%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:44:05 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 12 unt; 3 def)
% Number of atoms : 159 ( 35 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 162 ( 72 ~; 75 |; 4 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 56 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( X0 = empty_set
& X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( X0 = empty_set
& X1 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0,X1] :
( union(X0,X1) = empty_set
<~> ( X0 = empty_set
& X1 = empty_set ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
( empty_set != sK3
| empty_set != sK2
| empty_set != union(sK2,sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
( empty_set = sK3
| empty_set = union(sK2,sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
( empty_set = sK2
| empty_set = union(sK2,sK3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0) ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f39,plain,
! [X0] : member(X0,empty_set),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X1,X0)
| subset(X0,X1)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f22]) ).
fof(f52,definition,
( spl4_1
<=> empty_set = union(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f53,plain,
( empty_set = union(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( empty_set != union(sK2,sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f56,definition,
( spl4_2
<=> empty_set = sK2 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f57,plain,
( empty_set = sK2
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( empty_set != sK2
| spl4_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl4_3
<=> empty_set = sK3 ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f61,plain,
( empty_set = sK3
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( empty_set != sK3
| spl4_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f29,f60,f56,f52]) ).
fof(f64,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f30,f60,f52]) ).
fof(f65,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f31,f56,f52]) ).
fof(f66,plain,
( empty_set != union(sK2,empty_set)
| spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f54,f61]) ).
fof(f67,plain,
( empty_set != union(empty_set,empty_set)
| spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[],[f66,f57]) ).
fof(f75,plain,
! [X0] : ~ subset(empty_set,X0),
inference(resolution,[],[f44,f39]) ).
fof(f77,plain,
! [X0] :
( subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f40,f75]) ).
fof(f90,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,union(empty_set,X1)) ),
inference(resolution,[],[f38,f39]) ).
fof(f110,plain,
! [X0] : member(X0,union(empty_set,empty_set)),
inference(resolution,[],[f90,f39]) ).
fof(f120,plain,
! [X0] : ~ subset(union(empty_set,empty_set),X0),
inference(resolution,[],[f110,f44]) ).
fof(f125,plain,
empty_set = union(empty_set,empty_set),
inference(resolution,[],[f120,f77]) ).
fof(f126,plain,
( $false
| spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f125,f67]) ).
fof(f127,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f128,plain,
( empty_set = union(empty_set,sK3)
| ~ spl4_1
| ~ spl4_2 ),
inference(forward_demodulation,[],[f53,f57]) ).
fof(f129,plain,
( ! [X0] :
( ~ member(X0,empty_set)
| member(X0,sK3) )
| ~ spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f37,f128]) ).
fof(f131,plain,
( ! [X0] : member(X0,sK3)
| ~ spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f129,f39]) ).
fof(f135,plain,
( ! [X0] : ~ subset(sK3,X0)
| ~ spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f131,f44]) ).
fof(f141,plain,
( empty_set = sK3
| ~ spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f135,f77]) ).
fof(f142,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f141,f62]) ).
fof(f143,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f145,plain,
( ! [X0] :
( ~ member(X0,empty_set)
| member(X0,sK2) )
| ~ spl4_1 ),
inference(superposition,[],[f36,f53]) ).
fof(f146,plain,
( ! [X0] : member(X0,sK2)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f145,f39]) ).
fof(f151,plain,
( ! [X0] : ~ subset(sK2,X0)
| ~ spl4_1 ),
inference(resolution,[],[f146,f44]) ).
fof(f161,plain,
( empty_set = sK2
| ~ spl4_1 ),
inference(resolution,[],[f151,f77]) ).
fof(f162,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f161,f58]) ).
fof(f163,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f162]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f143]) ).
cnf(s6,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f163]) ).
cnf(s7,plain,
spl4_1,
inference(rat,[],[s4,s2,s3]) ).
cnf(s8,plain,
spl4_2,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl4_3,
inference(rat,[],[s1,s8,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s5,s8,s7,s9]) ).
fof(f164,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 02:19:40 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.13/0.45 % (2927510)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (2927521)% WARNING: option uhcvi not known.
% 0.13/0.45 % (2927521)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=478376545:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.45 % (2927521) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2927510-2927521"...
% 0.13/0.45 % (2927521)...printing done.
% 0.13/0.45 % (2927521)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (2927521)------------------------------
% 0.13/0.45 % (2927521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (2927521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (2927521)CaDiCaL version: 2.1.3
% 0.13/0.45 % (2927521)Termination reason: Refutation
% 0.13/0.45 % (2927521)Time elapsed: 0.003 s
% 0.13/0.45 % (2927521)Peak memory usage: 12 MB
% 0.13/0.45 % (2927521)Instructions burned: 5 (million)
% 0.13/0.45 % (2927510)Success in time 0.027 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------