%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET926+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 : n018.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 12:42:20 PM UTC 2026
% Result : Theorem 3.77s 1.41s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 14 unt; 3 def)
% Number of atoms : 48 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 12 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
| set_difference(singleton(X0),X1) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
| set_difference(singleton(X0),X1) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( empty_set != set_difference(singleton(X0),X1)
& singleton(X0) != set_difference(singleton(X0),X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
( empty_set != set_difference(singleton(sK0),sK1)
& singleton(sK0) != set_difference(singleton(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),X1) = empty_set
| ~ in(X0,X1) )
& ( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),X1) = singleton(X0)
| in(X0,X1) )
& ( ~ in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
singleton(sK0) != set_difference(singleton(sK0),sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
empty_set != set_difference(singleton(sK0),sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,definition,
~ sP2(empty_set),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f21,plain,
sP2(set_difference(singleton(sK0),sK1)),
inference(inequality_splitting,[],[f15,f20]) ).
fof(f22,definition,
~ sP3(singleton(sK0)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f23,plain,
sP3(set_difference(singleton(sK0),sK1)),
inference(inequality_splitting,[],[f14,f22]) ).
fof(f28,plain,
( sP2(empty_set)
| ~ in(sK0,sK1) ),
inference(superposition,[],[f21,f17]) ).
fof(f29,plain,
~ in(sK0,sK1),
inference(forward_subsumption_resolution,[],[f28,f20]) ).
fof(f31,definition,
( spl5_1
<=> in(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f32,plain,
( ~ in(sK0,sK1)
| spl5_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f39,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f29,f31]) ).
fof(f40,plain,
( sP3(singleton(sK0))
| in(sK0,sK1) ),
inference(superposition,[],[f23,f19]) ).
fof(f42,plain,
in(sK0,sK1),
inference(forward_subsumption_resolution,[],[f40,f22]) ).
fof(f43,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f42,f32]) ).
fof(f44,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f43]) ).
cnf(s2,plain,
~ spl5_1,
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
spl5_1,
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f45,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET926+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:13:24 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.77/1.41 % (2961343)Detected formulas, will run a generic FOF schedule.
% 3.77/1.41 % (2961449)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=2994058166:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.77/1.41 % (2961452)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2485553186:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.77/1.41 % (2961451)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=3808172941:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.77/1.41 % (2961448)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=3991894869:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.77/1.41 % (2961452)First to succeed.
% 3.77/1.41 % (2961452)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2961343"
% 3.77/1.41 % (2961454)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2196267236:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.77/1.41 % (2961453)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=41274027:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.77/1.41 % (2961455)dis-21_1_sil=8000:lcm=predicate:random_seed=4107694345: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)
% 3.77/1.41 % (2961455)Also succeeded, but the first one will report.
% 3.77/1.41 % (2961453)Also succeeded, but the first one will report.
% 3.77/1.41 % (2961454)Also succeeded, but the first one will report.
% 3.77/1.41 % (2961452)Refutation found. Thanks to Tanya!
% 3.77/1.41 % SZS status Theorem for theBenchmark
% 3.77/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.41 % (2961452)------------------------------
% 3.77/1.41 % (2961452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.41 % (2961452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.41 % (2961452)CaDiCaL version: 2.1.3
% 3.77/1.41 % (2961452)Termination reason: Refutation
% 3.77/1.41 % (2961452)Time elapsed: 0.003 s
% 3.77/1.41 % (2961452)Peak memory usage: 89 MB
% 3.77/1.41 % (2961452)Instructions burned: 1 (million)
% 3.77/1.41 % (2961452)------------------------------
% 3.77/1.41 % (2961452)------------------------------
% 3.77/1.41 % (2961343)Success in time 0.463 s
% 3.77/1.41 % Vampire exiting
%------------------------------------------------------------------------------