[],[f274,f262,f257,f117,f133]) ).
tff(f257,plain,
( spl8_18
<=> in(sK7,sK4(sK6,sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f262,plain,
( spl8_19
<=> ( 'left:(Tree)>Tree'(sK6) = sK4(sK6,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f274,plain,
( in(sK7,sK6)
| ( 'empty:Tree' = sK6 )
| ~ spl8_18
| ~ spl8_19 ),
inference(resolution,[],[f266,f99]) ).
tff(f99,plain,
! [X0: 'Tree',X1: $int] :
( ~ in(X1,'left:(Tree)>Tree'(X0))
| in(X1,X0)
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f67]) ).
tff(f266,plain,
( in(sK7,'left:(Tree)>Tree'(sK6))
| ~ spl8_18
| ~ spl8_19 ),
inference(backward_demodulation,[],[f259,f264]) ).
tff(f264,plain,
( ( 'left:(Tree)>Tree'(sK6) = sK4(sK6,sK7) )
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f262]) ).
tff(f259,plain,
( in(sK7,sK4(sK6,sK7))
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f257]) ).
tff(f265,plain,
( ~ spl8_2
| spl8_4
| spl8_19
| spl8_3
| ~ spl8_6 ),
inference(avatar_split_clause,[],[f245,f144,f129,f262,f133,f121]) ).
tff(f245,plain,
( ( sK7 = 'val:(Tree)>Int'(sK6) )
| ( 'left:(Tree)>Tree'(sK6) = sK4(sK6,sK7) )
| ( 'empty:Tree' = sK6 )
| ~ sP1(sK6,sK7)
| ~ spl8_6 ),
inference(resolution,[],[f146,f86]) ).
tff(f86,plain,
! [X0: 'Tree',X1: $int] :
( ~ $less(X1,'val:(Tree)>Int'(X0))
| ( 'val:(Tree)>Int'(X0) = X1 )
| ~ sP1(X0,X1)
| ( 'empty:Tree' = X0 )
| ( 'left:(Tree)>Tree'(X0) = sK4(X0,X1) ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f260,plain,
( ~ spl8_2
| spl8_3
| spl8_18
| spl8_4
| ~ spl8_6 ),
inference(avatar_split_clause,[],[f246,f144,f133,f257,f129,f121]) ).
tff(f246,plain,
( ( 'empty:Tree' = sK6 )
| in(sK7,sK4(sK6,sK7))
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ~ sP1(sK6,sK7)
| ~ spl8_6 ),
inference(resolution,[],[f146,f87]) ).
tff(f87,plain,
! [X0: 'Tree',X1: $int] :
( ~ $less(X1,'val:(Tree)>Int'(X0))
| ~ sP1(X0,X1)
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 )
| in(X1,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
tff(f167,plain,
( ~ spl8_1
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f165]) ).
tff(f165,plain,
( $false
| ~ spl8_1
| ~ spl8_4 ),
inference(resolution,[],[f163,f113]) ).
tff(f113,plain,
! [X1: $int] : ~ in(X1,'empty:Tree'),
inference(equality_resolution,[],[f103]) ).
tff(f103,plain,
! [X0: 'Tree',X1: $int] :
( ( 'empty:Tree' != X0 )
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f67]) ).
tff(f163,plain,
( in(sK7,'empty:Tree')
| ~ spl8_1
| ~ spl8_4 ),
inference(forward_demodulation,[],[f119,f135]) ).
tff(f135,plain,
( ( 'empty:Tree' = sK6 )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f162,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f159]) ).
tff(f159,plain,
( $false
| ~ spl8_2
| ~ spl8_4 ),
inference(resolution,[],[f156,f112]) ).
tff(f112,plain,
! [X1: $int] : ~ sP1('empty:Tree',X1),
inference(equality_resolution,[],[f88]) ).
tff(f88,plain,
! [X0: 'Tree',X1: $int] :
( ( 'empty:Tree' != X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
tff(f156,plain,
( sP1('empty:Tree',sK7)
| ~ spl8_2
| ~ spl8_4 ),
inference(backward_demodulation,[],[f123,f135]) ).
tff(f152,plain,
( spl8_7
| spl8_4
| spl8_3
| spl8_6
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f137,f121,f144,f129,f133,f149]) ).
