%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET063+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:39:52 PM UTC 2026
% Result : Theorem 3.50s 1.46s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 61 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 64 ( 25 ~; 20 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X0,X1)
& subclass(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f44,conjecture,
! [X0] :
( subclass(X0,null_class)
=> X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( subclass(X0,null_class)
=> X0 = null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
? [X0] :
( null_class != X0
& subclass(X0,null_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f48,plain,
( null_class != sK0
& subclass(sK0,null_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f50,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f49]) ).
fof(f51,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,[],[f47]) ).
fof(f52,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,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f52]) ).
fof(f54,plain,
subclass(sK0,null_class),
inference(cnf_transformation,[],[f48]) ).
fof(f55,plain,
null_class != sK0,
inference(cnf_transformation,[],[f48]) ).
fof(f58,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f50]) ).
fof(f61,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f63,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f66,plain,
! [X0] : subclass(null_class,X0),
inference(resolution,[],[f61,f63]) ).
fof(f69,plain,
( ~ subclass(null_class,sK0)
| null_class = sK0 ),
inference(resolution,[],[f58,f54]) ).
fof(f74,plain,
null_class = sK0,
inference(forward_subsumption_resolution,[],[f69,f66]) ).
fof(f75,plain,
$false,
inference(forward_subsumption_resolution,[],[f74,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n003.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 00:28:57 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.50/1.46 % (1074828)Detected formulas, will run a generic FOF schedule.
% 3.50/1.46 % (1074835)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=166111623:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.46 % (1074836)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1099861727:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.46 % (1074836)Refutation not found, incomplete strategy
% 3.50/1.46 % (1074836)------------------------------
% 3.50/1.46 % (1074836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.46 % (1074836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.46 % (1074836)CaDiCaL version: 2.1.3
% 3.50/1.46 % (1074836)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.46 % (1074836)Time elapsed: 0.002 s
% 3.50/1.46 % (1074836)Peak memory usage: 88 MB
% 3.50/1.46 % (1074833)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=3352048714:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.46 % (1074834)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=3039602982:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.46 % (1074837)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1786899318:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.46 % (1074839)dis-21_1_sil=8000:lcm=predicate:random_seed=813163961: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)
% 3.50/1.46 % (1074838)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=391590311:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.46 % (1074837)First to succeed.
% 3.50/1.46 % (1074837)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1074828"
% 3.50/1.46 % (1074839)Also succeeded, but the first one will report.
% 3.50/1.46 % (1074838)Also succeeded, but the first one will report.
% 3.50/1.46 % (1074836)------------------------------
% 3.50/1.46 % (1074836)------------------------------
% 3.50/1.46 % (1074837)Refutation found. Thanks to Tanya!
% 3.50/1.46 % SZS status Theorem for theBenchmark
% 3.50/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.46 % (1074837)------------------------------
% 3.50/1.46 % (1074837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.46 % (1074837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.46 % (1074837)CaDiCaL version: 2.1.3
% 3.50/1.46 % (1074837)Termination reason: Refutation
% 3.50/1.46 % (1074837)Time elapsed: 0.002 s
% 3.50/1.46 % (1074837)Peak memory usage: 88 MB
% 3.50/1.46 % (1074837)Instructions burned: 1 (million)
% 3.50/1.46 % (1074837)------------------------------
% 3.50/1.46 % (1074837)------------------------------
% 3.50/1.46 % (1074828)Success in time 0.41 s
% 3.50/1.46 % Vampire exiting
%------------------------------------------------------------------------------