%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU221+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 : n004.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 12:52:27 PM UTC 2026
% Result : Theorem 0.33s 0.46s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 74 ( 10 unt; 2 def)
% Number of atoms : 260 ( 54 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 320 ( 134 ~; 128 |; 36 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f9,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f34,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f36,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f48,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f51,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f50]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f74,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f73]) ).
fof(f83,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f84,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f85,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f86,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f87,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f134,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f136,plain,
! [X0,X1] :
( ~ one_to_one(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ function(X1)
| apply(X1,apply(function_inverse(X1),X0)) = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f137,plain,
function(sK13),
inference(cnf_transformation,[],[f74]) ).
fof(f138,plain,
relation(sK13),
inference(cnf_transformation,[],[f74]) ).
fof(f139,plain,
one_to_one(sK13),
inference(cnf_transformation,[],[f74]) ).
fof(f140,plain,
~ one_to_one(function_inverse(sK13)),
inference(cnf_transformation,[],[f74]) ).
fof(f144,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(equality_resolution,[],[f134]) ).
fof(f190,plain,
( ~ relation(sK13)
| relation(function_inverse(sK13)) ),
inference(resolution,[],[f88,f137]) ).
fof(f191,plain,
relation(function_inverse(sK13)),
inference(forward_subsumption_resolution,[],[f190,f138]) ).
fof(f290,plain,
( ~ relation(function_inverse(sK13))
| in(sK1(function_inverse(sK13)),relation_dom(function_inverse(sK13)))
| ~ function(function_inverse(sK13)) ),
inference(resolution,[],[f84,f140]) ).
fof(f291,plain,
( in(sK1(function_inverse(sK13)),relation_dom(function_inverse(sK13)))
| ~ function(function_inverse(sK13)) ),
inference(forward_subsumption_resolution,[],[f290,f191]) ).
fof(f293,definition,
( spl14_1
<=> function(function_inverse(sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f294,plain,
( function(function_inverse(sK13))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f295,plain,
( ~ function(function_inverse(sK13))
| spl14_1 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f297,definition,
( spl14_2
<=> in(sK1(function_inverse(sK13)),relation_dom(function_inverse(sK13))) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f299,plain,
( in(sK1(function_inverse(sK13)),relation_dom(function_inverse(sK13)))
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f300,plain,
( ~ spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f291,f297,f293]) ).
fof(f301,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl14_1 ),
inference(resolution,[],[f295,f87]) ).
fof(f302,plain,
( ~ function(sK13)
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f301,f138]) ).
fof(f303,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f302,f137]) ).
fof(f304,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f305,plain,
( ~ relation(function_inverse(sK13))
| in(sK0(function_inverse(sK13)),relation_dom(function_inverse(sK13)))
| ~ function(function_inverse(sK13)) ),
inference(resolution,[],[f85,f140]) ).
fof(f306,plain,
( in(sK0(function_inverse(sK13)),relation_dom(function_inverse(sK13)))
| ~ function(function_inverse(sK13)) ),
inference(forward_subsumption_resolution,[],[f305,f191]) ).
fof(f307,plain,
( in(sK0(function_inverse(sK13)),relation_dom(function_inverse(sK13)))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f306,f294]) ).
fof(f310,plain,
( ~ relation(function_inverse(sK13))
| sK1(function_inverse(sK13)) != sK0(function_inverse(sK13))
| ~ function(function_inverse(sK13)) ),
inference(resolution,[],[f86,f140]) ).
fof(f311,plain,
( sK1(function_inverse(sK13)) != sK0(function_inverse(sK13))
| ~ function(function_inverse(sK13)) ),
inference(forward_subsumption_resolution,[],[f310,f191]) ).
fof(f312,plain,
( sK1(function_inverse(sK13)) != sK0(function_inverse(sK13))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f311,f294]) ).
fof(f343,plain,
( ~ relation(function_inverse(sK13))
| apply(function_inverse(sK13),sK0(function_inverse(sK13))) = apply(function_inverse(sK13),sK1(function_inverse(sK13)))
| ~ function(function_inverse(sK13)) ),
inference(resolution,[],[f83,f140]) ).
fof(f344,plain,
( apply(function_inverse(sK13),sK0(function_inverse(sK13))) = apply(function_inverse(sK13),sK1(function_inverse(sK13)))
| ~ function(function_inverse(sK13)) ),
inference(forward_subsumption_resolution,[],[f343,f191]) ).
fof(f345,plain,
( apply(function_inverse(sK13),sK0(function_inverse(sK13))) = apply(function_inverse(sK13),sK1(function_inverse(sK13)))
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f344,f294]) ).
fof(f367,plain,
! [X0] :
( ~ relation(sK13)
| ~ in(X0,relation_rng(sK13))
| ~ function(sK13)
| apply(sK13,apply(function_inverse(sK13),X0)) = X0 ),
inference(resolution,[],[f136,f139]) ).
fof(f381,plain,
! [X0] :
( ~ in(X0,relation_rng(sK13))
| ~ function(sK13)
| apply(sK13,apply(function_inverse(sK13),X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f367,f138]) ).
