TSTP Solution File: SWW678_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW678_1 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 07:27:55 EDT 2024
% Result : Theorem 1.26s 0.57s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 45
% Syntax : Number of formulae : 201 ( 6 unt; 18 typ; 0 def)
% Number of atoms : 828 ( 191 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 958 ( 313 ~; 391 |; 160 &)
% ( 34 <=>; 57 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 205 ( 106 atm; 0 fun; 0 num; 99 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 22 ( 14 >; 8 *; 0 +; 0 <<)
% Number of predicates : 24 ( 18 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 209 ( 165 !; 44 ?; 209 :)
% 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,
sK4: ( $int * 'Tree' ) > 'Tree' ).
tff(func_def_10,type,
sK5: ( $int * 'Tree' ) > 'Tree' ).
tff(func_def_11,type,
sK6: 'Tree' ).
tff(func_def_12,type,
sK7: $int ).
tff(func_def_13,type,
sK8: 'Tree' > $int ).
tff(func_def_14,type,
sK9: 'Tree' > $int ).
tff(pred_def_1,type,
searchtree: 'Tree' > $o ).
tff(pred_def_2,type,
in: ( $int * 'Tree' ) > $o ).
tff(pred_def_6,type,
sP0: ( $int * 'Tree' ) > $o ).
tff(pred_def_7,type,
sP1: ( 'Tree' * $int ) > $o ).
tff(pred_def_8,type,
sP2: 'Tree' > $o ).
tff(pred_def_9,type,
sP3: ( 'Tree' * $int ) > $o ).
tff(f3603,plain,
$false,
inference(avatar_sat_refutation,[],[f130,f131,f2817,f2821,f2824,f2979,f2988,f3003,f3033,f3037,f3039,f3060,f3074,f3151,f3162,f3436,f3456,f3461,f3545,f3575,f3579,f3602]) ).
tff(f3602,plain,
( ~ spl10_1
| spl10_3
| spl10_4
| spl10_7
| spl10_26
| ~ spl10_54 ),
inference(avatar_contradiction_clause,[],[f3601]) ).
tff(f3601,plain,
( $false
| ~ spl10_1
| spl10_3
| spl10_4
| spl10_7
| spl10_26
| ~ spl10_54 ),
inference(subsumption_resolution,[],[f3600,f3543]) ).
tff(f3543,plain,
( sP0(sK7,sK6)
| ~ spl10_54 ),
inference(avatar_component_clause,[],[f3542]) ).
tff(f3542,plain,
( spl10_54
<=> sP0(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_54])]) ).
tff(f3600,plain,
( ~ sP0(sK7,sK6)
| ~ spl10_1
| spl10_3
| spl10_4
| spl10_7
| spl10_26 ),
inference(subsumption_resolution,[],[f3599,f2974]) ).
tff(f2974,plain,
( ~ $less(sK7,'val:(Tree)>Int'(sK6))
| spl10_26 ),
inference(avatar_component_clause,[],[f2972]) ).
tff(f2972,plain,
( spl10_26
<=> $less(sK7,'val:(Tree)>Int'(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_26])]) ).
tff(f3599,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| ~ sP0(sK7,sK6)
| ~ spl10_1
| spl10_3
| spl10_4
| spl10_7
| spl10_26 ),
inference(subsumption_resolution,[],[f3598,f2801]) ).
tff(f2801,plain,
( ~ in(sK7,'right:(Tree)>Tree'(sK6))
| spl10_4 ),
inference(avatar_component_clause,[],[f2799]) ).
tff(f2799,plain,
( spl10_4
<=> in(sK7,'right:(Tree)>Tree'(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).
tff(f3598,plain,
( in(sK7,'right:(Tree)>Tree'(sK6))
| $less(sK7,'val:(Tree)>Int'(sK6))
| ~ sP0(sK7,sK6)
| ~ spl10_1
| spl10_3
| spl10_7
| spl10_26 ),
inference(superposition,[],[f79,f3578]) ).
tff(f3578,plain,
( ( 'right:(Tree)>Tree'(sK6) = sK4(sK7,sK6) )
| ~ spl10_1
| spl10_3
| spl10_7
| spl10_26 ),
inference(subsumption_resolution,[],[f3547,f2974]) ).
tff(f3547,plain,
( ( 'right:(Tree)>Tree'(sK6) = sK4(sK7,sK6) )
| $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl10_1
| spl10_3
| spl10_7 ),
inference(subsumption_resolution,[],[f3546,f2796]) ).
