%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:42:12 PM UTC 2026
% Result : Theorem 2.73s 1.38s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 13 unt; 3 def)
% Number of atoms : 103 ( 21 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 113 ( 45 ~; 43 |; 19 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 37 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f7,conjecture,
union(empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(f8,negated_conjecture,
union(empty_set) != empty_set,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
empty_set != union(empty_set),
inference(flattening,[],[f8]) ).
fof(f11,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK1(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK1(X0,X1),sK2(X0,X1))
& in(sK2(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK3(X0,X5))
& in(sK3(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f15]) ).
fof(f20,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK2(X0,X1),X0)
| in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
empty_set != union(empty_set),
inference(cnf_transformation,[],[f9]) ).
fof(f32,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f20]) ).
fof(f36,definition,
! [X0,X1] :
( sQ6_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ6_eqProxy])],[equality_proxy_definition]) ).
fof(f40,plain,
! [X0,X1] :
( sQ6_eqProxy(union(X0),X1)
| in(sK2(X0,X1),X0)
| in(sK1(X0,X1),X1) ),
inference(equality_proxy_replacement,[],[f25,f36]) ).
fof(f41,plain,
~ sQ6_eqProxy(empty_set,union(empty_set)),
inference(equality_proxy_replacement,[],[f31,f36]) ).
fof(f43,plain,
! [X0,X1] :
( sQ6_eqProxy(X1,X0)
| ~ sQ6_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f36]) ).
fof(f45,plain,
~ sQ6_eqProxy(union(empty_set),empty_set),
inference(resolution,[],[f43,f41]) ).
fof(f56,plain,
( in(sK2(empty_set,empty_set),empty_set)
| in(sK1(empty_set,empty_set),empty_set) ),
inference(resolution,[],[f40,f45]) ).
fof(f58,definition,
( spl7_1
<=> in(sK1(empty_set,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f59,plain,
( in(sK1(empty_set,empty_set),empty_set)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl7_2
<=> in(sK2(empty_set,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f62,plain,
( in(sK2(empty_set,empty_set),empty_set)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f56,f61,f58]) ).
fof(f64,plain,
( $false
| ~ spl7_2 ),
inference(resolution,[],[f62,f32]) ).
fof(f67,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f68,plain,
( $false
| ~ spl7_1 ),
inference(resolution,[],[f59,f32]) ).
fof(f71,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f68]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s2,plain,
~ spl7_2,
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
~ spl7_1,
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f72,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n014.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 03:04:33 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.73/1.38 % (1397291)Detected formulas, will run a generic FOF schedule.
% 2.73/1.38 % (1397302)dis-21_1_sil=8000:lcm=predicate:random_seed=3666182910: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)
% 2.73/1.38 % (1397302)First to succeed.
% 2.73/1.38 % (1397302)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1397291"
% 2.73/1.38 % (1397296)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=3201141255:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.38 % (1397297)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=2555763597:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.38 % (1397298)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=1066915614:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.38 % (1397300)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4234854305:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.38 % (1397299)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=78178620:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.38 % (1397301)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=150642186:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.38 % (1397299)Refutation not found, incomplete strategy
% 2.73/1.38 % (1397299)------------------------------
% 2.73/1.38 % (1397299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.38 % (1397299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.38 % (1397299)CaDiCaL version: 2.1.3
% 2.73/1.38 % (1397299)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.38 % (1397299)Time elapsed: 0.001 s
% 2.73/1.38 % (1397299)Peak memory usage: 88 MB
% 2.73/1.38 % (1397300)Also succeeded, but the first one will report.
% 2.73/1.38 % (1397301)Also succeeded, but the first one will report.
% 2.73/1.38 % (1397302)Refutation found. Thanks to Tanya!
% 2.73/1.38 % SZS status Theorem for theBenchmark
% 2.73/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.38 % (1397302)------------------------------
% 2.73/1.38 % (1397302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.38 % (1397302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.38 % (1397302)CaDiCaL version: 2.1.3
% 2.73/1.38 % (1397302)Termination reason: Refutation
% 2.73/1.38 % (1397302)Time elapsed: 0.002 s
% 2.73/1.38 % (1397302)Peak memory usage: 89 MB
% 2.73/1.38 % (1397302)Instructions burned: 2 (million)
% 2.73/1.38 % (1397302)------------------------------
% 2.73/1.38 % (1397302)------------------------------
% 2.73/1.38 % (1397291)Success in time 0.303 s
% 2.73/1.38 % Vampire exiting
%------------------------------------------------------------------------------