tff(f137,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ( 'empty:Tree' = sK6 )
| ( 'right:(Tree)>Tree'(sK6) = sK5(sK6,sK7) )
| ~ spl8_2 ),
inference(resolution,[],[f123,f85]) ).
tff(f85,plain,
! [X0: 'Tree',X1: $int] :
( ~ sP1(X0,X1)
| ( 'val:(Tree)>Int'(X0) = X1 )
| $less(X1,'val:(Tree)>Int'(X0))
| ( 'empty:Tree' = X0 )
| ( 'right:(Tree)>Tree'(X0) = sK5(X0,X1) ) ),
inference(cnf_transformation,[],[f59]) ).
tff(f136,plain,
( ~ spl8_3
| spl8_4
| spl8_1 ),
inference(avatar_split_clause,[],[f127,f117,f133,f129]) ).
tff(f127,plain,
( ( 'empty:Tree' = sK6 )
| ( sK7 != 'val:(Tree)>Int'(sK6) )
| spl8_1 ),
inference(constrained_resolution,[],[f118,f115]) ).
tff(f115,plain,
! [X0: 'Tree'] :
( in('val:(Tree)>Int'(X0),X0)
| ( 'empty:Tree' = X0 ) ),
inference(equality_resolution,[],[f98]) ).
tff(f98,plain,
! [X0: 'Tree',X1: $int] :
( in(X1,X0)
| ( 'empty:Tree' = X0 )
| ( 'val:(Tree)>Int'(X0) != X1 ) ),
inference(cnf_transformation,[],[f67]) ).
tff(f118,plain,
( ~ in(sK7,sK6)
| spl8_1 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f125,plain,
( ~ spl8_2
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f97,f117,f121]) ).
tff(f97,plain,
( ~ in(sK7,sK6)
| ~ sP1(sK6,sK7) ),
inference(cnf_transformation,[],[f64]) ).
tff(f124,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f96,f121,f117]) ).
tff(f96,plain,
( sP1(sK6,sK7)
| in(sK7,sK6) ),
inference(cnf_transformation,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW678=1 : TPTP v8.1.0. Released v6.4.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 21:01:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.40/0.54 % (32725)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.40/0.54 % (32724)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.40/0.54 % (32726)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.40/0.54 % (32717)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 1.40/0.54 % (32717)Refutation not found, incomplete strategy% (32717)------------------------------
% 1.40/0.54 % (32717)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.54 % (32717)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.54 % (32717)Termination reason: Refutation not found, incomplete strategy
% 1.40/0.54
% 1.40/0.54 % (32717)Memory used [KB]: 5500
% 1.40/0.54 % (32717)Time elapsed: 0.128 s
% 1.40/0.54 % (32717)Instructions burned: 3 (million)
% 1.40/0.54 % (32717)------------------------------
% 1.40/0.54 % (32717)------------------------------
% 1.40/0.54 % (32718)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 1.40/0.54 % (32725)Instruction limit reached!
% 1.40/0.54 % (32725)------------------------------
% 1.40/0.54 % (32725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.40/0.54 % (32725)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.40/0.54 % (32725)Termination reason: Unknown
% 1.40/0.54 % (32725)Termination phase: Property scanning
% 1.40/0.54
% 1.40/0.54 % (32725)Memory used [KB]: 895
% 1.40/0.54 % (32725)Time elapsed: 0.003 s
% 1.40/0.54 % (32725)Instructions burned: 2 (million)
% 1.40/0.54 % (32725)------------------------------
% 1.40/0.54 % (32725)------------------------------
% 1.53/0.55 % (32733)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.53/0.55 % (32734)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/47Mi)
% 1.53/0.55 % (32732)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 1.53/0.55 % (32739)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=41:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/41Mi)
% 1.53/0.55 % (32716)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 1.53/0.56 % (32713)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.53/0.56 % (32713)Instruction limit reached!
