%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:42:16 PM UTC 2026
% Result : Theorem 2.68s 1.37s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 3 def)
% Number of atoms : 84 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 44 ~; 29 |; 15 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
~ ( in(X2,X0)
& X2 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
~ ( in(X2,X0)
& X2 != X1 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
~ ( in(X2,X0)
& X2 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_zfmisc_1) ).
fof(f9,plain,
? [X0,X1] :
( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
( ~ in(X2,X0)
| X1 = X2 ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ? [X2] :
( in(X2,X0)
& X2 != X1 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
( sK2 != singleton(sK3)
& empty_set != sK2
& ! [X2] :
( ~ in(X2,sK2)
| sK3 = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ( in(sK4(X0,X1),X0)
& sK4(X0,X1) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f10]) ).
fof(f19,plain,
! [X2] :
( ~ in(X2,sK2)
| sK3 = X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
sK2 != singleton(sK3),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| sK4(X0,X1) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f25,plain,
~ sQ5_eqProxy(sK2,singleton(sK3)),
inference(equality_proxy_replacement,[],[f21,f24]) ).
fof(f26,plain,
~ sQ5_eqProxy(empty_set,sK2),
inference(equality_proxy_replacement,[],[f20,f24]) ).
fof(f27,plain,
! [X2] :
( sQ5_eqProxy(sK3,X2)
| ~ in(X2,sK2) ),
inference(equality_proxy_replacement,[],[f19,f24]) ).
fof(f28,plain,
! [X0,X1] :
( sQ5_eqProxy(singleton(X1),X0)
| sQ5_eqProxy(empty_set,X0)
| in(sK4(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f23,f24,f24]) ).
fof(f29,plain,
! [X0,X1] :
( ~ sQ5_eqProxy(sK4(X0,X1),X1)
| sQ5_eqProxy(empty_set,X0)
| sQ5_eqProxy(singleton(X1),X0) ),
inference(equality_proxy_replacement,[],[f22,f24,f24,f24]) ).
fof(f31,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f24]) ).
fof(f34,plain,
~ sQ5_eqProxy(singleton(sK3),sK2),
inference(resolution,[],[f31,f25]) ).
fof(f36,plain,
( sQ5_eqProxy(empty_set,sK2)
| in(sK4(sK2,sK3),sK2) ),
inference(resolution,[],[f34,f28]) ).
fof(f39,definition,
( spl6_1
<=> in(sK4(sK2,sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f42,definition,
( spl6_2
<=> sQ5_eqProxy(empty_set,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f43,plain,
( sQ5_eqProxy(empty_set,sK2)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f36,f42,f39]) ).
fof(f45,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f43,f26]) ).
fof(f46,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f49,plain,
! [X0,X1] :
( ~ sQ5_eqProxy(X1,sK4(X0,X1))
| sQ5_eqProxy(singleton(X1),X0)
| sQ5_eqProxy(empty_set,X0) ),
inference(resolution,[],[f29,f31]) ).
fof(f50,plain,
! [X0] :
( sQ5_eqProxy(singleton(sK3),X0)
| sQ5_eqProxy(empty_set,X0)
| ~ in(sK4(X0,sK3),sK2) ),
inference(resolution,[],[f49,f27]) ).
fof(f53,plain,
( sQ5_eqProxy(empty_set,sK2)
| ~ in(sK4(sK2,sK3),sK2) ),
inference(resolution,[],[f50,f34]) ).
fof(f56,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f53,f42,f39]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
~ spl6_2,
inference(sat_conversion,[],[f46]) ).
cnf(s3,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
~ spl6_1,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:13:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.68/1.37 % (4175214)Detected formulas, will run a generic FOF schedule.
% 2.68/1.37 % (4175225)dis-21_1_sil=8000:lcm=predicate:random_seed=483682503: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)
% 2.68/1.37 % (4175225)First to succeed.
% 2.68/1.37 % (4175225)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4175214"
% 2.68/1.37 % (4175221)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=958969729:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.37 % (4175220)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=4009436751:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.37 % (4175223)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2208376983:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.37 % (4175222)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3297199237:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.37 % (4175219)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=1359168785:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.37 % (4175223)Also succeeded, but the first one will report.
% 2.68/1.37 % (4175222)Also succeeded, but the first one will report.
% 2.68/1.37 % (4175224)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2058703377:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.37 % (4175224)Also succeeded, but the first one will report.
% 2.68/1.37 % (4175225)Refutation found. Thanks to Tanya!
% 2.68/1.37 % SZS status Theorem for theBenchmark
% 2.68/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.37 % (4175225)------------------------------
% 2.68/1.37 % (4175225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.37 % (4175225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.37 % (4175225)CaDiCaL version: 2.1.3
% 2.68/1.37 % (4175225)Termination reason: Refutation
% 2.68/1.37 % (4175225)Time elapsed: 0.002 s
% 2.68/1.37 % (4175225)Peak memory usage: 89 MB
% 2.68/1.37 % (4175225)Instructions burned: 1 (million)
% 2.68/1.37 % (4175225)------------------------------
% 2.68/1.37 % (4175225)------------------------------
% 2.68/1.37 % (4175214)Success in time 0.296 s
% 2.68/1.37 % Vampire exiting
%------------------------------------------------------------------------------