tff(f2796,plain,
( ( 'empty:Tree' != sK6 )
| spl10_3 ),
inference(avatar_component_clause,[],[f2795]) ).
tff(f2795,plain,
( spl10_3
<=> ( 'empty:Tree' = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).
tff(f3546,plain,
( ( 'right:(Tree)>Tree'(sK6) = sK4(sK7,sK6) )
| ( 'empty:Tree' = sK6 )
| $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl10_1
| spl10_7 ),
inference(subsumption_resolution,[],[f3499,f2815]) ).
tff(f2815,plain,
( ( sK7 != 'val:(Tree)>Int'(sK6) )
| spl10_7 ),
inference(avatar_component_clause,[],[f2814]) ).
tff(f2814,plain,
( spl10_7
<=> ( sK7 = 'val:(Tree)>Int'(sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).
tff(f3499,plain,
( ( 'right:(Tree)>Tree'(sK6) = sK4(sK7,sK6) )
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ( 'empty:Tree' = sK6 )
| $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl10_1 ),
inference(resolution,[],[f684,f124]) ).
tff(f124,plain,
( sP1(sK6,sK7)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f123]) ).
tff(f123,plain,
( spl10_1
<=> sP1(sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
tff(f684,plain,
! [X0: $int,X1: 'Tree'] :
( ~ sP1(X1,X0)
| ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) )
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| $less(X0,'val:(Tree)>Int'(X1)) ),
inference(resolution,[],[f78,f72]) ).
tff(f72,plain,
! [X0: 'Tree',X1: $int] :
( sP0(X1,X0)
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: 'Tree',X1: $int] :
( ( sP1(X0,X1)
| ( ~ sP0(X1,X0)
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( ( ( sP0(X1,X0)
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f47]) ).
tff(f47,plain,
! [X0: 'Tree',X1: $int] :
( ( sP1(X0,X1)
| ( ~ sP0(X1,X0)
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( ( ( sP0(X1,X0)
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: 'Tree',X1: $int] :
( sP1(X0,X1)
<=> ( ( sP0(X1,X0)
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f78,plain,
! [X0: $int,X1: 'Tree'] :
( ~ sP0(X0,X1)
| $less(X0,'val:(Tree)>Int'(X1))
| ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: $int,X1: 'Tree'] :
( ( sP0(X0,X1)
| ( ! [X2: 'Tree'] :
( ~ in(X0,X2)
| ( 'right:(Tree)>Tree'(X1) != X2 ) )
& ~ $less(X0,'val:(Tree)>Int'(X1)) )
| ( ! [X3: 'Tree'] :
( ~ in(X0,X3)
| ( 'left:(Tree)>Tree'(X1) != X3 ) )
& $less(X0,'val:(Tree)>Int'(X1)) ) )
& ( ( ( ( in(X0,sK4(X0,X1))
& ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) ) )
| $less(X0,'val:(Tree)>Int'(X1)) )
& ( ( in(X0,sK5(X0,X1))
& ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f51,f53,f52]) ).
tff(f52,plain,
! [X0: $int,X1: 'Tree'] :
( ? [X4: 'Tree'] :
( in(X0,X4)
& ( 'right:(Tree)>Tree'(X1) = X4 ) )
=> ( in(X0,sK4(X0,X1))
& ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f53,plain,
! [X0: $int,X1: 'Tree'] :
( ? [X5: 'Tree'] :
( in(X0,X5)
& ( 'left:(Tree)>Tree'(X1) = X5 ) )
=> ( in(X0,sK5(X0,X1))
& ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f51,plain,
! [X0: $int,X1: 'Tree'] :
( ( sP0(X0,X1)
| ( ! [X2: 'Tree'] :
( ~ in(X0,X2)
| ( 'right:(Tree)>Tree'(X1) != X2 ) )
& ~ $less(X0,'val:(Tree)>Int'(X1)) )
| ( ! [X3: 'Tree'] :
( ~ in(X0,X3)
| ( 'left:(Tree)>Tree'(X1) != X3 ) )
& $less(X0,'val:(Tree)>Int'(X1)) ) )
& ( ( ( ? [X4: 'Tree'] :
( in(X0,X4)
& ( 'right:(Tree)>Tree'(X1) = X4 ) )
| $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X5: 'Tree'] :
( in(X0,X5)
& ( 'left:(Tree)>Tree'(X1) = X5 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f50]) ).
tff(f50,plain,
! [X1: $int,X0: 'Tree'] :
( ( sP0(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)) ) )
& ( ( ( ? [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)) ) )
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f49]) ).
