%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU044+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:51:50 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 9 unt; 3 def)
% Number of atoms : 285 ( 11 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 313 ( 107 ~; 155 |; 26 &)
% ( 13 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 92 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<=> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<=> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f37,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f60,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f60]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<~> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f66,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<~> ( in(X1,relation_dom(X2))
& in(apply(X2,X1),X0) ) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f67]) ).
fof(f89,plain,
! [X0,X1] :
( ~ relation(X1)
| relation(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f90,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| function(relation_rng_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
( ~ in(apply(sK13,sK12),sK11)
| ~ in(sK12,relation_dom(sK13))
| ~ in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f113,plain,
( in(apply(sK13,sK12),sK11)
| in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f114,plain,
( in(sK12,relation_dom(sK13))
| in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f115,plain,
function(sK13),
inference(cnf_transformation,[],[f66]) ).
fof(f116,plain,
relation(sK13),
inference(cnf_transformation,[],[f66]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1))
| relation_rng_restriction(X0,X2) != X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(X3,relation_dom(X2))
| ~ in(X3,relation_dom(X1))
| relation_rng_restriction(X0,X2) != X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(X1))
| relation_rng_restriction(X0,X2) != X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f128,plain,
! [X2,X3,X0] :
( ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(equality_resolution,[],[f125]) ).
fof(f129,plain,
! [X2,X3,X0] :
( ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| in(X3,relation_dom(X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(equality_resolution,[],[f124]) ).
fof(f130,plain,
! [X2,X3,X0] :
( ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(equality_resolution,[],[f123]) ).
fof(f143,plain,
! [X0,X1] :
( ~ relation(relation_rng_restriction(X0,X1))
| relation(X1) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f145,plain,
! [X0,X1] :
( ~ function(relation_rng_restriction(X0,X1))
| relation(X1)
| function(X1) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f157,plain,
~ relation(sK13),
inference(consistent_polarity_flipping,[],[f116]) ).
fof(f158,plain,
~ function(sK13),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f159,plain,
( ~ in(sK12,relation_dom(sK13))
| ~ in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f160,plain,
( ~ in(apply(sK13,sK12),sK11)
| ~ in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
inference(consistent_polarity_flipping,[],[f113]) ).
fof(f161,plain,
( in(apply(sK13,sK12),sK11)
| in(sK12,relation_dom(sK13))
| in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f163,plain,
! [X2,X3,X0] :
( function(relation_rng_restriction(X0,X2))
| relation(relation_rng_restriction(X0,X2))
| function(X2)
| relation(X2)
| in(apply(X2,X3),X0)
| in(X3,relation_dom(X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(consistent_polarity_flipping,[],[f128]) ).
fof(f164,plain,
! [X2,X3,X0] :
( function(relation_rng_restriction(X0,X2))
| relation(relation_rng_restriction(X0,X2))
| function(X2)
| relation(X2)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(consistent_polarity_flipping,[],[f129]) ).
fof(f165,plain,
! [X2,X3,X0] :
( function(relation_rng_restriction(X0,X2))
| relation(relation_rng_restriction(X0,X2))
| function(X2)
| relation(X2)
| ~ in(apply(X2,X3),X0)
| in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(consistent_polarity_flipping,[],[f130]) ).
fof(f173,definition,
( spl16_1
<=> in(sK12,relation_dom(relation_rng_restriction(sK11,sK13))) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f174,plain,
( ~ in(sK12,relation_dom(relation_rng_restriction(sK11,sK13)))
| spl16_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f175,plain,
( in(sK12,relation_dom(relation_rng_restriction(sK11,sK13)))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f177,definition,
( spl16_2
<=> in(sK12,relation_dom(sK13)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f178,plain,
( ~ in(sK12,relation_dom(sK13))
| spl16_2 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f181,definition,
( spl16_3
<=> in(apply(sK13,sK12),sK11) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f182,plain,
( ~ in(apply(sK13,sK12),sK11)
| spl16_3 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f183,plain,
( in(apply(sK13,sK12),sK11)
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
( spl16_1
| spl16_2
| spl16_3 ),
inference(avatar_split_clause,[],[f161,f181,f177,f173]) ).
fof(f185,plain,
( ~ spl16_1
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f160,f181,f173]) ).
fof(f186,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f159,f177,f173]) ).
fof(f230,plain,
! [X2,X3,X0] :
( relation(relation_rng_restriction(X0,X2))
| function(X2)
| relation(X2)
| ~ in(X3,relation_dom(X2))
| in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(forward_subsumption_resolution,[],[f164,f145]) ).
fof(f231,plain,
! [X2,X3,X0] :
( in(X3,relation_dom(relation_rng_restriction(X0,X2)))
| relation(X2)
| ~ in(X3,relation_dom(X2))
| function(X2) ),
inference(forward_subsumption_resolution,[],[f230,f143]) ).
fof(f235,plain,
( relation(sK13)
| ~ in(sK12,relation_dom(sK13))
| function(sK13)
| spl16_1 ),
inference(resolution,[],[f231,f174]) ).
