%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU219+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:52:26 PM UTC 2026
% Result : Theorem 0.29s 0.46s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 13 unt; 2 def)
% Number of atoms : 90 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 31 ~; 29 |; 13 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f36,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f51,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f51]) ).
fof(f70,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(relation_inverse(X0))
& relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,plain,
? [X0] :
( ( relation_rng(X0) != relation_dom(function_inverse(X0))
| relation_dom(X0) != relation_rng(function_inverse(X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f75,plain,
? [X0] :
( ( relation_rng(X0) != relation_dom(function_inverse(X0))
| relation_dom(X0) != relation_rng(function_inverse(X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f74]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f128,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f129,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f132,plain,
( relation_dom(sK11) != relation_rng(function_inverse(sK11))
| relation_rng(sK11) != relation_dom(function_inverse(sK11)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f133,plain,
function(sK11),
inference(cnf_transformation,[],[f75]) ).
fof(f134,plain,
relation(sK11),
inference(cnf_transformation,[],[f75]) ).
fof(f135,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f75]) ).
fof(f143,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ relation(X0)
| function(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f158,plain,
~ function(sK11),
inference(consistent_polarity_flipping,[],[f133]) ).
fof(f162,definition,
( spl12_1
<=> relation_rng(sK11) = relation_dom(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f164,plain,
( relation_rng(sK11) != relation_dom(function_inverse(sK11))
| spl12_1 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f166,definition,
( spl12_2
<=> relation_dom(sK11) = relation_rng(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f168,plain,
( relation_dom(sK11) != relation_rng(function_inverse(sK11))
| spl12_2 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f132,f166,f162]) ).
fof(f248,plain,
relation_dom(sK11) = relation_rng(relation_inverse(sK11)),
inference(resolution,[],[f128,f134]) ).
fof(f265,plain,
relation_rng(sK11) = relation_dom(relation_inverse(sK11)),
inference(resolution,[],[f129,f134]) ).
fof(f301,plain,
( ~ relation(sK11)
| function(sK11)
| function_inverse(sK11) = relation_inverse(sK11) ),
inference(resolution,[],[f143,f135]) ).
fof(f306,plain,
( function(sK11)
| function_inverse(sK11) = relation_inverse(sK11) ),
inference(forward_subsumption_resolution,[],[f301,f134]) ).
fof(f309,plain,
function_inverse(sK11) = relation_inverse(sK11),
inference(forward_subsumption_resolution,[],[f306,f158]) ).
fof(f316,plain,
( relation_rng(sK11) != relation_dom(relation_inverse(sK11))
| spl12_1 ),
inference(superposition,[],[f164,f309]) ).
fof(f368,plain,
( $false
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f316,f265]) ).
fof(f369,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f371,plain,
( relation_dom(sK11) != relation_rng(relation_inverse(sK11))
| spl12_2 ),
inference(forward_demodulation,[],[f168,f309]) ).
fof(f372,plain,
( $false
| spl12_2 ),
inference(forward_subsumption_resolution,[],[f371,f248]) ).
fof(f373,plain,
spl12_2,
inference(avatar_contradiction_clause,[],[f372]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f169]) ).
cnf(s8,plain,
spl12_1,
inference(sat_conversion,[],[f369]) ).
cnf(s9,plain,
spl12_2,
inference(sat_conversion,[],[f373]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
fof(f374,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU219+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n020.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:09:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.29/0.46 % (4014720)Will run a generic schedule for satisfiability detection.
% 0.29/0.46 % (4014726)% WARNING: option uhcvi not known.
% 0.29/0.46 % (4014726)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3186015871:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.29/0.46 % (4014726) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4014720-4014726"...
% 0.29/0.46 % (4014726)...printing done.
% 0.29/0.46 % (4014726)Refutation found. Thanks to Tanya!
% 0.29/0.46 % SZS status Theorem for theBenchmark
% 0.29/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.46 % (4014726)------------------------------
% 0.29/0.46 % (4014726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.46 % (4014726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.46 % (4014726)CaDiCaL version: 2.1.3
% 0.29/0.46 % (4014726)Termination reason: Refutation
% 0.29/0.46 % (4014726)Time elapsed: 0.004 s
% 0.29/0.46 % (4014726)Peak memory usage: 12 MB
% 0.29/0.46 % (4014726)Instructions burned: 8 (million)
% 0.29/0.46 % (4014720)Success in time 0.034 s
% 0.29/0.46 % Vampire exiting
%------------------------------------------------------------------------------