%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU025+1 : 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 : n016.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 12:51:48 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 19 unt; 5 def)
% Number of atoms : 219 ( 49 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 229 ( 90 ~; 103 |; 18 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f36,axiom,
! [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,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
fof(f51,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f51]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f73]) ).
fof(f77,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,[],[f36]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
? [X0] :
( ( relation_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0] :
( ( relation_dom(X0) != relation_dom(relation_composition(X0,function_inverse(X0)))
| relation_dom(X0) != relation_rng(relation_composition(X0,function_inverse(X0))) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f79]) ).
fof(f90,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f130,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f135,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f136,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f138,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f139,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
( relation_dom(sK11) != relation_rng(relation_composition(sK11,function_inverse(sK11)))
| relation_dom(sK11) != relation_dom(relation_composition(sK11,function_inverse(sK11))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f141,plain,
function(sK11),
inference(cnf_transformation,[],[f80]) ).
fof(f142,plain,
relation(sK11),
inference(cnf_transformation,[],[f80]) ).
fof(f143,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f80]) ).
fof(f150,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| function(X0) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f158,plain,
! [X0] : ~ subset(X0,X0),
inference(consistent_polarity_flipping,[],[f130]) ).
fof(f161,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f135]) ).
fof(f162,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0)
| relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f136]) ).
fof(f163,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| function(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f164,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| function(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(consistent_polarity_flipping,[],[f138]) ).
fof(f165,plain,
~ one_to_one(sK11),
inference(consistent_polarity_flipping,[],[f143]) ).
fof(f166,plain,
~ function(sK11),
inference(consistent_polarity_flipping,[],[f141]) ).
fof(f168,definition,
( spl12_1
<=> relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f172,definition,
( spl12_2
<=> relation_dom(sK11) = relation_rng(relation_composition(sK11,function_inverse(sK11))) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f174,plain,
( relation_dom(sK11) != relation_rng(relation_composition(sK11,function_inverse(sK11)))
| spl12_2 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f140,f172,f168]) ).
fof(f242,plain,
( ~ relation(sK11)
| function(sK11)
| relation_rng(sK11) = relation_dom(function_inverse(sK11)) ),
inference(resolution,[],[f163,f165]) ).
fof(f247,plain,
( function(sK11)
| relation_rng(sK11) = relation_dom(function_inverse(sK11)) ),
inference(forward_subsumption_resolution,[],[f242,f142]) ).
fof(f250,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f247,f166]) ).
fof(f251,plain,
( ~ relation(sK11)
| function(sK11)
| relation_dom(sK11) = relation_rng(function_inverse(sK11)) ),
inference(resolution,[],[f164,f165]) ).
fof(f256,plain,
( function(sK11)
| relation_dom(sK11) = relation_rng(function_inverse(sK11)) ),
inference(forward_subsumption_resolution,[],[f251,f142]) ).
fof(f259,plain,
relation_dom(sK11) = relation_rng(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f256,f166]) ).
fof(f278,definition,
( spl12_6
<=> relation(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f280,plain,
( ~ relation(function_inverse(sK11))
| spl12_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f284,plain,
! [X0] :
( subset(relation_rng(X0),relation_rng(sK11))
| ~ relation(function_inverse(sK11))
| ~ relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK11))) ),
inference(superposition,[],[f161,f250]) ).
fof(f286,definition,
( spl12_7
<=> ! [X0] :
( subset(relation_rng(X0),relation_rng(sK11))
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f287,plain,
( ! [X0] :
( subset(relation_rng(X0),relation_rng(sK11))
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( ~ spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f284,f286,f278]) ).
fof(f292,plain,
! [X0] :
( subset(relation_rng(sK11),relation_rng(X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK11))
| relation_rng(function_inverse(sK11)) = relation_rng(relation_composition(X0,function_inverse(sK11))) ),
inference(superposition,[],[f162,f250]) ).
fof(f294,definition,
( spl12_8
<=> ! [X0] :
( subset(relation_rng(sK11),relation_rng(X0))
| relation_rng(function_inverse(sK11)) = relation_rng(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f295,plain,
( ! [X0] :
( subset(relation_rng(sK11),relation_rng(X0))
| relation_rng(function_inverse(sK11)) = relation_rng(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f296,plain,
( ~ spl12_6
| spl12_8 ),
inference(avatar_split_clause,[],[f292,f294,f278]) ).