fof(f237,plain,
( ~ in(sK12,relation_dom(sK13))
| function(sK13)
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f235,f157]) ).
fof(f242,plain,
( ~ in(sK12,relation_dom(sK13))
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f237,f158]) ).
fof(f243,plain,
( ~ spl16_2
| spl16_1 ),
inference(avatar_split_clause,[],[f242,f173,f177]) ).
fof(f257,plain,
! [X2,X3,X0] :
( relation(relation_rng_restriction(X0,X2))
| function(X2)
| relation(X2)
| ~ in(apply(X2,X3),X0)
| in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(forward_subsumption_resolution,[],[f165,f145]) ).
fof(f258,plain,
! [X2,X3,X0] :
( in(X3,relation_dom(relation_rng_restriction(X0,X2)))
| relation(X2)
| ~ in(apply(X2,X3),X0)
| function(X2) ),
inference(forward_subsumption_resolution,[],[f257,f143]) ).
fof(f259,plain,
( relation(sK13)
| ~ in(apply(sK13,sK12),sK11)
| function(sK13)
| spl16_1 ),
inference(resolution,[],[f258,f174]) ).
fof(f261,plain,
( ~ in(apply(sK13,sK12),sK11)
| function(sK13)
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f259,f157]) ).
fof(f262,plain,
( function(sK13)
| spl16_1
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f261,f183]) ).
fof(f263,plain,
( $false
| spl16_1
| ~ spl16_3 ),
inference(forward_subsumption_resolution,[],[f262,f158]) ).
fof(f264,plain,
( spl16_1
| ~ spl16_3 ),
inference(avatar_contradiction_clause,[],[f263]) ).
fof(f282,plain,
! [X2,X3,X0] :
( relation(relation_rng_restriction(X0,X2))
| function(X2)
| relation(X2)
| in(apply(X2,X3),X0)
| in(X3,relation_dom(X2))
| ~ in(X3,relation_dom(relation_rng_restriction(X0,X2))) ),
inference(forward_subsumption_resolution,[],[f163,f145]) ).
fof(f283,plain,
! [X2,X3,X0] :
( ~ in(X3,relation_dom(relation_rng_restriction(X0,X2)))
| relation(X2)
| in(apply(X2,X3),X0)
| in(X3,relation_dom(X2))
| function(X2) ),
inference(forward_subsumption_resolution,[],[f282,f143]) ).
fof(f293,plain,
( relation(sK13)
| in(apply(sK13,sK12),sK11)
| in(sK12,relation_dom(sK13))
| function(sK13)
| ~ spl16_1 ),
inference(resolution,[],[f283,f175]) ).
fof(f297,plain,
( in(apply(sK13,sK12),sK11)
| in(sK12,relation_dom(sK13))
| function(sK13)
| ~ spl16_1 ),
inference(forward_subsumption_resolution,[],[f293,f157]) ).
fof(f298,plain,
( in(sK12,relation_dom(sK13))
| function(sK13)
| ~ spl16_1
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f297,f182]) ).
fof(f299,plain,
( function(sK13)
| ~ spl16_1
| spl16_2
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f298,f178]) ).
fof(f300,plain,
( $false
| ~ spl16_1
| spl16_2
| spl16_3 ),
inference(forward_subsumption_resolution,[],[f299,f158]) ).
fof(f301,plain,
( ~ spl16_1
| spl16_2
| spl16_3 ),
inference(avatar_contradiction_clause,[],[f300]) ).
cnf(s1,plain,
( spl16_1
| spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f184]) ).
cnf(s2,plain,
( ~ spl16_1
| ~ spl16_3 ),
inference(sat_conversion,[],[f185]) ).
cnf(s3,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f186]) ).
cnf(s7,plain,
( spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f243]) ).
cnf(s10,plain,
( spl16_1
| ~ spl16_3 ),
inference(sat_conversion,[],[f264]) ).
cnf(s14,plain,
( ~ spl16_1
| spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f301]) ).
cnf(s15,plain,
spl16_1,
inference(rat,[],[s1,s7,s10]) ).
cnf(s16,plain,
~ spl16_2,
inference(rat,[],[s3,s15]) ).
cnf(s17,plain,
~ spl16_3,
inference(rat,[],[s2,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s14,s15,s17,s16]) ).
fof(f302,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU044+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:32:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (4179876)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (4179882)% WARNING: option uhcvi not known.
% 0.11/0.45 % (4179882)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2319209354:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (4179882) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4179876-4179882"...
% 0.11/0.45 % (4179882)...printing done.
% 0.11/0.45 % (4179882)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (4179882)------------------------------
% 0.11/0.45 % (4179882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (4179882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (4179882)CaDiCaL version: 2.1.3
% 0.11/0.45 % (4179882)Termination reason: Refutation
% 0.11/0.45 % (4179882)Time elapsed: 0.004 s
% 0.11/0.45 % (4179882)Peak memory usage: 12 MB
% 0.11/0.45 % (4179882)Instructions burned: 8 (million)
% 0.11/0.45 % (4179876)Success in time 0.036 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------