%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:52:28 PM UTC 2026
% Result : Theorem 0.44s 0.47s
% Output : Refutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 64 ( 13 unt; 1 def)
% Number of atoms : 228 ( 53 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 267 ( 103 ~; 113 |; 25 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 92 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f16,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f26,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(f43,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f45,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(f46,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,X0)
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f57,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f64,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f65,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f64]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f69]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f74]) ).
fof(f77,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f78,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,X0)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f77]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| empty_set = X2
| apply(X0,X1) != X2 ),
inference(cnf_transformation,[],[f58]) ).
fof(f91,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f103,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X1,X0)
| ~ in(X1,relation_dom(X2))
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3)
| relation_dom_restriction(X2,X0) != X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f137,plain,
function(sK12),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
relation(sK12),
inference(cnf_transformation,[],[f78]) ).
fof(f139,plain,
in(sK11,sK10),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
apply(relation_dom_restriction(sK12,sK10),sK11) != apply(sK12,sK11),
inference(cnf_transformation,[],[f78]) ).
fof(f146,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[],[f89]) ).
fof(f150,plain,
! [X2,X3,X0] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(equality_resolution,[],[f134]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0)
| apply(X0,X1) = empty_set ),
inference(consistent_polarity_flipping,[],[f146]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ in(X1,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| in(X1,X0)
| in(X1,relation_dom(X2))
| ~ function(X2) ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f161,plain,
! [X2,X3,X0] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(consistent_polarity_flipping,[],[f150]) ).
fof(f163,plain,
~ in(sK11,sK10),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f314,plain,
! [X2,X3,X0] :
( ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(forward_subsumption_resolution,[],[f161,f103]) ).
fof(f315,plain,
! [X2,X3,X0] :
( in(X3,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| apply(X2,X3) = apply(relation_dom_restriction(X2,X0),X3) ),
inference(forward_subsumption_resolution,[],[f314,f91]) ).
fof(f318,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
| ~ relation(relation_dom_restriction(X0,X2))
| ~ function(relation_dom_restriction(X0,X2))
| empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
inference(resolution,[],[f315,f152]) ).
fof(f322,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
| ~ function(relation_dom_restriction(X0,X2))
| empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
inference(forward_subsumption_resolution,[],[f318,f91]) ).
fof(f324,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,X1) = apply(relation_dom_restriction(X0,X2),X1)
| empty_set = apply(relation_dom_restriction(X0,X2),X1) ),
inference(forward_subsumption_resolution,[],[f322,f103]) ).
fof(f845,plain,
! [X0,X1] :
( ~ relation(sK12)
| apply(sK12,X0) = apply(relation_dom_restriction(sK12,X1),X0)
| empty_set = apply(relation_dom_restriction(sK12,X1),X0) ),
inference(resolution,[],[f324,f137]) ).
fof(f846,plain,
! [X0,X1] :
( apply(sK12,X0) = apply(relation_dom_restriction(sK12,X1),X0)
| empty_set = apply(relation_dom_restriction(sK12,X1),X0) ),
inference(forward_subsumption_resolution,[],[f845,f138]) ).
fof(f1318,plain,
( apply(sK12,sK11) != apply(sK12,sK11)
| empty_set = apply(relation_dom_restriction(sK12,sK10),sK11) ),
inference(superposition,[],[f140,f846]) ).
fof(f1323,plain,
empty_set = apply(relation_dom_restriction(sK12,sK10),sK11),
inference(trivial_inequality_removal,[],[f1318]) ).
fof(f1328,plain,
empty_set != apply(sK12,sK11),
inference(superposition,[],[f140,f1323]) ).
fof(f1334,definition,
( spl13_35
<=> in(sK11,relation_dom(relation_dom_restriction(sK12,sK10))) ),
introduced(definition,[new_symbols(definition,[spl13_35])],[avatar_definition]) ).
fof(f1335,plain,
( ~ in(sK11,relation_dom(relation_dom_restriction(sK12,sK10)))
| spl13_35 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1336,plain,
( in(sK11,relation_dom(relation_dom_restriction(sK12,sK10)))
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1420,plain,
( ~ relation(sK12)
| in(sK11,sK10)
| in(sK11,relation_dom(sK12))
| ~ function(sK12)
| ~ spl13_35 ),
inference(resolution,[],[f1336,f156]) ).
