%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU290+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:52:44 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 17 unt; 2 def)
% Number of atoms : 224 ( 70 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 254 ( 90 ~; 89 |; 48 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 95 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( ( ( X1 = empty_set
=> X0 = empty_set )
=> ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) ) )
& ( X1 = empty_set
=> ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f7,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f44,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f45,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f53,conjecture,
! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( in(X2,X0)
=> ( X1 = empty_set
| in(apply(X3,X2),relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
fof(f54,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) )
=> ( in(X2,X0)
=> ( X1 = empty_set
| in(apply(X3,X2),relation_rng(X3)) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f68,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f4]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( ( quasi_total(X2,X0,X1)
<=> X0 = relation_dom_as_subset(X0,X1,X2) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( quasi_total(X2,X0,X1)
<=> X2 = empty_set )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f73]) ).
fof(f76,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f86,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f95,plain,
? [X0,X1,X2,X3] :
( empty_set != X1
& ~ in(apply(X3,X2),relation_rng(X3))
& in(X2,X0)
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f96,plain,
? [X0,X1,X2,X3] :
( empty_set != X1
& ~ in(apply(X3,X2),relation_rng(X3))
& in(X2,X0)
& function(X3)
& quasi_total(X3,X0,X1)
& relation_of2_as_subset(X3,X0,X1) ),
inference(flattening,[],[f95]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( ( ( ( quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) != X0 )
& ( X0 = relation_dom_as_subset(X0,X1,X2)
| ~ quasi_total(X2,X0,X1) ) )
| ( empty_set != X0
& X1 = empty_set ) )
& ( X0 = empty_set
| ( ( quasi_total(X2,X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| ~ quasi_total(X2,X0,X1) ) )
| empty_set != X1 ) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f74]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK0(X0,X1) )
| ~ in(sK0(X0,X1),X1) )
& ( ( in(sK1(X0,X1),relation_dom(X0))
& sK0(X0,X1) = apply(X0,sK1(X0,X1)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK2(X0,X5),relation_dom(X0))
& apply(X0,sK2(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f101]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f121,plain,
( empty_set != sK21
& ~ in(apply(sK23,sK22),relation_rng(sK23))
& in(sK22,sK20)
& function(sK23)
& quasi_total(sK23,sK20,sK21)
& relation_of2_as_subset(sK23,sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23)],[f96]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ quasi_total(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = X0
| empty_set = X1
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f136,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f141,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f198,plain,
relation_of2_as_subset(sK23,sK20,sK21),
inference(cnf_transformation,[],[f121]) ).
fof(f199,plain,
quasi_total(sK23,sK20,sK21),
inference(cnf_transformation,[],[f121]) ).
fof(f200,plain,
function(sK23),
inference(cnf_transformation,[],[f121]) ).
fof(f201,plain,
in(sK22,sK20),
inference(cnf_transformation,[],[f121]) ).
fof(f202,plain,
~ in(apply(sK23,sK22),relation_rng(sK23)),
inference(cnf_transformation,[],[f121]) ).
fof(f203,plain,
empty_set != sK21,
inference(cnf_transformation,[],[f121]) ).
fof(f211,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f136]) ).
fof(f212,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f211]) ).
fof(f295,plain,
relation_of2(sK23,sK20,sK21),
inference(resolution,[],[f189,f198]) ).
fof(f329,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f141,f125]) ).
fof(f348,plain,
relation_dom_as_subset(sK20,sK21,sK23) = relation_dom(sK23),
inference(resolution,[],[f188,f295]) ).
fof(f360,plain,
( ~ in(sK22,relation_dom(sK23))
| ~ relation(sK23)
| ~ function(sK23) ),
inference(resolution,[],[f212,f202]) ).
fof(f366,plain,
( ~ in(sK22,relation_dom(sK23))
| ~ relation(sK23) ),
inference(forward_subsumption_resolution,[],[f360,f200]) ).
fof(f369,definition,
( spl24_3
<=> relation(sK23) ),
introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition]) ).
fof(f373,definition,
( spl24_4
<=> in(sK22,relation_dom(sK23)) ),
introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition]) ).
fof(f375,plain,
( ~ in(sK22,relation_dom(sK23))
| spl24_4 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f376,plain,
( ~ spl24_3
| ~ spl24_4 ),
inference(avatar_split_clause,[],[f366,f373,f369]) ).
fof(f389,plain,
( sK20 = relation_dom_as_subset(sK20,sK21,sK23)
| empty_set = sK21
| ~ relation_of2_as_subset(sK23,sK20,sK21) ),
inference(resolution,[],[f130,f199]) ).
fof(f391,plain,
( sK20 = relation_dom_as_subset(sK20,sK21,sK23)
| ~ relation_of2_as_subset(sK23,sK20,sK21) ),
inference(forward_subsumption_resolution,[],[f389,f203]) ).
fof(f392,plain,
sK20 = relation_dom_as_subset(sK20,sK21,sK23),
inference(forward_subsumption_resolution,[],[f391,f198]) ).
fof(f393,plain,
sK20 = relation_dom(sK23),
inference(superposition,[],[f392,f348]) ).
fof(f504,plain,
relation(sK23),
inference(resolution,[],[f329,f198]) ).
fof(f507,plain,
( ~ in(sK22,sK20)
| spl24_4 ),
inference(forward_demodulation,[],[f375,f393]) ).
fof(f512,plain,
spl24_3,
inference(avatar_split_clause,[],[f504,f369]) ).
fof(f513,plain,
( $false
| spl24_4 ),
inference(forward_subsumption_resolution,[],[f507,f201]) ).
fof(f514,plain,
spl24_4,
inference(avatar_contradiction_clause,[],[f513]) ).
cnf(s3,plain,
( ~ spl24_3
| ~ spl24_4 ),
inference(sat_conversion,[],[f376]) ).
cnf(s8,plain,
spl24_3,
inference(sat_conversion,[],[f512]) ).
cnf(s9,plain,
spl24_4,
inference(sat_conversion,[],[f514]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s3,s9,s8]) ).
fof(f531,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU290+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:27:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.47 % (3201210)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3201217)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3764436214:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3201216)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3201215)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1373313681_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3201216)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1229776592:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3201218)dis+10_1_sil=32000:sp=arity:random_seed=1142754518:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3201219)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=202206817:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3201221)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4119894854:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (3201220)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1973900291:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (3201218) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3201210-3201218"...
% 0.16/0.47 % (3201218)...printing done.
% 0.16/0.47 % (3201218)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3201218)------------------------------
% 0.16/0.47 % (3201218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3201218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3201218)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3201218)Termination reason: Refutation
% 0.16/0.47 % (3201218)Time elapsed: 0.011 s
% 0.16/0.47 % (3201218)Peak memory usage: 12 MB
% 0.16/0.47 % (3201218)Instructions burned: 14 (million)
% 0.16/0.47 % (3201210)Success in time 0.046 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------