%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:48:04 PM UTC 2026
% Result : Theorem 2.20s 0.95s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 11 unt; 2 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 115 ( 49 ~; 40 |; 12 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 90 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f9,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(f13,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(f15,axiom,
! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f23,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( subset(relation_dom(X2),X0)
& subset(relation_rng(X2),X1) )
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f28,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(relation_rng(X3),X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
? [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X2,X1)
& subset(relation_rng(X3),X1)
& relation_of2_as_subset(X3,X2,X0) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) )
& ( subset(X2,cartesian_product2(X0,X1))
| ~ relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f37,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,[],[f13]) ).
fof(f38,plain,
( ~ relation_of2_as_subset(sK6,sK5,sK4)
& subset(relation_rng(sK6),sK4)
& relation_of2_as_subset(sK6,sK5,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f29]) ).
fof(f40,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ subset(X2,cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
! [X2,X0,X1] :
( subset(relation_dom(X2),X0)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f53,plain,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f38]) ).
fof(f54,plain,
subset(relation_rng(sK6),sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f55,plain,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f56,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f60,plain,
~ relation_of2(sK6,sK5,sK4),
inference(resolution,[],[f48,f55]) ).
fof(f62,plain,
~ subset(sK6,cartesian_product2(sK5,sK4)),
inference(resolution,[],[f42,f60]) ).
fof(f64,plain,
! [X0] :
( ~ subset(sK6,X0)
| ~ subset(X0,cartesian_product2(sK5,sK4)) ),
inference(resolution,[],[f62,f56]) ).
fof(f72,plain,
( ~ subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4))
| ~ relation(sK6) ),
inference(resolution,[],[f64,f57]) ).
fof(f74,definition,
( spl7_1
<=> relation(sK6) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f76,plain,
( ~ relation(sK6)
| spl7_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl7_2
<=> subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4)) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f80,plain,
( ~ subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4))
| spl7_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f72,f78,f74]) ).
fof(f82,plain,
( ! [X0,X1] : ~ element(sK6,powerset(cartesian_product2(X0,X1)))
| spl7_1 ),
inference(resolution,[],[f76,f40]) ).
fof(f85,plain,
( ! [X0,X1] : ~ relation_of2_as_subset(sK6,X0,X1)
| spl7_1 ),
inference(resolution,[],[f82,f43]) ).
fof(f94,plain,
( $false
| spl7_1 ),
inference(resolution,[],[f85,f53]) ).
fof(f96,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f101,plain,
( ~ subset(relation_dom(sK6),sK5)
| ~ subset(relation_rng(sK6),sK4)
| spl7_2 ),
inference(resolution,[],[f80,f50]) ).
fof(f106,plain,
( ~ subset(relation_dom(sK6),sK5)
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f101,f54]) ).
fof(f109,plain,
( ! [X0] : ~ relation_of2_as_subset(sK6,sK5,X0)
| spl7_2 ),
inference(resolution,[],[f106,f52]) ).
fof(f114,plain,
( $false
| spl7_2 ),
inference(resolution,[],[f109,f53]) ).
fof(f116,plain,
spl7_2,
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(sat_conversion,[],[f81]) ).
cnf(s2,plain,
spl7_1,
inference(sat_conversion,[],[f96]) ).
cnf(s5,plain,
spl7_2,
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s2]) ).
fof(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:26:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.20/0.95 % (4143376)Detected formulas, will run a generic FOF schedule.
% 2.20/0.95 % (4143386)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1994381792:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.20/0.95 % (4143386)First to succeed.
% 2.20/0.95 % (4143386)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4143376"
% 2.20/0.95 % (4143385)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2955915820:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.20/0.95 % (4143384)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3804648406:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.20/0.95 % (4143381)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=324909760:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.20/0.95 % (4143383)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3724417858:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.20/0.95 % (4143382)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1815548121:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.20/0.95 % (4143387)dis-21_1_sil=8000:lcm=predicate:random_seed=1703564710:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.20/0.95 % (4143384)Refutation not found, incomplete strategy
% 2.20/0.95 % (4143384)------------------------------
% 2.20/0.95 % (4143384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/0.95 % (4143384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.95 % (4143384)CaDiCaL version: 2.1.3
% 2.20/0.95 % (4143384)Termination reason: Refutation not found, incomplete strategy
% 2.20/0.95 % (4143384)Time elapsed: 0.001 s
% 2.20/0.95 % (4143384)Peak memory usage: 87 MB
% 2.20/0.95 % (4143385)Refutation not found, incomplete strategy
% 2.20/0.95 % (4143385)------------------------------
% 2.20/0.95 % (4143385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/0.95 % (4143385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.95 % (4143385)CaDiCaL version: 2.1.3
% 2.20/0.95 % (4143385)Termination reason: Refutation not found, incomplete strategy
% 2.20/0.95 % (4143385)Time elapsed: 0.001 s
% 2.20/0.95 % (4143385)Peak memory usage: 87 MB
% 2.20/0.95 % (4143387)Also succeeded, but the first one will report.
% 2.20/0.95 % (4143386)Refutation found. Thanks to Tanya!
% 2.20/0.95 % SZS status Theorem for theBenchmark
% 2.20/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.20/0.95 % (4143386)------------------------------
% 2.20/0.95 % (4143386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/0.95 % (4143386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.95 % (4143386)CaDiCaL version: 2.1.3
% 2.20/0.95 % (4143386)Termination reason: Refutation
% 2.20/0.95 % (4143386)Time elapsed: 0.002 s
% 2.20/0.95 % (4143386)Peak memory usage: 89 MB
% 2.20/0.95 % (4143386)Instructions burned: 3 (million)
% 2.20/0.95 % (4143386)------------------------------
% 2.20/0.95 % (4143386)------------------------------
% 2.20/0.95 % (4143376)Success in time 0.277 s
% 2.20/0.95 % Vampire exiting
%------------------------------------------------------------------------------