tff(f49,plain,
! [X1: $int,X0: 'Tree'] :
( ( sP0(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)) ) )
& ( ( ( ? [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)) ) )
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X1: $int,X0: 'Tree'] :
( sP0(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)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f79,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,sK4(X0,X1))
| $less(X0,'val:(Tree)>Int'(X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f3579,plain,
( ~ spl10_4
| spl10_3
| spl10_6 ),
inference(avatar_split_clause,[],[f3473,f2810,f2795,f2799]) ).
tff(f2810,plain,
( spl10_6
<=> sP3(sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).
tff(f3473,plain,
( ~ in(sK7,'right:(Tree)>Tree'(sK6))
| spl10_3
| spl10_6 ),
inference(subsumption_resolution,[],[f3470,f2796]) ).
tff(f3470,plain,
( ~ in(sK7,'right:(Tree)>Tree'(sK6))
| ( 'empty:Tree' = sK6 )
| spl10_6 ),
inference(resolution,[],[f2812,f104]) ).
tff(f104,plain,
! [X0: 'Tree',X1: $int] :
( sP3(X0,X1)
| ~ in(X1,'right:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f69]) ).
tff(f69,plain,
! [X0: 'Tree',X1: $int] :
( ( sP3(X0,X1)
| ( ~ in(X1,'right:(Tree)>Tree'(X0))
& ~ in(X1,'left:(Tree)>Tree'(X0))
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( ( ( in(X1,'right:(Tree)>Tree'(X0))
| in(X1,'left:(Tree)>Tree'(X0))
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f68]) ).
tff(f68,plain,
! [X1: 'Tree',X0: $int] :
( ( sP3(X1,X0)
| ( ~ 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 ) )
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f67]) ).
tff(f67,plain,
! [X1: 'Tree',X0: $int] :
( ( sP3(X1,X0)
| ( ~ 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 ) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f45]) ).
tff(f45,plain,
! [X1: 'Tree',X0: $int] :
( sP3(X1,X0)
<=> ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f2812,plain,
( ~ sP3(sK6,sK7)
| spl10_6 ),
inference(avatar_component_clause,[],[f2810]) ).
tff(f3575,plain,
( ~ spl10_1
| spl10_3
| spl10_7
| spl10_54 ),
inference(avatar_contradiction_clause,[],[f3574]) ).
tff(f3574,plain,
( $false
| ~ spl10_1
| spl10_3
| spl10_7
| spl10_54 ),
inference(subsumption_resolution,[],[f3573,f124]) ).
tff(f3573,plain,
( ~ sP1(sK6,sK7)
| spl10_3
| spl10_7
| spl10_54 ),
inference(subsumption_resolution,[],[f3572,f2796]) ).
tff(f3572,plain,
( ( 'empty:Tree' = sK6 )
| ~ sP1(sK6,sK7)
| spl10_7
| spl10_54 ),
inference(subsumption_resolution,[],[f3568,f2815]) ).
tff(f3568,plain,
( ( sK7 = 'val:(Tree)>Int'(sK6) )
| ( 'empty:Tree' = sK6 )
| ~ sP1(sK6,sK7)
| spl10_54 ),
inference(resolution,[],[f3544,f72]) ).
tff(f3544,plain,
( ~ sP0(sK7,sK6)
| spl10_54 ),
inference(avatar_component_clause,[],[f3542]) ).
tff(f3545,plain,
( ~ spl10_54
| ~ spl10_26
| spl10_5
| ~ spl10_27 ),
inference(avatar_split_clause,[],[f3531,f2976,f2803,f2972,f3542]) ).
tff(f2803,plain,
( spl10_5
<=> in(sK7,'left:(Tree)>Tree'(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).
tff(f2976,plain,
( spl10_27
<=> ( 'left:(Tree)>Tree'(sK6) = sK5(sK7,sK6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_27])]) ).
tff(f3531,plain,
( ~ $less(sK7,'val:(Tree)>Int'(sK6))
| ~ sP0(sK7,sK6)
| spl10_5
| ~ spl10_27 ),
inference(subsumption_resolution,[],[f3530,f2805]) ).
tff(f2805,plain,
( ~ in(sK7,'left:(Tree)>Tree'(sK6))
| spl10_5 ),
inference(avatar_component_clause,[],[f2803]) ).
tff(f3530,plain,
( in(sK7,'left:(Tree)>Tree'(sK6))
| ~ $less(sK7,'val:(Tree)>Int'(sK6))
| ~ sP0(sK7,sK6)
| ~ spl10_27 ),
inference(superposition,[],[f77,f2978]) ).
