%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n017.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 12:39:54 PM UTC 2026
% Result : Theorem 3.53s 1.44s
% Output : Refutation 3.53s
% 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 : 70 ( 26 ~; 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 : 34 ( 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',inductive_defn) ).
fof(f30,axiom,
? [X0] :
( member(X0,universal_class)
& inductive(X0)
& ! [X1] :
( inductive(X1)
=> subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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(f58,plain,
? [X0] :
( member(X0,universal_class)
& inductive(X0)
& ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f62,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(f63,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,[],[f62]) ).
fof(f64,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))],[f63]) ).
fof(f67,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(f68,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,[],[f67]) ).
fof(f90,plain,
( member(sK4,universal_class)
& inductive(sK4)
& ! [X1] :
( subclass(sK4,X1)
| ~ inductive(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f58]) ).
fof(f98,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[],[f46]) ).
fof(f99,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f104,plain,
! [X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f113,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f160,plain,
inductive(sK4),
inference(cnf_transformation,[],[f90]) ).
fof(f238,plain,
member(null_class,sK4),
inference(resolution,[],[f113,f160]) ).
fof(f243,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f104,f99]) ).
fof(f253,plain,
! [X0] : ~ member(null_class,X0),
inference(resolution,[],[f243,f98]) ).
fof(f259,plain,
$false,
inference(resolution,[],[f253,f238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:23:21 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.53/1.44 % (3107796)Detected formulas, will run a generic FOF schedule.
% 3.53/1.44 % (3107804)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=947009338:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.44 % (3107804)Refutation not found, incomplete strategy
% 3.53/1.44 % (3107804)------------------------------
% 3.53/1.44 % (3107804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (3107804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (3107804)CaDiCaL version: 2.1.3
% 3.53/1.44 % (3107804)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.44 % (3107804)Time elapsed: 0.0000 s
% 3.53/1.44 % (3107804)Peak memory usage: 87 MB
% 3.53/1.44 % (3107803)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1692438659:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.44 % (3107802)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3831982994:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.44 % (3107801)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2889363042:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.44 % (3107806)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1485194154:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.44 % (3107807)dis-21_1_sil=8000:lcm=predicate:random_seed=3973299994:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.53/1.44 % (3107805)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3828754075:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.44 % (3107805)Refutation not found, incomplete strategy
% 3.53/1.44 % (3107805)------------------------------
% 3.53/1.44 % (3107805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (3107805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (3107805)CaDiCaL version: 2.1.3
% 3.53/1.44 % (3107805)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.44 % (3107805)Time elapsed: 0.001 s
% 3.53/1.44 % (3107805)Peak memory usage: 86 MB
% 3.53/1.44 % (3107807)First to succeed.
% 3.53/1.44 % (3107807)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3107796"
% 3.53/1.44 % (3107806)Also succeeded, but the first one will report.
% 3.53/1.44 % (3107804)------------------------------
% 3.53/1.44 % (3107804)------------------------------
% 3.53/1.44 % (3107815)lrs+10_1_sil=8000:sp=occurrence:random_seed=3215515033:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.44 % (3107815)Also succeeded, but the first one will report.
% 3.53/1.44 % (3107805)------------------------------
% 3.53/1.44 % (3107805)------------------------------
% 3.53/1.44 % (3107807)Refutation found. Thanks to Tanya!
% 3.53/1.44 % SZS status Theorem for theBenchmark
% 3.53/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.44 % (3107807)------------------------------
% 3.53/1.44 % (3107807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (3107807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (3107807)CaDiCaL version: 2.1.3
% 3.53/1.44 % (3107807)Termination reason: Refutation
% 3.53/1.44 % (3107807)Time elapsed: 0.004 s
% 3.53/1.44 % (3107807)Peak memory usage: 88 MB
% 3.53/1.44 % (3107807)Instructions burned: 6 (million)
% 3.53/1.44 % (3107807)------------------------------
% 3.53/1.44 % (3107807)------------------------------
% 3.53/1.44 % (3107796)Success in time 0.416 s
% 3.53/1.44 % Vampire exiting
%------------------------------------------------------------------------------