%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET925+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 : n009.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 3.46s 1.42s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 4 unt; 3 def)
% Number of atoms : 70 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 27 ~; 26 |; 3 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 22 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f9,plain,
? [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) )
& ( in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f13,plain,
( ( ~ in(sK2,sK3)
| empty_set != set_difference(singleton(sK2),sK3) )
& ( in(sK2,sK3)
| empty_set = set_difference(singleton(sK2),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f14,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,[],[f7]) ).
fof(f19,plain,
( in(sK2,sK3)
| empty_set = set_difference(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
( ~ in(sK2,sK3)
| empty_set != set_difference(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0,X1] :
( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f24,plain,
( ~ in(sK2,sK3)
| ~ sQ4_eqProxy(empty_set,set_difference(singleton(sK2),sK3)) ),
inference(equality_proxy_replacement,[],[f20,f23]) ).
fof(f25,plain,
( in(sK2,sK3)
| sQ4_eqProxy(empty_set,set_difference(singleton(sK2),sK3)) ),
inference(equality_proxy_replacement,[],[f19,f23]) ).
fof(f26,plain,
! [X0,X1] :
( sQ4_eqProxy(empty_set,set_difference(singleton(X0),X1))
| ~ in(X0,X1) ),
inference(equality_proxy_replacement,[],[f22,f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sQ4_eqProxy(empty_set,set_difference(singleton(X0),X1))
| in(X0,X1) ),
inference(equality_proxy_replacement,[],[f21,f23]) ).
fof(f31,definition,
( spl5_1
<=> sQ4_eqProxy(empty_set,set_difference(singleton(sK2),sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f32,plain,
( sQ4_eqProxy(empty_set,set_difference(singleton(sK2),sK3))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,definition,
( spl5_2
<=> in(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f36,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f25,f34,f31]) ).
fof(f37,plain,
( ~ sQ4_eqProxy(empty_set,set_difference(singleton(sK2),sK3))
| spl5_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f39,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f24,f34,f31]) ).
fof(f43,plain,
( ~ in(sK2,sK3)
| spl5_1 ),
inference(resolution,[],[f26,f37]) ).
fof(f44,plain,
( ~ spl5_2
| spl5_1 ),
inference(avatar_split_clause,[],[f43,f31,f34]) ).
fof(f46,plain,
( in(sK2,sK3)
| ~ spl5_1 ),
inference(resolution,[],[f27,f32]) ).
fof(f48,plain,
( spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f46,f31,f34]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s5,plain,
spl5_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl5_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET925+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.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 03:10:30 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.46/1.42 % (2628931)Detected formulas, will run a generic FOF schedule.
% 3.46/1.42 % (2628936)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=1142846903:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.42 % (2628942)dis-21_1_sil=8000:lcm=predicate:random_seed=4013759027: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)
% 3.46/1.42 % (2628937)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=3936948180:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.42 % (2628940)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1615939038:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.42 % (2628941)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3899851930:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.42 % (2628938)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=3556184585:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.42 % (2628939)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1251887966:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.42 % (2628942)First to succeed.
% 3.46/1.42 % (2628942)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2628931"
% 3.46/1.42 % (2628940)Also succeeded, but the first one will report.
% 3.46/1.42 % (2628939)Also succeeded, but the first one will report.
% 3.46/1.42 % (2628941)Also succeeded, but the first one will report.
% 3.46/1.42 % (2628942)Refutation found. Thanks to Tanya!
% 3.46/1.42 % SZS status Theorem for theBenchmark
% 3.46/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.42 % (2628942)------------------------------
% 3.46/1.42 % (2628942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.42 % (2628942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.42 % (2628942)CaDiCaL version: 2.1.3
% 3.46/1.42 % (2628942)Termination reason: Refutation
% 3.46/1.42 % (2628942)Time elapsed: 0.002 s
% 3.46/1.42 % (2628942)Peak memory usage: 89 MB
% 3.46/1.42 % (2628942)Instructions burned: 1 (million)
% 3.46/1.42 % (2628942)------------------------------
% 3.46/1.42 % (2628942)------------------------------
% 3.46/1.42 % (2628931)Success in time 0.402 s
% 3.46/1.42 % Vampire exiting
%------------------------------------------------------------------------------