%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:43:19 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 2 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 26 ~; 28 |; 2 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f12,conjecture,
! [X0] : equal_set(union(X0,empty_set),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI18) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(union(X0,empty_set),X0),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
? [X0] : ~ equal_set(union(X0,empty_set),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f47,plain,
~ equal_set(union(sK3,empty_set),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f58,plain,
( ~ subset(union(sK3,empty_set),sK3)
| ~ subset(sK3,union(sK3,empty_set)) ),
inference(resolution,[],[f23,f47]) ).
fof(f60,definition,
( spl4_1
<=> subset(sK3,union(sK3,empty_set)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f62,plain,
( ~ subset(sK3,union(sK3,empty_set))
| spl4_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl4_2
<=> subset(union(sK3,empty_set),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f66,plain,
( ~ subset(union(sK3,empty_set),sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f58,f64,f60]) ).
fof(f68,plain,
( ~ member(sK0(sK3,union(sK3,empty_set)),union(sK3,empty_set))
| spl4_1 ),
inference(resolution,[],[f62,f22]) ).
fof(f69,plain,
( member(sK0(sK3,union(sK3,empty_set)),sK3)
| spl4_1 ),
inference(resolution,[],[f62,f21]) ).
fof(f83,plain,
( ~ member(sK0(sK3,union(sK3,empty_set)),sK3)
| spl4_1 ),
inference(resolution,[],[f68,f31]) ).
fof(f85,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f83,f69]) ).
fof(f86,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f85]) ).
fof(f109,plain,
( ~ member(sK0(union(sK3,empty_set),sK3),sK3)
| spl4_2 ),
inference(resolution,[],[f66,f22]) ).
fof(f110,plain,
( member(sK0(union(sK3,empty_set),sK3),union(sK3,empty_set))
| spl4_2 ),
inference(resolution,[],[f66,f21]) ).
fof(f151,plain,
( member(sK0(union(sK3,empty_set),sK3),sK3)
| member(sK0(union(sK3,empty_set),sK3),empty_set)
| spl4_2 ),
inference(resolution,[],[f110,f29]) ).
fof(f155,plain,
( member(sK0(union(sK3,empty_set),sK3),empty_set)
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f151,f109]) ).
fof(f156,plain,
( $false
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f155,f32]) ).
fof(f157,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f156]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f157]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f158,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n004.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 00:58:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43 % (4043846)Will run a generic schedule for satisfiability detection.
% 0.10/0.43 % (4043855)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4226839370:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.43 % (4043855) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4043846-4043855"...
% 0.10/0.43 % (4043855)...printing done.
% 0.10/0.43 % (4043855)Refutation found. Thanks to Tanya!
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (4043855)------------------------------
% 0.10/0.44 % (4043855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (4043855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (4043855)CaDiCaL version: 2.1.3
% 0.10/0.44 % (4043855)Termination reason: Refutation
% 0.10/0.44 % (4043855)Time elapsed: 0.003 s
% 0.10/0.44 % (4043855)Peak memory usage: 12 MB
% 0.10/0.44 % (4043855)Instructions burned: 7 (million)
% 0.10/0.44 % (4043846)Success in time 0.028 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------