tff(f2978,plain,
( ( 'left:(Tree)>Tree'(sK6) = sK5(sK7,sK6) )
| ~ spl10_27 ),
inference(avatar_component_clause,[],[f2976]) ).
tff(f77,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,sK5(X0,X1))
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f3461,plain,
( ~ spl10_6
| spl10_2 ),
inference(avatar_split_clause,[],[f3458,f127,f2810]) ).
tff(f127,plain,
( spl10_2
<=> in(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
tff(f3458,plain,
( ~ sP3(sK6,sK7)
| spl10_2 ),
inference(resolution,[],[f129,f106]) ).
tff(f106,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
| ~ sP3(X1,X0) ),
inference(cnf_transformation,[],[f70]) ).
tff(f70,plain,
! [X0: $int,X1: 'Tree'] :
( ( in(X0,X1)
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> sP3(X1,X0) ),
inference(definition_folding,[],[f39,f45]) ).
tff(f39,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,[],[f38]) ).
tff(f38,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,[],[f30]) ).
tff(f30,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,[],[f29]) ).
tff(f29,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,[],[f28]) ).
tff(f28,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/benchmark/theBenchmark.p',formula_005) ).
tff(f129,plain,
( ~ in(sK7,sK6)
| spl10_2 ),
inference(avatar_component_clause,[],[f127]) ).
tff(f3456,plain,
( spl10_1
| spl10_3
| ~ spl10_5
| ~ spl10_26 ),
inference(avatar_contradiction_clause,[],[f3455]) ).
tff(f3455,plain,
( $false
| spl10_1
| spl10_3
| ~ spl10_5
| ~ spl10_26 ),
inference(subsumption_resolution,[],[f3454,f2796]) ).
tff(f3454,plain,
( ( 'empty:Tree' = sK6 )
| spl10_1
| ~ spl10_5
| ~ spl10_26 ),
inference(subsumption_resolution,[],[f3453,f2973]) ).
tff(f2973,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl10_26 ),
inference(avatar_component_clause,[],[f2972]) ).
tff(f3453,plain,
( ~ $less(sK7,'val:(Tree)>Int'(sK6))
| ( 'empty:Tree' = sK6 )
| spl10_1
| ~ spl10_5 ),
inference(subsumption_resolution,[],[f3451,f2804]) ).
tff(f2804,plain,
( in(sK7,'left:(Tree)>Tree'(sK6))
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f2803]) ).
tff(f3451,plain,
( ~ in(sK7,'left:(Tree)>Tree'(sK6))
| ~ $less(sK7,'val:(Tree)>Int'(sK6))
| ( 'empty:Tree' = sK6 )
| spl10_1 ),
inference(resolution,[],[f533,f125]) ).
tff(f125,plain,
( ~ sP1(sK6,sK7)
| spl10_1 ),
inference(avatar_component_clause,[],[f123]) ).
tff(f533,plain,
! [X0: $int,X1: 'Tree'] :
( sP1(X1,X0)
| ~ in(X0,'left:(Tree)>Tree'(X1))
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(resolution,[],[f117,f75]) ).
tff(f75,plain,
! [X0: 'Tree',X1: $int] :
( ~ sP0(X1,X0)
| sP1(X0,X1)
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f117,plain,
! [X0: $int,X1: 'Tree'] :
( sP0(X0,X1)
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ~ in(X0,'left:(Tree)>Tree'(X1)) ),
inference(equality_resolution,[],[f81]) ).
tff(f81,plain,
! [X3: 'Tree',X0: $int,X1: 'Tree'] :
( sP0(X0,X1)
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ~ in(X0,X3)
| ( 'left:(Tree)>Tree'(X1) != X3 ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f3436,plain,
( ~ spl10_4
| spl10_26
| spl10_1
| spl10_3 ),
inference(avatar_split_clause,[],[f3435,f2795,f123,f2972,f2799]) ).
tff(f3435,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| ~ in(sK7,'right:(Tree)>Tree'(sK6))
| spl10_1
| spl10_3 ),
inference(subsumption_resolution,[],[f3429,f2796]) ).
tff(f3429,plain,
( $less(sK7,'val:(Tree)>Int'(sK6))
| ~ in(sK7,'right:(Tree)>Tree'(sK6))
| ( 'empty:Tree' = sK6 )
| spl10_1 ),
inference(resolution,[],[f506,f125]) ).