fof(f384,plain,
! [X0] :
( ~ in(X0,relation_rng(sK13))
| apply(sK13,apply(function_inverse(sK13),X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f381,f137]) ).
fof(f385,plain,
( ~ relation(sK13)
| ~ function(sK13)
| ~ function(function_inverse(sK13))
| ~ relation(function_inverse(sK13))
| relation_dom(function_inverse(sK13)) = relation_rng(sK13) ),
inference(resolution,[],[f144,f139]) ).
fof(f403,plain,
( ~ function(sK13)
| ~ function(function_inverse(sK13))
| ~ relation(function_inverse(sK13))
| relation_dom(function_inverse(sK13)) = relation_rng(sK13) ),
inference(forward_subsumption_resolution,[],[f385,f138]) ).
fof(f410,plain,
( ~ function(function_inverse(sK13))
| ~ relation(function_inverse(sK13))
| relation_dom(function_inverse(sK13)) = relation_rng(sK13) ),
inference(forward_subsumption_resolution,[],[f403,f137]) ).
fof(f412,plain,
( ~ relation(function_inverse(sK13))
| relation_dom(function_inverse(sK13)) = relation_rng(sK13)
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f410,f294]) ).
fof(f422,plain,
( relation_dom(function_inverse(sK13)) = relation_rng(sK13)
| ~ spl14_1 ),
inference(forward_subsumption_resolution,[],[f412,f191]) ).
fof(f424,plain,
( in(sK0(function_inverse(sK13)),relation_rng(sK13))
| ~ spl14_1 ),
inference(superposition,[],[f307,f422]) ).
fof(f426,plain,
( in(sK1(function_inverse(sK13)),relation_rng(sK13))
| ~ spl14_1
| ~ spl14_2 ),
inference(superposition,[],[f299,f422]) ).
fof(f642,plain,
( sK0(function_inverse(sK13)) = apply(sK13,apply(function_inverse(sK13),sK0(function_inverse(sK13))))
| ~ spl14_1 ),
inference(resolution,[],[f384,f424]) ).
fof(f643,plain,
( sK1(function_inverse(sK13)) = apply(sK13,apply(function_inverse(sK13),sK1(function_inverse(sK13))))
| ~ spl14_1
| ~ spl14_2 ),
inference(resolution,[],[f384,f426]) ).
fof(f645,plain,
( sK1(function_inverse(sK13)) = apply(sK13,apply(function_inverse(sK13),sK0(function_inverse(sK13))))
| ~ spl14_1
| ~ spl14_2 ),
inference(forward_demodulation,[],[f643,f345]) ).
fof(f646,plain,
( sK1(function_inverse(sK13)) = sK0(function_inverse(sK13))
| ~ spl14_1
| ~ spl14_2 ),
inference(forward_demodulation,[],[f645,f642]) ).
fof(f647,plain,
( $false
| ~ spl14_1
| ~ spl14_2 ),
inference(forward_subsumption_resolution,[],[f646,f312]) ).
fof(f648,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_contradiction_clause,[],[f647]) ).
cnf(s1,plain,
( ~ spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f300]) ).
cnf(s2,plain,
spl14_1,
inference(sat_conversion,[],[f304]) ).
cnf(s5,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f648]) ).
cnf(s6,plain,
~ spl14_2,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s2]) ).
fof(f649,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 04:08:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.33/0.46 % (4140112)Will run a generic schedule for satisfiability detection.
% 0.33/0.46 % (4140122)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2308903637:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.46 % (4140118)% WARNING: option uhcvi not known.
% 0.33/0.46 % (4140117)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3735317432_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.46 % (4140120)dis+10_1_sil=32000:sp=arity:random_seed=1438201148:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.46 % (4140119)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4047839220:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.46 % (4140121)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1026824337:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.46 % (4140123)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1277895656:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.46 % (4140118)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4124570182:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.46 % TRYING [1]
% 0.33/0.46 % TRYING [2]
% 0.33/0.46 % TRYING [3]
% 0.33/0.46 % TRYING [4]
% 0.33/0.46 % (4140121) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4140112-4140121"...
% 0.33/0.46 % (4140121)...printing done.
% 0.33/0.46 % (4140121)Refutation found. Thanks to Tanya!
% 0.33/0.46 % SZS status Theorem for theBenchmark
% 0.33/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/0.47 % (4140121)------------------------------
% 0.33/0.47 % (4140121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.47 % (4140121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.47 % (4140121)CaDiCaL version: 2.1.3
% 0.33/0.47 % (4140121)Termination reason: Refutation
% 0.33/0.47 % (4140121)Time elapsed: 0.015 s
% 0.33/0.47 % (4140121)Peak memory usage: 13 MB
% 0.33/0.47 % (4140121)Instructions burned: 24 (million)
% 0.33/0.47 % (4140112)Success in time 0.049 s
% 0.33/0.47 % Vampire exiting
%------------------------------------------------------------------------------