%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU263+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 : n012.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 12:52:38 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 13 unt; 2 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 121 ( 52 ~; 47 |; 8 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 113 ( 0 sgn 105 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f43,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(f45,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
subset(relation_rng(sK6),sK4),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation(X2) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation_of2_as_subset(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f59,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f61,plain,
relation_of2_as_subset(sK6,sK5,sK4),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f62,plain,
~ relation_of2_as_subset(sK6,sK5,sK3),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f63,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| relation(X0) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f70,plain,
~ relation_of2(sK6,sK5,sK4),
inference(resolution,[],[f58,f61]) ).
fof(f72,plain,
subset(relation_dom(sK6),sK5),
inference(resolution,[],[f59,f62]) ).
fof(f94,plain,
! [X0,X1] :
( ~ subset(cartesian_product2(relation_dom(X0),relation_rng(X0)),X1)
| relation(X0)
| subset(X0,X1) ),
inference(resolution,[],[f63,f49]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[],[f54,f53]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ subset(relation_dom(X0),X1)
| subset(X0,cartesian_product2(X1,X2))
| relation(X0)
| ~ subset(relation_rng(X0),X2) ),
inference(resolution,[],[f94,f43]) ).
fof(f291,plain,
! [X0] :
( subset(sK6,cartesian_product2(sK5,X0))
| relation(sK6)
| ~ subset(relation_rng(sK6),X0) ),
inference(resolution,[],[f120,f72]) ).
fof(f302,definition,
( spl7_12
<=> relation(sK6) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
fof(f304,plain,
( relation(sK6)
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f310,definition,
( spl7_14
<=> ! [X0] :
( subset(sK6,cartesian_product2(sK5,X0))
| ~ subset(relation_rng(sK6),X0) ) ),
introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition]) ).
fof(f311,plain,
( ! [X0] :
( subset(sK6,cartesian_product2(sK5,X0))
| ~ subset(relation_rng(sK6),X0) )
| ~ spl7_14 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( spl7_12
| spl7_14 ),
inference(avatar_split_clause,[],[f291,f310,f302]) ).
fof(f314,plain,
( ! [X0,X1] : relation_of2_as_subset(sK6,X0,X1)
| ~ spl7_12 ),
inference(resolution,[],[f304,f95]) ).
fof(f316,plain,
( $false
| ~ spl7_12 ),
inference(backward_subsumption_resolution,[],[f62,f314]) ).
fof(f318,plain,
~ spl7_12,
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f417,plain,
( ! [X0] :
( relation_of2(sK6,sK5,X0)
| ~ subset(relation_rng(sK6),X0) )
| ~ spl7_14 ),
inference(resolution,[],[f311,f34]) ).
fof(f454,plain,
( ~ subset(relation_rng(sK6),sK4)
| ~ spl7_14 ),
inference(resolution,[],[f417,f70]) ).
fof(f460,plain,
( $false
| ~ spl7_14 ),
inference(forward_subsumption_resolution,[],[f454,f47]) ).
fof(f461,plain,
~ spl7_14,
inference(avatar_contradiction_clause,[],[f460]) ).
cnf(s11,plain,
( spl7_12
| spl7_14 ),
inference(sat_conversion,[],[f312]) ).
cnf(s12,plain,
~ spl7_12,
inference(sat_conversion,[],[f318]) ).
cnf(s15,plain,
~ spl7_14,
inference(sat_conversion,[],[f461]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s11,s15,s12]) ).
fof(f462,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 28 04:23:04 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.32 Running first-order model finding
% 0.07/0.32 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
% 0.07/0.36 % (3011522)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (3011528)% WARNING: option uhcvi not known.
% 0.07/0.36 % (3011532)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1193282009:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % (3011531)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=696131121:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % (3011530)dis+10_1_sil=32000:sp=arity:random_seed=1775766081:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (3011527)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3818138419_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (3011529)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2568645818:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (3011528)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3118351825:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (3011533)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4003721293:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % TRYING [2]
% 0.07/0.36 % TRYING [3]
% 0.07/0.36 % (3011528) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3011522-3011528"...
% 0.07/0.36 % (3011528)...printing done.
% 0.07/0.36 % (3011528)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (3011528)------------------------------
% 0.07/0.36 % (3011528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (3011528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (3011528)CaDiCaL version: 2.1.3
% 0.07/0.36 % (3011528)Termination reason: Refutation
% 0.07/0.36 % (3011528)Time elapsed: 0.006 s
% 0.07/0.36 % (3011528)Peak memory usage: 12 MB
% 0.07/0.36 % (3011528)Instructions burned: 15 (million)
% 0.07/0.36 % (3011522)Success in time 0.031 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------