tff(f506,plain,
! [X0: $int,X1: 'Tree'] :
( sP1(X1,X0)
| $less(X0,'val:(Tree)>Int'(X1))
| ~ in(X0,'right:(Tree)>Tree'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(resolution,[],[f116,f75]) ).
tff(f116,plain,
! [X0: $int,X1: 'Tree'] :
( sP0(X0,X1)
| ~ in(X0,'right:(Tree)>Tree'(X1))
| $less(X0,'val:(Tree)>Int'(X1)) ),
inference(equality_resolution,[],[f82]) ).
tff(f82,plain,
! [X2: 'Tree',X0: $int,X1: 'Tree'] :
( sP0(X0,X1)
| ~ in(X0,X2)
| ( 'right:(Tree)>Tree'(X1) != X2 )
| $less(X0,'val:(Tree)>Int'(X1)) ),
inference(cnf_transformation,[],[f54]) ).
tff(f3162,plain,
( spl10_3
| spl10_32 ),
inference(avatar_contradiction_clause,[],[f3161]) ).
tff(f3161,plain,
( $false
| spl10_3
| spl10_32 ),
inference(subsumption_resolution,[],[f3160,f84]) ).
tff(f84,plain,
searchtree(sK6),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
( ( ~ in(sK7,sK6)
| ~ sP1(sK6,sK7) )
& ( in(sK7,sK6)
| sP1(sK6,sK7) )
& searchtree(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f56,f57]) ).
tff(f57,plain,
( ? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ~ sP1(X0,X1) )
& ( in(X1,X0)
| sP1(X0,X1) )
& searchtree(X0) )
=> ( ( ~ in(sK7,sK6)
| ~ sP1(sK6,sK7) )
& ( in(sK7,sK6)
| sP1(sK6,sK7) )
& searchtree(sK6) ) ),
introduced(choice_axiom,[]) ).
tff(f56,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ~ sP1(X0,X1) )
& ( in(X1,X0)
| sP1(X0,X1) )
& searchtree(X0) ),
inference(flattening,[],[f55]) ).
tff(f55,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ~ sP1(X0,X1) )
& ( in(X1,X0)
| sP1(X0,X1) )
& searchtree(X0) ),
inference(nnf_transformation,[],[f42]) ).
tff(f42,plain,
? [X0: 'Tree',X1: $int] :
( ( sP1(X0,X1)
<~> in(X1,X0) )
& searchtree(X0) ),
inference(definition_folding,[],[f36,f41,f40]) ).
tff(f36,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,[],[f35]) ).
tff(f35,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,[],[f25]) ).
tff(f25,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,[],[f24]) ).
tff(f24,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,[],[f23]) ).
tff(f23,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/benchmark/theBenchmark.p',formula_007) ).
tff(f3160,plain,
( ~ searchtree(sK6)
| spl10_3
| spl10_32 ),
inference(subsumption_resolution,[],[f3158,f2796]) ).
tff(f3158,plain,
( ( 'empty:Tree' = sK6 )
| ~ searchtree(sK6)
| spl10_32 ),
inference(resolution,[],[f96,f3059]) ).
tff(f3059,plain,
( ~ sP2(sK6)
| spl10_32 ),
inference(avatar_component_clause,[],[f3057]) ).
tff(f3057,plain,
( spl10_32
<=> sP2(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_32])]) ).
tff(f96,plain,
! [X0: 'Tree'] :
( sP2(X0)
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f66,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ( ~ sP2(X0)
& ( 'empty:Tree' != X0 ) ) )
& ( sP2(X0)
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ) ),
inference(flattening,[],[f65]) ).
tff(f65,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ( ~ sP2(X0)
& ( 'empty:Tree' != X0 ) ) )
& ( sP2(X0)
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ) ),
inference(nnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( sP2(X0)
| ( 'empty:Tree' = X0 ) ) ),
inference(definition_folding,[],[f37,f43]) ).
tff(f43,plain,
! [X0: 'Tree'] :
( sP2(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)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
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 ) ) ),
inference(ennf_transformation,[],[f27]) ).
tff(f27,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,[],[f26]) ).
tff(f26,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/benchmark/theBenchmark.p',formula_006) ).
tff(f3151,plain,
( ~ spl10_28
| ~ spl10_26 ),
inference(avatar_split_clause,[],[f3148,f2972,f2985]) ).
tff(f2985,plain,
( spl10_28
<=> $less('val:(Tree)>Int'(sK6),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_28])]) ).
