%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU361+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 12:53:00 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 13 unt; 2 def)
% Number of atoms : 238 ( 13 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 290 ( 112 ~; 102 |; 46 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(f5,axiom,
! [X0,X1] :
( rel_str(X0)
=> element(join_on_relstr(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(f22,axiom,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
=> ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) ) )
& ( ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) )
=> ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_0) ).
fof(f23,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ( ex_sup_of_relstr_set(X0,empty_set)
& ex_inf_of_relstr_set(X0,the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f24,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> related(X0,bottom_of_relstr(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> related(X0,bottom_of_relstr(X0),X1) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f30,plain,
! [X0] :
( ( antisymmetric_relstr(X0)
& rel_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
=> ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X3)
=> related(X0,X1,X3) ) ) ) )
& ( ( relstr_set_smaller(X0,X2,X1)
& ! [X4] :
( element(X4,the_carrier(X0))
=> ( relstr_set_smaller(X0,X2,X4)
=> related(X0,X1,X4) ) ) )
=> ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) ) ) ) ) ),
inference(rectify,[],[f22]) ).
fof(f31,plain,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> relstr_set_smaller(X0,empty_set,X1) ) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f32,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) )
=> ex_sup_of_relstr_set(X0,empty_set) ),
inference(pure_predicate_removal,[],[f23]) ).
fof(f36,plain,
! [X0] :
( bottom_of_relstr(X0) = join_on_relstr(X0,empty_set)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0,X1] :
( element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( related(X0,X1,X3)
| ~ relstr_set_smaller(X0,X2,X3)
| ~ element(X3,the_carrier(X0)) ) )
| join_on_relstr(X0,X2) != X1
| ~ ex_sup_of_relstr_set(X0,X2) )
& ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
| ~ relstr_set_smaller(X0,X2,X1)
| ? [X4] :
( ~ related(X0,X1,X4)
& relstr_set_smaller(X0,X2,X4)
& element(X4,the_carrier(X0)) ) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( relstr_set_smaller(X0,X2,X1)
& ! [X3] :
( related(X0,X1,X3)
| ~ relstr_set_smaller(X0,X2,X3)
| ~ element(X3,the_carrier(X0)) ) )
| join_on_relstr(X0,X2) != X1
| ~ ex_sup_of_relstr_set(X0,X2) )
& ( ( X1 = join_on_relstr(X0,X2)
& ex_sup_of_relstr_set(X0,X2) )
| ~ relstr_set_smaller(X0,X2,X1)
| ? [X4] :
( ~ related(X0,X1,X4)
& relstr_set_smaller(X0,X2,X4)
& element(X4,the_carrier(X0)) ) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ex_sup_of_relstr_set(X0,empty_set)
| empty_carrier(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f48,plain,
! [X0] :
( ex_sup_of_relstr_set(X0,empty_set)
| empty_carrier(X0)
| ~ antisymmetric_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ~ related(X0,bottom_of_relstr(X0),X1)
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ~ related(X0,bottom_of_relstr(X0),X1)
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& antisymmetric_relstr(X0)
& lower_bounded_relstr(X0)
& rel_str(X0) ),
inference(flattening,[],[f49]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0] :
( ~ rel_str(X0)
| bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( element(join_on_relstr(X0,X1),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ element(X1,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X2)
| join_on_relstr(X0,X2) != X1
| ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X3)
| related(X0,X1,X3) ),
inference(cnf_transformation,[],[f46]) ).
fof(f80,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0)
| ex_sup_of_relstr_set(X0,empty_set) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
element(sK9,the_carrier(sK8)),
inference(cnf_transformation,[],[f50]) ).
fof(f82,plain,
~ related(sK8,bottom_of_relstr(sK8),sK9),
inference(cnf_transformation,[],[f50]) ).
fof(f83,plain,
rel_str(sK8),
inference(cnf_transformation,[],[f50]) ).
fof(f84,plain,
lower_bounded_relstr(sK8),
inference(cnf_transformation,[],[f50]) ).
fof(f85,plain,
antisymmetric_relstr(sK8),
inference(cnf_transformation,[],[f50]) ).
fof(f86,plain,
~ empty_carrier(sK8),
inference(cnf_transformation,[],[f50]) ).
fof(f88,plain,
! [X0,X1] :
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f92,plain,
! [X2,X3,X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ element(join_on_relstr(X0,X2),the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X2)
| ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X3)
| related(X0,join_on_relstr(X0,X2),X3) ),
inference(equality_resolution,[],[f72]) ).
fof(f97,plain,
! [X2,X3,X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ element(join_on_relstr(X0,X2),the_carrier(X0))
| ex_sup_of_relstr_set(X0,X2)
| ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X3)
| related(X0,join_on_relstr(X0,X2),X3) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f98,plain,
! [X0] :
( ~ ex_sup_of_relstr_set(X0,empty_set)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f106,plain,
bottom_of_relstr(sK8) = join_on_relstr(sK8,empty_set),
inference(resolution,[],[f56,f83]) ).
fof(f120,definition,
( spl10_1
<=> ex_sup_of_relstr_set(sK8,empty_set) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f122,plain,
( ex_sup_of_relstr_set(sK8,empty_set)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f147,plain,
! [X2,X3,X0] :
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ex_sup_of_relstr_set(X0,X2)
| ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X3)
| related(X0,join_on_relstr(X0,X2),X3) ),
inference(forward_subsumption_resolution,[],[f97,f57]) ).
