%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET584+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 : n010.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 12:44:00 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 9 unt; 2 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 40 ~; 38 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 49 !; 5 ?)
% 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,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(union(X0,X2),union(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th33) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(union(X0,X2),union(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1,X2] :
( ~ subset(union(X0,X2),union(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f13]) ).
fof(f18,plain,
( ~ subset(union(sK2,sK4),union(sK3,sK4))
& subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f9]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
~ subset(union(sK2,sK4),union(sK3,sK4)),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
member(sK0(union(sK2,sK4),union(sK3,sK4)),union(sK2,sK4)),
inference(resolution,[],[f23,f32]) ).
fof(f36,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,sK3) ),
inference(resolution,[],[f22,f31]) ).
fof(f45,plain,
( member(sK0(union(sK2,sK4),union(sK3,sK4)),sK4)
| member(sK0(union(sK2,sK4),union(sK3,sK4)),sK2) ),
inference(resolution,[],[f19,f33]) ).
fof(f50,definition,
( spl5_1
<=> member(sK0(union(sK2,sK4),union(sK3,sK4)),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f52,plain,
( member(sK0(union(sK2,sK4),union(sK3,sK4)),sK2)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl5_2
<=> member(sK0(union(sK2,sK4),union(sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f56,plain,
( member(sK0(union(sK2,sK4),union(sK3,sK4)),sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f45,f54,f50]) ).
fof(f60,plain,
( ! [X0] : member(sK0(union(sK2,sK4),union(sK3,sK4)),union(X0,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f56,f20]) ).
fof(f81,plain,
( subset(union(sK2,sK4),union(sK3,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f60,f24]) ).
fof(f87,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f81,f32]) ).
fof(f88,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f93,plain,
( member(sK0(union(sK2,sK4),union(sK3,sK4)),sK3)
| ~ spl5_1 ),
inference(resolution,[],[f52,f36]) ).
fof(f128,plain,
( ! [X0] : member(sK0(union(sK2,sK4),union(sK3,sK4)),union(sK3,X0))
| ~ spl5_1 ),
inference(resolution,[],[f93,f21]) ).
fof(f178,plain,
( subset(union(sK2,sK4),union(sK3,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f128,f24]) ).
fof(f185,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f178,f32]) ).
fof(f186,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f185]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f88]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f186]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f187,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET584+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 02:13:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.44 % (1500329)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (1500339)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1101570309:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (1500339) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1500329-1500339"...
% 0.10/0.44 % (1500339)...printing done.
% 0.10/0.44 % (1500339)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (1500339)------------------------------
% 0.10/0.44 % (1500339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (1500339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (1500339)CaDiCaL version: 2.1.3
% 0.10/0.44 % (1500339)Termination reason: Refutation
% 0.10/0.44 % (1500339)Time elapsed: 0.004 s
% 0.10/0.44 % (1500339)Peak memory usage: 12 MB
% 0.10/0.44 % (1500339)Instructions burned: 9 (million)
% 0.10/0.44 % (1500329)Success in time 0.037 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------