%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:42:55 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 69 ( 25 ~; 22 |; 17 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( member(null_class,X0)
& subclass(image(successor_relation,X0),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).
fof(f30,axiom,
? [X0] :
( member(X0,universal_class)
& inductive(X0)
& ! [X1] :
( inductive(X1)
=> subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).
fof(f44,conjecture,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f45,negated_conjecture,
~ member(null_class,universal_class),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
~ member(null_class,universal_class),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f52,plain,
? [X0] :
( member(X0,universal_class)
& inductive(X0)
& ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f61,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f62,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f86,plain,
! [X0] :
( ( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) )
& ( ( member(null_class,X0)
& subclass(image(successor_relation,X0),X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f87,plain,
! [X0] :
( ( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) )
& ( ( member(null_class,X0)
& subclass(image(successor_relation,X0),X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
( member(sK1,universal_class)
& inductive(sK1)
& ! [X1] :
( subclass(sK1,X1)
| ~ inductive(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f52]) ).
fof(f103,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f159,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f162,plain,
inductive(sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f190,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[],[f46]) ).
fof(f228,plain,
member(null_class,sK1),
inference(resolution,[],[f159,f162]) ).
fof(f384,plain,
! [X0] :
( ~ subclass(sK1,X0)
| member(null_class,X0) ),
inference(resolution,[],[f103,f228]) ).
fof(f635,plain,
member(null_class,universal_class),
inference(resolution,[],[f384,f106]) ).
fof(f637,plain,
$false,
inference(forward_subsumption_resolution,[],[f635,f190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n002.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 00:30:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 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
% 0.13/0.44 % (4047048)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (4047058)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3829640306:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.44 % (4047054)% WARNING: option uhcvi not known.
% 0.13/0.44 % (4047053)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2176481648_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.44 % (4047057)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3388913096:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.44 % (4047054)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1929895606:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.44 % (4047058) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4047048-4047058"...
% 0.13/0.44 % (4047055)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=642699339:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.44 % (4047056)dis+10_1_sil=32000:sp=arity:random_seed=3153361142:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.44 % (4047059)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1556460423:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.44 % (4047058)...printing done.
% 0.13/0.44 % (4047058)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (4047058)------------------------------
% 0.13/0.44 % (4047058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (4047058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (4047058)CaDiCaL version: 2.1.3
% 0.13/0.44 % (4047058)Termination reason: Refutation
% 0.13/0.44 % (4047058)Time elapsed: 0.008 s
% 0.13/0.44 % (4047058)Peak memory usage: 12 MB
% 0.13/0.44 % (4047058)Instructions burned: 20 (million)
% 0.13/0.44 % (4047048)Success in time 0.034 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------