%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW679_1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:40:38 PM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 154 ( 41 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 163 ( 51 ~; 45 |; 33 &)
% ( 8 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 25 ( 14 atm; 0 fun; 0 num; 11 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 23 !; 6 ?; 29 :)
% 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,
sK0: 'Tree' > $int ).
tff(func_def_10,type,
sK1: 'Tree' > $int ).
tff(func_def_11,type,
sK2: 'Tree' ).
tff(func_def_12,type,
sK3: $int ).
tff(pred_def_1,type,
searchtree: 'Tree' > $o ).
tff(pred_def_2,type,
in: ( $int * 'Tree' ) > $o ).
tff(f7,axiom,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ( X0 = 'empty:Tree' )
=> $true )
& ( ( X0 != 'empty:Tree' )
=> ( searchtree('left:(Tree)>Tree'(X0))
& searchtree('right:(Tree)>Tree'(X0))
& ! [X1: $int] :
( in(X1,'left:(Tree)>Tree'(X0))
=> $lesseq(X1,'val:(Tree)>Int'(X0)) )
& ! [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
=> $greater(X1,'val:(Tree)>Int'(X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_006) ).
tff(f8,conjecture,
! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( X0 = 'empty:Tree' )
=> $true )
& ( ( X0 != 'empty:Tree' )
=> ( ( ( X1 = 'val:(Tree)>Int'(X0) )
=> $true )
& ( ( X1 != 'val:(Tree)>Int'(X0) )
=> ( ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( ( X2 = 'left:(Tree)>Tree'(X0) )
& searchtree(X2) ) )
& ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( ( X3 = 'right:(Tree)>Tree'(X0) )
& searchtree(X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_007) ).
tff(f9,negated_conjecture,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( X0 = 'empty:Tree' )
=> $true )
& ( ( X0 != 'empty:Tree' )
=> ( ( ( X1 = 'val:(Tree)>Int'(X0) )
=> $true )
& ( ( X1 != 'val:(Tree)>Int'(X0) )
=> ( ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( ( X2 = 'left:(Tree)>Tree'(X0) )
& searchtree(X2) ) )
& ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( ( X3 = 'right:(Tree)>Tree'(X0) )
& searchtree(X3) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
tff(f10,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ( X0 = 'empty:Tree' )
=> $true )
& ( ( X0 != 'empty:Tree' )
=> ( searchtree('left:(Tree)>Tree'(X0))
& searchtree('right:(Tree)>Tree'(X0))
& ! [X1: $int] :
( in(X1,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X1) )
& ! [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X1) ) ) ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f23,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ( X0 = 'empty:Tree' )
=> $true )
& ( ( X0 != 'empty:Tree' )
=> ( 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(rectify,[],[f10]) ).
tff(f26,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( $true
| ( 'empty:Tree' != X0 ) )
& ( ( searchtree('left:(Tree)>Tree'(X0))
& searchtree('right:(Tree)>Tree'(X0))
& ! [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'left:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'right:(Tree)>Tree'(X0)) ) )
| ( 'empty:Tree' = X0 ) ) ) ),
inference(ennf_transformation,[],[f23]) ).
tff(f27,plain,
? [X0: 'Tree',X1: $int] :
( ( ( $false
& ( X0 = 'empty:Tree' ) )
| ( ( ( $false
& ( X1 = 'val:(Tree)>Int'(X0) ) )
| ( ( ( ! [X2: 'Tree'] :
( ( 'left:(Tree)>Tree'(X0) != X2 )
| ~ searchtree(X2) )
& $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ( 'right:(Tree)>Tree'(X0) != X3 )
| ~ searchtree(X3) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( X1 != 'val:(Tree)>Int'(X0) ) ) )
& ( X0 != 'empty:Tree' ) ) )
& searchtree(X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f49,plain,
! [X0: 'Tree'] :
( searchtree('right:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f50,plain,
! [X0: 'Tree'] :
( searchtree('left:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f58,plain,
! [X2: 'Tree',X3: 'Tree'] :
( ~ searchtree(X3)
| ( 'right:(Tree)>Tree'(sK2) != X3 )
| ~ searchtree(X2)
| ( 'left:(Tree)>Tree'(sK2) != X2 )
| ( sK3 = 'val:(Tree)>Int'(sK2) ) ),
inference(cnf_transformation,[],[f27]) ).