% 1.53/0.56 % (32713)------------------------------
% 1.53/0.56 % (32713)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56 % (32713)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56 % (32713)Termination reason: Unknown
% 1.53/0.56 % (32713)Termination phase: Including theory axioms
% 1.53/0.56
% 1.53/0.56 % (32713)Memory used [KB]: 895
% 1.53/0.56 % (32713)Time elapsed: 0.002 s
% 1.53/0.56 % (32713)Instructions burned: 2 (million)
% 1.53/0.56 % (32713)------------------------------
% 1.53/0.56 % (32713)------------------------------
% 1.53/0.56 % (32716)Refutation not found, incomplete strategy% (32716)------------------------------
% 1.53/0.56 % (32716)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56 % (32716)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56 % (32716)Termination reason: Refutation not found, incomplete strategy
% 1.53/0.56
% 1.53/0.56 % (32716)Memory used [KB]: 5500
% 1.53/0.56 % (32716)Time elapsed: 0.133 s
% 1.53/0.56 % (32716)Instructions burned: 4 (million)
% 1.53/0.56 % (32716)------------------------------
% 1.53/0.56 % (32716)------------------------------
% 1.53/0.56 % (32732)Refutation not found, incomplete strategy% (32732)------------------------------
% 1.53/0.56 % (32732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56 % (32732)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56 % (32732)Termination reason: Refutation not found, incomplete strategy
% 1.53/0.56
% 1.53/0.56 % (32732)Memory used [KB]: 1023
% 1.53/0.56 % (32732)Time elapsed: 0.133 s
% 1.53/0.56 % (32732)Instructions burned: 4 (million)
% 1.53/0.56 % (32732)------------------------------
% 1.53/0.56 % (32732)------------------------------
% 1.53/0.56 % (32726)Instruction limit reached!
% 1.53/0.56 % (32726)------------------------------
% 1.53/0.56 % (32726)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56 % (32726)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56 % (32726)Termination reason: Unknown
% 1.53/0.56 % (32726)Termination phase: Property scanning
% 1.53/0.56
% 1.53/0.56 % (32726)Memory used [KB]: 1023
% 1.53/0.56 % (32726)Time elapsed: 0.002 s
% 1.53/0.56 % (32726)Instructions burned: 2 (million)
% 1.53/0.56 % (32726)------------------------------
% 1.53/0.56 % (32726)------------------------------
% 1.53/0.56 % (32738)dis+1011_1:1_bd=off:canc=force:ev=cautious:nwc=5.0:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 1.53/0.56 % (32715)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.53/0.56 % (32729)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.53/0.56 % (32736)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 1.53/0.56 % (32729)Instruction limit reached!
% 1.53/0.56 % (32729)------------------------------
% 1.53/0.56 % (32729)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56 % (32729)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56 % (32729)Termination reason: Unknown
% 1.53/0.56 % (32729)Termination phase: Saturation
% 1.53/0.56
% 1.53/0.56 % (32729)Memory used [KB]: 1023
% 1.53/0.56 % (32729)Time elapsed: 0.003 s
% 1.53/0.56 % (32729)Instructions burned: 3 (million)
% 1.53/0.56 % (32729)------------------------------
% 1.53/0.56 % (32729)------------------------------
% 1.53/0.56 % (32722)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.53/0.56 % (32722)Instruction limit reached!
% 1.53/0.56 % (32722)------------------------------
% 1.53/0.56 % (32722)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.56 % (32722)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.56 % (32722)Termination reason: Unknown
% 1.53/0.56 % (32722)Termination phase: Property scanning
% 1.53/0.56
% 1.53/0.56 % (32722)Memory used [KB]: 1023
% 1.53/0.56 % (32722)Time elapsed: 0.003 s
% 1.53/0.56 % (32722)Instructions burned: 3 (million)
% 1.53/0.56 % (32722)------------------------------
% 1.53/0.56 % (32722)------------------------------
% 1.53/0.57 % (32724)First to succeed.
% 1.53/0.57 % (32724)Refutation found. Thanks to Tanya!
% 1.53/0.57 % SZS status Theorem for theBenchmark
% 1.53/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.53/0.57 % (32724)------------------------------
% 1.53/0.57 % (32724)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.53/0.57 % (32724)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.53/0.57 % (32724)Termination reason: Refutation
% 1.53/0.57
% 1.53/0.57 % (32724)Memory used [KB]: 6012
% 1.53/0.57 % (32724)Time elapsed: 0.140 s
% 1.53/0.57 % (32724)Instructions burned: 15 (million)
% 1.53/0.57 % (32724)------------------------------
% 1.53/0.57 % (32724)------------------------------
% 1.53/0.57 % (32709)Success in time 0.216 s
%------------------------------------------------------------------------------