tff(f3148,plain,
( ~ $less('val:(Tree)>Int'(sK6),sK7)
| ~ spl10_26 ),
inference(resolution,[],[f2973,f187]) ).
tff(f187,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(resolution,[],[f17,f16]) ).
tff(f16,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(theory_axiom_143,[]) ).
tff(f3074,plain,
( ~ spl10_32
| spl10_28
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f3072,f2799,f2985,f3057]) ).
tff(f3072,plain,
( $less('val:(Tree)>Int'(sK6),sK7)
| ~ sP2(sK6)
| ~ spl10_4 ),
inference(resolution,[],[f2800,f91]) ).
tff(f91,plain,
! [X3: $int,X0: 'Tree'] :
( ~ in(X3,'right:(Tree)>Tree'(X0))
| $less('val:(Tree)>Int'(X0),X3)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f64,plain,
! [X0: 'Tree'] :
( ( sP2(X0)
| ( ~ $less('val:(Tree)>Int'(X0),sK8(X0))
& in(sK8(X0),'right:(Tree)>Tree'(X0)) )
| ( $less('val:(Tree)>Int'(X0),sK9(X0))
& in(sK9(X0),'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>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)) )
| ~ sP2(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f61,f63,f62]) ).
tff(f62,plain,
! [X0: 'Tree'] :
( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
=> ( ~ $less('val:(Tree)>Int'(X0),sK8(X0))
& in(sK8(X0),'right:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f63,plain,
! [X0: 'Tree'] :
( ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
=> ( $less('val:(Tree)>Int'(X0),sK9(X0))
& in(sK9(X0),'left:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f61,plain,
! [X0: 'Tree'] :
( ( sP2(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)) )
& ( ( ! [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)) )
| ~ sP2(X0) ) ),
inference(rectify,[],[f60]) ).
tff(f60,plain,
! [X0: 'Tree'] :
( ( sP2(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)) )
& ( ( ! [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)) )
| ~ sP2(X0) ) ),
inference(flattening,[],[f59]) ).
tff(f59,plain,
! [X0: 'Tree'] :
( ( sP2(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)) )
& ( ( ! [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)) )
| ~ sP2(X0) ) ),
inference(nnf_transformation,[],[f43]) ).
tff(f2800,plain,
( in(sK7,'right:(Tree)>Tree'(sK6))
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f2799]) ).
tff(f3060,plain,
( ~ spl10_32
| ~ spl10_28
| ~ spl10_5 ),
inference(avatar_split_clause,[],[f3052,f2803,f2985,f3057]) ).
tff(f3052,plain,
( ~ $less('val:(Tree)>Int'(sK6),sK7)
| ~ sP2(sK6)
| ~ spl10_5 ),
inference(resolution,[],[f2804,f90]) ).
tff(f90,plain,
! [X0: 'Tree',X4: $int] :
( ~ in(X4,'left:(Tree)>Tree'(X0))
| ~ $less('val:(Tree)>Int'(X0),X4)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f3039,plain,
( spl10_3
| spl10_1
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f3038,f2814,f123,f2795]) ).
tff(f3038,plain,
( ( 'empty:Tree' = sK6 )
| spl10_1
| ~ spl10_7 ),
inference(subsumption_resolution,[],[f2996,f125]) ).
tff(f2996,plain,
( sP1(sK6,sK7)
| ( 'empty:Tree' = sK6 )
| ~ spl10_7 ),
inference(superposition,[],[f111,f2816]) ).
tff(f2816,plain,
( ( sK7 = 'val:(Tree)>Int'(sK6) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f2814]) ).
tff(f111,plain,
! [X0: 'Tree'] :
( sP1(X0,'val:(Tree)>Int'(X0))
| ( 'empty:Tree' = X0 ) ),
inference(equality_resolution,[],[f74]) ).
tff(f74,plain,
! [X0: 'Tree',X1: $int] :
( sP1(X0,X1)
| ( 'val:(Tree)>Int'(X0) != X1 )
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f48]) ).
tff(f3037,plain,
( ~ spl10_2
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f3036]) ).
tff(f3036,plain,
( $false
| ~ spl10_2
| ~ spl10_3 ),
inference(subsumption_resolution,[],[f128,f3017]) ).
tff(f3017,plain,
( ! [X0: $int] : ~ in(X0,sK6)
| ~ spl10_3 ),
inference(backward_demodulation,[],[f133,f2797]) ).
tff(f2797,plain,
( ( 'empty:Tree' = sK6 )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f2795]) ).