fof(f148,plain,
! [X0,X1] :
( ~ rel_str(sK8)
| ex_sup_of_relstr_set(sK8,X0)
| ~ element(X1,the_carrier(sK8))
| ~ relstr_set_smaller(sK8,X0,X1)
| related(sK8,join_on_relstr(sK8,X0),X1) ),
inference(resolution,[],[f147,f85]) ).
fof(f149,plain,
! [X0,X1] :
( related(sK8,join_on_relstr(sK8,X0),X1)
| ~ element(X1,the_carrier(sK8))
| ~ relstr_set_smaller(sK8,X0,X1)
| ex_sup_of_relstr_set(sK8,X0) ),
inference(forward_subsumption_resolution,[],[f148,f83]) ).
fof(f151,plain,
! [X0] :
( related(sK8,bottom_of_relstr(sK8),X0)
| ~ element(X0,the_carrier(sK8))
| ~ relstr_set_smaller(sK8,empty_set,X0)
| ex_sup_of_relstr_set(sK8,empty_set) ),
inference(superposition,[],[f149,f106]) ).
fof(f153,definition,
( spl10_6
<=> ! [X0] :
( related(sK8,bottom_of_relstr(sK8),X0)
| ~ relstr_set_smaller(sK8,empty_set,X0)
| ~ element(X0,the_carrier(sK8)) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f154,plain,
( ! [X0] :
( related(sK8,bottom_of_relstr(sK8),X0)
| ~ relstr_set_smaller(sK8,empty_set,X0)
| ~ element(X0,the_carrier(sK8)) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( spl10_1
| spl10_6 ),
inference(avatar_split_clause,[],[f151,f153,f120]) ).
fof(f159,plain,
( ~ relstr_set_smaller(sK8,empty_set,sK9)
| ~ element(sK9,the_carrier(sK8))
| ~ spl10_6 ),
inference(resolution,[],[f154,f82]) ).
fof(f162,plain,
( ~ relstr_set_smaller(sK8,empty_set,sK9)
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f159,f81]) ).
fof(f177,plain,
( ~ element(sK9,the_carrier(sK8))
| ~ rel_str(sK8)
| ~ spl10_6 ),
inference(resolution,[],[f162,f88]) ).
fof(f178,plain,
( ~ rel_str(sK8)
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f177,f81]) ).
fof(f179,plain,
( $false
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f178,f83]) ).
fof(f180,plain,
~ spl10_6,
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f181,plain,
( ~ lower_bounded_relstr(sK8)
| ~ antisymmetric_relstr(sK8)
| empty_carrier(sK8)
| ~ rel_str(sK8)
| ~ spl10_1 ),
inference(resolution,[],[f122,f98]) ).
fof(f186,plain,
( ~ antisymmetric_relstr(sK8)
| empty_carrier(sK8)
| ~ rel_str(sK8)
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f181,f84]) ).
fof(f189,plain,
( empty_carrier(sK8)
| ~ rel_str(sK8)
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f186,f85]) ).
fof(f191,plain,
( ~ rel_str(sK8)
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f189,f86]) ).
fof(f192,plain,
( $false
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f191,f83]) ).
fof(f193,plain,
~ spl10_1,
inference(avatar_contradiction_clause,[],[f192]) ).
cnf(s3,plain,
( spl10_1
| spl10_6 ),
inference(sat_conversion,[],[f155]) ).
cnf(s5,plain,
~ spl10_6,
inference(sat_conversion,[],[f180]) ).
cnf(s6,plain,
~ spl10_1,
inference(sat_conversion,[],[f193]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s5,s6]) ).
fof(f194,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 04:54:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.44 % (4160201)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (4160206)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4041349785_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.44 % TRYING [1]
% 0.11/0.44 % TRYING [2]
% 0.11/0.44 % TRYING [3]
% 0.11/0.44 % TRYING [4]
% 0.11/0.44 % (4160207)% WARNING: option uhcvi not known.
% 0.11/0.44 % (4160207)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1624106839:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.44 % (4160208)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3837364349:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.44 % (4160212)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2379537208:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.44 % (4160210)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2950475530:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.44 % (4160211)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3698720993:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.44 % (4160209)dis+10_1_sil=32000:sp=arity:random_seed=3614564347:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % TRYING [5]
% 0.11/0.44 % (4160209) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4160201-4160209"...
% 0.11/0.44 % (4160207) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4160201-4160207"...
% 0.11/0.44 % (4160210) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4160201-4160210"...
% 0.11/0.44 % (4160207)...printing done.
% 0.11/0.44 % (4160209)...printing done.
% 0.11/0.44 % (4160211) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4160201-4160211"...
% 0.11/0.44 % (4160207)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (4160207)------------------------------
% 0.11/0.44 % (4160207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (4160207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (4160207)CaDiCaL version: 2.1.3
% 0.11/0.44 % (4160207)Termination reason: Refutation
% 0.11/0.44 % (4160207)Time elapsed: 0.006 s
% 0.11/0.44 % (4160207)Peak memory usage: 12 MB
% 0.11/0.44 % (4160207)Instructions burned: 7 (million)
% 0.11/0.44 % (4160201)Success in time 0.038 s
% 0.11/0.44 % Vampire exiting
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