fof(f1424,plain,
( in(sK11,sK10)
| in(sK11,relation_dom(sK12))
| ~ function(sK12)
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1420,f138]) ).
fof(f1425,plain,
( in(sK11,relation_dom(sK12))
| ~ function(sK12)
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1424,f163]) ).
fof(f1426,plain,
( in(sK11,relation_dom(sK12))
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1425,f137]) ).
fof(f1466,plain,
( ~ relation(sK12)
| ~ function(sK12)
| empty_set = apply(sK12,sK11)
| ~ spl13_35 ),
inference(resolution,[],[f1426,f152]) ).
fof(f1469,plain,
( ~ function(sK12)
| empty_set = apply(sK12,sK11)
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1466,f138]) ).
fof(f1470,plain,
( empty_set = apply(sK12,sK11)
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1469,f137]) ).
fof(f1471,plain,
( $false
| ~ spl13_35 ),
inference(forward_subsumption_resolution,[],[f1470,f1328]) ).
fof(f1472,plain,
~ spl13_35,
inference(avatar_contradiction_clause,[],[f1471]) ).
fof(f1474,plain,
( ~ relation(sK12)
| ~ function(sK12)
| apply(relation_dom_restriction(sK12,sK10),sK11) = apply(sK12,sK11)
| spl13_35 ),
inference(resolution,[],[f1335,f315]) ).
fof(f1489,plain,
( ~ function(sK12)
| apply(relation_dom_restriction(sK12,sK10),sK11) = apply(sK12,sK11)
| spl13_35 ),
inference(forward_subsumption_resolution,[],[f1474,f138]) ).
fof(f1491,plain,
( apply(relation_dom_restriction(sK12,sK10),sK11) = apply(sK12,sK11)
| spl13_35 ),
inference(forward_subsumption_resolution,[],[f1489,f137]) ).
fof(f1493,plain,
( $false
| spl13_35 ),
inference(forward_subsumption_resolution,[],[f1491,f140]) ).
fof(f1494,plain,
spl13_35,
inference(avatar_contradiction_clause,[],[f1493]) ).
cnf(s37,plain,
~ spl13_35,
inference(sat_conversion,[],[f1472]) ).
cnf(s41,plain,
spl13_35,
inference(sat_conversion,[],[f1494]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s37,s41]) ).
fof(f1495,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:10:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.44/0.47 % (3650528)Will run a generic schedule for satisfiability detection.
% 0.44/0.47 % (3650535)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1838882787:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.44/0.47 % (3650534)% WARNING: option uhcvi not known.
% 0.44/0.47 % (3650533)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3371327101_2999 on theBenchmark for (2999ds/0Mi)
% 0.44/0.47 % (3650534)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1993601051:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.44/0.47 % (3650536)dis+10_1_sil=32000:sp=arity:random_seed=1543347259:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.44/0.47 % (3650537)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2330899609:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.44/0.47 % (3650538)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=732158346:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.44/0.47 % (3650539)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=498368405:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.44/0.47 % TRYING [1]
% 0.44/0.47 % TRYING [2]
% 0.44/0.47 % TRYING [3]
% 0.44/0.47 % TRYING [4]
% 0.44/0.47 % (3650534) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3650528-3650534"...
% 0.44/0.47 % (3650536) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3650528-3650536"...
% 0.44/0.47 % (3650534)...printing done.
% 0.44/0.47 % (3650536)...printing done.
% 0.44/0.47 % (3650534)Refutation found. Thanks to Tanya!
% 0.44/0.47 % SZS status Theorem for theBenchmark
% 0.44/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.44/0.47 % (3650534)------------------------------
% 0.44/0.47 % (3650534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.44/0.47 % (3650534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.44/0.47 % (3650534)CaDiCaL version: 2.1.3
% 0.44/0.47 % (3650534)Termination reason: Refutation
% 0.44/0.47 % (3650534)Time elapsed: 0.039 s
% 0.44/0.47 % (3650534)Peak memory usage: 13 MB
% 0.44/0.47 % (3650534)Instructions burned: 56 (million)
% 0.44/0.47 % (3650528)Success in time 0.077 s
% 0.44/0.47 % Vampire exiting
%------------------------------------------------------------------------------