tff(f133,plain,
! [X0: $int] : ~ in(X0,'empty:Tree'),
inference(resolution,[],[f105,f121]) ).
tff(f121,plain,
! [X1: $int] : ~ sP3('empty:Tree',X1),
inference(equality_resolution,[],[f99]) ).
tff(f99,plain,
! [X0: 'Tree',X1: $int] :
( ( 'empty:Tree' != X0 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tff(f105,plain,
! [X0: $int,X1: 'Tree'] :
( sP3(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
tff(f128,plain,
( in(sK7,sK6)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f127]) ).
tff(f3033,plain,
( ~ spl10_1
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f3032]) ).
tff(f3032,plain,
( $false
| ~ spl10_1
| ~ spl10_3 ),
inference(resolution,[],[f3013,f124]) ).
tff(f3013,plain,
( ! [X1: $int] : ~ sP1(sK6,X1)
| ~ spl10_3 ),
inference(backward_demodulation,[],[f113,f2797]) ).
tff(f113,plain,
! [X1: $int] : ~ sP1('empty:Tree',X1),
inference(equality_resolution,[],[f71]) ).
tff(f71,plain,
! [X0: 'Tree',X1: $int] :
( ( 'empty:Tree' != X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tff(f3003,plain,
( spl10_3
| spl10_6
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f3002,f2814,f2810,f2795]) ).
tff(f3002,plain,
( ( 'empty:Tree' = sK6 )
| spl10_6
| ~ spl10_7 ),
inference(subsumption_resolution,[],[f2995,f2812]) ).
tff(f2995,plain,
( sP3(sK6,sK7)
| ( 'empty:Tree' = sK6 )
| ~ spl10_7 ),
inference(superposition,[],[f119,f2816]) ).
tff(f119,plain,
! [X0: 'Tree'] :
( sP3(X0,'val:(Tree)>Int'(X0))
| ( 'empty:Tree' = X0 ) ),
inference(equality_resolution,[],[f102]) ).
tff(f102,plain,
! [X0: 'Tree',X1: $int] :
( sP3(X0,X1)
| ( 'val:(Tree)>Int'(X0) != X1 )
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f69]) ).
tff(f2988,plain,
( spl10_7
| spl10_28
| spl10_26 ),
inference(avatar_split_clause,[],[f2981,f2972,f2985,f2814]) ).
tff(f2981,plain,
( $less('val:(Tree)>Int'(sK6),sK7)
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| spl10_26 ),
inference(resolution,[],[f2974,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f2979,plain,
( ~ spl10_26
| spl10_3
| spl10_7
| spl10_27
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f2966,f123,f2976,f2814,f2795,f2972]) ).
tff(f2966,plain,
( ( 'left:(Tree)>Tree'(sK6) = sK5(sK7,sK6) )
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ( 'empty:Tree' = sK6 )
| ~ $less(sK7,'val:(Tree)>Int'(sK6))
| ~ spl10_1 ),
inference(resolution,[],[f653,f124]) ).
tff(f653,plain,
! [X0: $int,X1: 'Tree'] :
( ~ sP1(X1,X0)
| ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) )
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ $less(X0,'val:(Tree)>Int'(X1)) ),
inference(resolution,[],[f76,f72]) ).
tff(f76,plain,
! [X0: $int,X1: 'Tree'] :
( ~ sP0(X0,X1)
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) ) ),
inference(cnf_transformation,[],[f54]) ).
tff(f2824,plain,
( ~ spl10_2
| spl10_6 ),
inference(avatar_split_clause,[],[f2820,f2810,f127]) ).
tff(f2820,plain,
( ~ in(sK7,sK6)
| spl10_6 ),
inference(resolution,[],[f2812,f105]) ).
tff(f2821,plain,
( spl10_3
| ~ spl10_5
| spl10_6 ),
inference(avatar_split_clause,[],[f2819,f2810,f2803,f2795]) ).
tff(f2819,plain,
( ~ in(sK7,'left:(Tree)>Tree'(sK6))
| ( 'empty:Tree' = sK6 )
| spl10_6 ),
inference(resolution,[],[f2812,f103]) ).
tff(f103,plain,
! [X0: 'Tree',X1: $int] :
( sP3(X0,X1)
| ~ in(X1,'left:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 ) ),
inference(cnf_transformation,[],[f69]) ).
tff(f2817,plain,
( ~ spl10_6
| spl10_3
| spl10_7
| spl10_5
| spl10_4 ),
inference(avatar_split_clause,[],[f2807,f2799,f2803,f2814,f2795,f2810]) ).