fof(f425,plain,
( ~ relation(sK11)
| function(sK11)
| spl12_6 ),
inference(resolution,[],[f280,f150]) ).
fof(f426,plain,
( function(sK11)
| spl12_6 ),
inference(forward_subsumption_resolution,[],[f425,f142]) ).
fof(f427,plain,
( $false
| spl12_6 ),
inference(forward_subsumption_resolution,[],[f426,f166]) ).
fof(f428,plain,
spl12_6,
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f429,plain,
( ! [X0] :
( subset(relation_rng(sK11),relation_rng(X0))
| relation_dom(sK11) = relation_rng(relation_composition(X0,function_inverse(sK11)))
| ~ relation(X0) )
| ~ spl12_8 ),
inference(forward_demodulation,[],[f295,f259]) ).
fof(f515,plain,
( relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11)))
| ~ relation(sK11)
| ~ spl12_7 ),
inference(resolution,[],[f287,f158]) ).
fof(f543,plain,
( relation_dom(sK11) = relation_dom(relation_composition(sK11,function_inverse(sK11)))
| ~ spl12_7 ),
inference(forward_subsumption_resolution,[],[f515,f142]) ).
fof(f544,plain,
( spl12_1
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f543,f286,f168]) ).
fof(f838,plain,
( relation_dom(sK11) = relation_rng(relation_composition(sK11,function_inverse(sK11)))
| ~ relation(sK11)
| ~ spl12_8 ),
inference(resolution,[],[f429,f158]) ).
fof(f861,plain,
( ~ relation(sK11)
| spl12_2
| ~ spl12_8 ),
inference(forward_subsumption_resolution,[],[f838,f174]) ).
fof(f862,plain,
( $false
| spl12_2
| ~ spl12_8 ),
inference(forward_subsumption_resolution,[],[f861,f142]) ).
fof(f863,plain,
( spl12_2
| ~ spl12_8 ),
inference(avatar_contradiction_clause,[],[f862]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s5,plain,
( ~ spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f288]) ).
cnf(s6,plain,
( ~ spl12_6
| spl12_8 ),
inference(sat_conversion,[],[f296]) ).
cnf(s22,plain,
spl12_6,
inference(sat_conversion,[],[f428]) ).
cnf(s26,plain,
( spl12_1
| ~ spl12_7 ),
inference(sat_conversion,[],[f544]) ).
cnf(s62,plain,
( spl12_2
| ~ spl12_8 ),
inference(sat_conversion,[],[f863]) ).
cnf(s67,plain,
spl12_8,
inference(rat,[],[s6,s22]) ).
cnf(s68,plain,
spl12_2,
inference(rat,[],[s62,s67]) ).
cnf(s69,plain,
spl12_7,
inference(rat,[],[s5,s22]) ).
cnf(s70,plain,
spl12_1,
inference(rat,[],[s26,s69]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s1,s68,s70]) ).
fof(f864,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU025+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:28:03 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.49 % (3230513)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (3230518)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2999413668_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (3230519)% WARNING: option uhcvi not known.
% 0.17/0.49 % TRYING [5]
% 0.17/0.49 % (3230519)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3254519228:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (3230520)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=591137766:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (3230521)dis+10_1_sil=32000:sp=arity:random_seed=4092496856:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (3230522)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3520279401:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (3230523)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=154752288:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (3230524)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3994982596:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [6]
% 0.17/0.49 % TRYING [7]
% 0.17/0.49 % (3230519) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3230513-3230519"...
% 0.17/0.49 % (3230519)...printing done.
% 0.17/0.49 % (3230519)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (3230519)------------------------------
% 0.17/0.49 % (3230519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3230519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3230519)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3230519)Termination reason: Refutation
% 0.17/0.49 % (3230519)Time elapsed: 0.016 s
% 0.17/0.49 % (3230519)Peak memory usage: 13 MB
% 0.17/0.49 % (3230519)Instructions burned: 21 (million)
% 0.17/0.49 % (3230513)Success in time 0.052 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------