tff(f64,plain,
sK3 != 'val:(Tree)>Int'(sK2),
inference(cnf_transformation,[],[f27]) ).
tff(f65,plain,
'empty:Tree' != sK2,
inference(cnf_transformation,[],[f27]) ).
tff(f66,plain,
searchtree(sK2),
inference(cnf_transformation,[],[f27]) ).
tff(f74,plain,
! [X2: 'Tree'] :
( ~ searchtree('right:(Tree)>Tree'(sK2))
| ~ searchtree(X2)
| ( 'left:(Tree)>Tree'(sK2) != X2 )
| ( sK3 = 'val:(Tree)>Int'(sK2) ) ),
inference(equality_resolution,[],[f58]) ).
tff(f75,plain,
( ~ searchtree('right:(Tree)>Tree'(sK2))
| ~ searchtree('left:(Tree)>Tree'(sK2))
| ( sK3 = 'val:(Tree)>Int'(sK2) ) ),
inference(equality_resolution,[],[f74]) ).
tff(f87,definition,
( spl4_1
<=> ( sK3 = 'val:(Tree)>Int'(sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f91,definition,
( spl4_2
<=> searchtree('left:(Tree)>Tree'(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f93,plain,
( ~ searchtree('left:(Tree)>Tree'(sK2))
| spl4_2 ),
inference(avatar_component_clause,[],[f91]) ).
tff(f100,definition,
( spl4_4
<=> ( 'empty:Tree' = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f101,plain,
( ( 'empty:Tree' != sK2 )
| spl4_4 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f107,definition,
( spl4_5
<=> searchtree('right:(Tree)>Tree'(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f109,plain,
( ~ searchtree('right:(Tree)>Tree'(sK2))
| spl4_5 ),
inference(avatar_component_clause,[],[f107]) ).
tff(f113,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f75,f107,f91,f87]) ).
tff(f119,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f64,f87]) ).
tff(f120,plain,
~ spl4_4,
inference(avatar_split_clause,[],[f65,f100]) ).
tff(f144,plain,
( ( 'empty:Tree' = sK2 )
| ~ searchtree(sK2)
| spl4_5 ),
inference(resolution,[],[f49,f109]) ).
tff(f147,plain,
( ~ searchtree(sK2)
| spl4_4
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f144,f101]) ).
tff(f148,plain,
( $false
| spl4_4
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f147,f66]) ).
tff(f149,plain,
( spl4_4
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f148]) ).
tff(f150,plain,
( ( 'empty:Tree' = sK2 )
| ~ searchtree(sK2)
| spl4_2 ),
inference(resolution,[],[f50,f93]) ).
tff(f153,plain,
( ~ searchtree(sK2)
| spl4_2
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f150,f101]) ).
tff(f154,plain,
( $false
| spl4_2
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f153,f66]) ).
tff(f155,plain,
( spl4_2
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f154]) ).
cnf(s8,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f113]) ).
cnf(s14,plain,
~ spl4_1,
inference(sat_conversion,[],[f119]) ).
cnf(s15,plain,
~ spl4_4,
inference(sat_conversion,[],[f120]) ).
cnf(s16,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f149]) ).
cnf(s17,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f155]) ).
cnf(s18,plain,
spl4_2,
inference(rat,[],[s17,s15]) ).
cnf(s19,plain,
spl4_5,
inference(rat,[],[s16,s15]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s8,s19,s18,s14]) ).
tff(f156,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW679_1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 14:25:24 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (2287849)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (2287858)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=418770196:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.26 % (2287855)% WARNING: option uhcvi not known.
% 0.09/0.26 % (2287858) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2287849-2287858"...
% 0.09/0.26 % (2287858)...printing done.
% 0.09/0.26 % (2287858)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (2287858)------------------------------
% 0.09/0.26 % (2287858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (2287858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (2287858)CaDiCaL version: 2.1.3
% 0.09/0.26 % (2287858)Termination reason: Refutation
% 0.09/0.26 % (2287858)Time elapsed: 0.003 s
% 0.09/0.26 % (2287858)Peak memory usage: 12 MB
% 0.09/0.26 % (2287858)Instructions burned: 6 (million)
% 0.09/0.26 % (2287849)Success in time 0.034 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------