tff(f2807,plain,
( in(sK7,'left:(Tree)>Tree'(sK6))
| ( sK7 = 'val:(Tree)>Int'(sK6) )
| ( 'empty:Tree' = sK6 )
| ~ sP3(sK6,sK7)
| spl10_4 ),
inference(resolution,[],[f2801,f100]) ).
tff(f100,plain,
! [X0: 'Tree',X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
| in(X1,'left:(Tree)>Tree'(X0))
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tff(f131,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f85,f127,f123]) ).
tff(f85,plain,
( in(sK7,sK6)
| sP1(sK6,sK7) ),
inference(cnf_transformation,[],[f58]) ).
tff(f130,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f86,f127,f123]) ).
tff(f86,plain,
( ~ in(sK7,sK6)
| ~ sP1(sK6,sK7) ),
inference(cnf_transformation,[],[f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWW678_1 : TPTP v8.2.0. Released v6.4.0.
% 0.15/0.17 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.38 % Computer : n008.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sat May 18 19:30:23 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.22/0.39 % (31966)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.40 % (31969)WARNING: value z3 for option sas not known
% 0.22/0.40 % (31969)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.40 % (31973)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.40 % (31970)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.40 % (31972)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.40 % (31971)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.40 % (31968)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.41 % (31967)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41 % (31967)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.41 % (31970)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.41 % (31968)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.41 % (31967)Terminated due to inappropriate strategy.
% 0.22/0.41 % (31967)------------------------------
% 0.22/0.41 % (31967)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (31968)Terminated due to inappropriate strategy.
% 0.22/0.41 % (31968)------------------------------
% 0.22/0.41 % (31968)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (31967)Termination reason: Inappropriate
% 0.22/0.41 % (31968)Termination reason: Inappropriate
% 0.22/0.41
% 0.22/0.41
% 0.22/0.41 % (31968)Memory used [KB]: 807
% 0.22/0.41 % (31967)Memory used [KB]: 807
% 0.22/0.41 % (31968)Time elapsed: 0.004 s
% 0.22/0.41 % (31967)Time elapsed: 0.004 s
% 0.22/0.41 % (31967)Instructions burned: 5 (million)
% 0.22/0.41 % (31968)Instructions burned: 5 (million)
% 0.22/0.41 % (31970)Terminated due to inappropriate strategy.
% 0.22/0.41 % (31970)------------------------------
% 0.22/0.41 % (31970)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (31970)Termination reason: Inappropriate
% 0.22/0.41
% 0.22/0.41 % (31970)Memory used [KB]: 807
% 0.22/0.41 % (31970)Time elapsed: 0.004 s
% 0.22/0.41 % (31970)Instructions burned: 5 (million)
% 0.22/0.41 % (31968)------------------------------
% 0.22/0.41 % (31968)------------------------------
% 0.22/0.41 % (31967)------------------------------
% 0.22/0.41 % (31967)------------------------------
% 0.22/0.41 % (31970)------------------------------
% 0.22/0.41 % (31970)------------------------------
% 0.22/0.43 % (31975)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.43 % (31974)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.43 % (31976)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.43 % (31974)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.43 % (31974)Terminated due to inappropriate strategy.
% 0.22/0.43 % (31974)------------------------------
% 0.22/0.43 % (31974)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43 % (31974)Termination reason: Inappropriate
% 0.22/0.43
% 0.22/0.43 % (31974)Memory used [KB]: 804
% 0.22/0.43 % (31974)Time elapsed: 0.003 s
% 0.22/0.43 % (31974)Instructions burned: 4 (million)
% 0.22/0.43 % (31974)------------------------------
% 0.22/0.43 % (31974)------------------------------
% 0.22/0.45 % (31977)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.26/0.56 % (31976)First to succeed.
% 1.26/0.57 % (31976)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31966"
% 1.26/0.57 % (31976)Refutation found. Thanks to Tanya!
% 1.26/0.57 % SZS status Theorem for theBenchmark
% 1.26/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.57 % (31976)------------------------------
% 1.26/0.57 % (31976)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.26/0.57 % (31976)Termination reason: Refutation
% 1.26/0.57
% 1.26/0.57 % (31976)Memory used [KB]: 2014
% 1.26/0.57 % (31976)Time elapsed: 0.141 s
% 1.26/0.57 % (31976)Instructions burned: 225 (million)
% 1.26/0.57 % (31966)Success in time 0.178 s
%------------------------------------------------------------------------------