%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU189+2 : 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 : n012.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 12:52:18 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 9 unt; 2 def)
% Number of atoms : 131 ( 39 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 135 ( 59 ~; 56 |; 10 &)
% ( 4 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f66,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f67,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f153,axiom,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f157,conjecture,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f158,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f157]) ).
fof(f161,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f215,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f216,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f215]) ).
fof(f217,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f218,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f217]) ).
fof(f297,plain,
? [X0] :
( ( relation_dom(X0) = empty_set
<~> relation_rng(X0) = empty_set )
& relation(X0) ),
inference(ennf_transformation,[],[f158]) ).
fof(f298,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f161]) ).
fof(f399,plain,
? [X0] :
( ( empty_set != relation_rng(X0)
| empty_set != relation_dom(X0) )
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(nnf_transformation,[],[f297]) ).
fof(f400,plain,
? [X0] :
( ( empty_set != relation_rng(X0)
| empty_set != relation_dom(X0) )
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& relation(X0) ),
inference(flattening,[],[f399]) ).
fof(f401,plain,
( ( empty_set != relation_rng(sK49)
| empty_set != relation_dom(sK49) )
& ( empty_set = relation_rng(sK49)
| empty_set = relation_dom(sK49) )
& relation(sK49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(X0,sK49)],[f400]) ).
fof(f520,plain,
empty(empty_set),
inference(cnf_transformation,[],[f57]) ).
fof(f530,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f531,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f652,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f153]) ).
fof(f653,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f153]) ).
fof(f658,plain,
relation(sK49),
inference(cnf_transformation,[],[f401]) ).
fof(f659,plain,
( empty_set = relation_rng(sK49)
| empty_set = relation_dom(sK49) ),
inference(cnf_transformation,[],[f401]) ).
fof(f660,plain,
( empty_set != relation_rng(sK49)
| empty_set != relation_dom(sK49) ),
inference(cnf_transformation,[],[f401]) ).
fof(f664,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f298]) ).
fof(f816,definition,
( spl52_1
<=> empty_set = relation_dom(sK49) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f817,plain,
( empty_set != relation_dom(sK49)
| spl52_1 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f818,plain,
( empty_set = relation_dom(sK49)
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f820,definition,
( spl52_2
<=> empty_set = relation_rng(sK49) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f821,plain,
( empty_set != relation_rng(sK49)
| spl52_2 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f822,plain,
( empty_set = relation_rng(sK49)
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f823,plain,
( spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f659,f820,f816]) ).
fof(f824,plain,
( ~ spl52_1
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f660,f820,f816]) ).
fof(f972,plain,
( ~ empty(empty_set)
| empty(sK49)
| ~ relation(sK49)
| ~ spl52_2 ),
inference(superposition,[],[f531,f822]) ).
fof(f974,plain,
( empty(sK49)
| ~ relation(sK49)
| ~ spl52_2 ),
inference(forward_subsumption_resolution,[],[f972,f520]) ).
fof(f975,plain,
( empty(sK49)
| ~ spl52_2 ),
inference(forward_subsumption_resolution,[],[f974,f658]) ).
fof(f976,plain,
( empty_set = sK49
| ~ spl52_2 ),
inference(resolution,[],[f975,f664]) ).
fof(f992,plain,
( empty_set != relation_dom(empty_set)
| spl52_1
| ~ spl52_2 ),
inference(superposition,[],[f817,f976]) ).
fof(f994,plain,
( $false
| spl52_1
| ~ spl52_2 ),
inference(forward_subsumption_resolution,[],[f992,f653]) ).
fof(f995,plain,
( spl52_1
| ~ spl52_2 ),
inference(avatar_contradiction_clause,[],[f994]) ).
fof(f996,plain,
( ~ empty(empty_set)
| empty(sK49)
| ~ relation(sK49)
| ~ spl52_1 ),
inference(superposition,[],[f530,f818]) ).
fof(f999,plain,
( empty(sK49)
| ~ relation(sK49)
| ~ spl52_1 ),
inference(forward_subsumption_resolution,[],[f996,f520]) ).
fof(f1000,plain,
( empty(sK49)
| ~ spl52_1 ),
inference(forward_subsumption_resolution,[],[f999,f658]) ).
fof(f1001,plain,
( empty_set = sK49
| ~ spl52_1 ),
inference(resolution,[],[f1000,f664]) ).
fof(f1003,plain,
( empty_set != relation_rng(empty_set)
| ~ spl52_1
| spl52_2 ),
inference(superposition,[],[f821,f1001]) ).
fof(f1007,plain,
( $false
| ~ spl52_1
| spl52_2 ),
inference(forward_subsumption_resolution,[],[f1003,f652]) ).
fof(f1008,plain,
( ~ spl52_1
| spl52_2 ),
inference(avatar_contradiction_clause,[],[f1007]) ).
cnf(s1,plain,
( spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f823]) ).
cnf(s2,plain,
( ~ spl52_1
| ~ spl52_2 ),
inference(sat_conversion,[],[f824]) ).
cnf(s3,plain,
( spl52_1
| ~ spl52_2 ),
inference(sat_conversion,[],[f995]) ).
cnf(s4,plain,
( ~ spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f1008]) ).
cnf(s5,plain,
spl52_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl52_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f1009,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 03:57:19 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.32 Running first-order model finding
% 0.08/0.32 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
% 0.08/0.37 % (3001903)Will run a generic schedule for satisfiability detection.
% 0.08/0.37 % (3001909)% WARNING: option uhcvi not known.
% 0.08/0.37 % (3001910)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1938768673:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.37 % (3001911)dis+10_1_sil=32000:sp=arity:random_seed=1862410300:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.37 % (3001908)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3986127763_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.37 % (3001909)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1890447884:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.37 % (3001912)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2793768808:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.37 % (3001913)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3271234497:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.37 % (3001914)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1002052236:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.37 % (3001911) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001903-3001911"...
% 0.08/0.37 % (3001909) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001903-3001909"...
% 0.08/0.37 % (3001911)...printing done.
% 0.08/0.37 % (3001909)...printing done.
% 0.08/0.37 % (3001911)Refutation found. Thanks to Tanya!
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.37 % (3001911)------------------------------
% 0.08/0.37 % (3001911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.37 % (3001911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.37 % (3001911)CaDiCaL version: 2.1.3
% 0.08/0.37 % (3001911)Termination reason: Refutation
% 0.08/0.37 % (3001911)Time elapsed: 0.007 s
% 0.08/0.37 % (3001911)Peak memory usage: 13 MB
% 0.08/0.37 % (3001911)Instructions burned: 19 (million)
% 0.08/0.37 % (3001903)Success in time 0.036 s
% 0.08/0.37 % Vampire exiting
%------------------------------------------------------------------------------