%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU026+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 : n009.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 0.14s 0.47s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 16 unt; 5 def)
% Number of atoms : 202 ( 47 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 224 ( 95 ~; 90 |; 21 &)
% ( 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 : 40 ( 1 sgn 38 !; 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(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(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_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0))
| relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0] :
( ( relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0))
| relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f79]) ).
fof(f97,plain,
( ( relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11))
| relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11)) )
& one_to_one(sK11)
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f80]) ).
fof(f105,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f145,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f150,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f151,plain,
! [X0,X1] :
( ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f153,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f154,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f155,plain,
function(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f156,plain,
relation(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f157,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
( relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11))
| relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f164,definition,
( spl12_1
<=> relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f168,definition,
( spl12_2
<=> relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f170,plain,
( relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11))
| spl12_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f158,f168,f164]) ).
fof(f312,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f153,f157]) ).
fof(f317,plain,
( relation_dom(sK11) = relation_rng(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f312,f156]) ).
fof(f320,plain,
relation_dom(sK11) = relation_rng(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f317,f155]) ).
fof(f341,definition,
( spl12_8
<=> relation(function_inverse(sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f343,plain,
( ~ relation(function_inverse(sK11))
| spl12_8 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f350,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ relation(sK11)
| ~ function(sK11) ),
inference(resolution,[],[f154,f157]) ).
fof(f355,plain,
( relation_rng(sK11) = relation_dom(function_inverse(sK11))
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f350,f156]) ).
fof(f358,plain,
relation_rng(sK11) = relation_dom(function_inverse(sK11)),
inference(forward_subsumption_resolution,[],[f355,f155]) ).
fof(f359,plain,
! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| relation_dom(function_inverse(sK11)) = relation_dom(relation_composition(function_inverse(sK11),X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK11)) ),
inference(superposition,[],[f150,f320]) ).
fof(f363,definition,
( spl12_10
<=> ! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| ~ relation(X0)
| relation_dom(function_inverse(sK11)) = relation_dom(relation_composition(function_inverse(sK11),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f364,plain,
( ! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| ~ relation(X0)
| relation_dom(function_inverse(sK11)) = relation_dom(relation_composition(function_inverse(sK11),X0)) )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( ~ spl12_8
| spl12_10 ),
inference(avatar_split_clause,[],[f359,f363,f341]) ).
fof(f366,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl12_8 ),
inference(resolution,[],[f343,f105]) ).
fof(f367,plain,
( ~ function(sK11)
| spl12_8 ),
inference(forward_subsumption_resolution,[],[f366,f156]) ).
fof(f368,plain,
( $false
| spl12_8 ),
inference(forward_subsumption_resolution,[],[f367,f155]) ).
fof(f369,plain,
spl12_8,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f371,plain,
! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK11))
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK11),X0))
| ~ relation(function_inverse(sK11))
| ~ relation(X0) ),
inference(superposition,[],[f151,f320]) ).
fof(f373,definition,
( spl12_11
<=> ! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK11))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK11),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f374,plain,
( ! [X0] :
( ~ subset(relation_dom(X0),relation_dom(sK11))
| ~ relation(X0)
| relation_rng(X0) = relation_rng(relation_composition(function_inverse(sK11),X0)) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( ~ spl12_8
| spl12_11 ),
inference(avatar_split_clause,[],[f371,f373,f341]) ).
fof(f416,plain,
( ~ relation(sK11)
| relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11))
| ~ spl12_11 ),
inference(resolution,[],[f374,f145]) ).
fof(f421,plain,
( relation_rng(sK11) = relation_rng(relation_composition(function_inverse(sK11),sK11))
| ~ spl12_11 ),
inference(forward_subsumption_resolution,[],[f416,f156]) ).
fof(f435,plain,
( spl12_1
| ~ spl12_11 ),
inference(avatar_split_clause,[],[f421,f373,f164]) ).
fof(f1293,plain,
( ! [X0] :
( ~ subset(relation_dom(sK11),relation_dom(X0))
| relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),X0))
| ~ relation(X0) )
| ~ spl12_10 ),
inference(forward_demodulation,[],[f364,f358]) ).
fof(f1303,plain,
( relation_rng(sK11) = relation_dom(relation_composition(function_inverse(sK11),sK11))
| ~ relation(sK11)
| ~ spl12_10 ),
inference(resolution,[],[f1293,f145]) ).
fof(f1337,plain,
( ~ relation(sK11)
| spl12_2
| ~ spl12_10 ),
inference(forward_subsumption_resolution,[],[f1303,f170]) ).
fof(f1339,plain,
( $false
| spl12_2
| ~ spl12_10 ),
inference(forward_subsumption_resolution,[],[f1337,f156]) ).
fof(f1340,plain,
( spl12_2
| ~ spl12_10 ),
inference(avatar_contradiction_clause,[],[f1339]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s13,plain,
( ~ spl12_8
| spl12_10 ),
inference(sat_conversion,[],[f365]) ).
cnf(s14,plain,
spl12_8,
inference(sat_conversion,[],[f369]) ).
cnf(s15,plain,
( ~ spl12_8
| spl12_11 ),
inference(sat_conversion,[],[f375]) ).
cnf(s21,plain,
( spl12_1
| ~ spl12_11 ),
inference(sat_conversion,[],[f435]) ).
cnf(s89,plain,
( spl12_2
| ~ spl12_10 ),
inference(sat_conversion,[],[f1340]) ).
cnf(s96,plain,
spl12_11,
inference(rat,[],[s15,s14]) ).
cnf(s102,plain,
spl12_1,
inference(rat,[],[s21,s96]) ).
cnf(s114,plain,
spl12_10,
inference(rat,[],[s13,s14]) ).
cnf(s115,plain,
spl12_2,
inference(rat,[],[s89,s114]) ).
cnf(s118,plain,
$false,
inference(rat,[],[s1,s115,s102]) ).
fof(f1347,plain,
$false,
inference(avatar_sat_refutation,[],[s118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU026+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:23:15 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 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
% 0.14/0.47 % (2635196)Will run a generic schedule for satisfiability detection.
% 0.14/0.47 % (2635204)dis+10_1_sil=32000:sp=arity:random_seed=165557201:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.47 % (2635202)% WARNING: option uhcvi not known.
% 0.14/0.47 % (2635201)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2937462769_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.47 % (2635202)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=28139988:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.47 % (2635203)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1527255463:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.47 % (2635206)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2201321155:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.47 % (2635205)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1899500217:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.47 % (2635207)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=198029763:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.47 % TRYING [1]
% 0.14/0.47 % TRYING [2]
% 0.14/0.47 % (2635204) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2635196-2635204"...
% 0.14/0.47 % TRYING [3]
% 0.14/0.47 % (2635204)...printing done.
% 0.14/0.47 % TRYING [4]
% 0.14/0.47 % (2635204)Refutation found. Thanks to Tanya!
% 0.14/0.47 % SZS status Theorem for theBenchmark
% 0.14/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.47 % (2635204)------------------------------
% 0.14/0.47 % (2635204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.47 % (2635204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.47 % (2635204)CaDiCaL version: 2.1.3
% 0.14/0.47 % (2635204)Termination reason: Refutation
% 0.14/0.47 % (2635204)Time elapsed: 0.012 s
% 0.14/0.47 % (2635204)Peak memory usage: 13 MB
% 0.14/0.47 % (2635204)Instructions burned: 30 (million)
% 0.14/0.47 % (2635196)Success in time 0.043 s
% 0.14/0.47 % Vampire exiting
%------------------------------------------------------------------------------