%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET911+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 : n026.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 12:42:17 PM UTC 2026
% Result : Theorem 3.53s 1.48s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 1 def)
% Number of atoms : 23 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 3 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f11,plain,
? [X0,X1] :
( singleton(X0) != set_intersection2(X1,singleton(X0))
& in(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
( singleton(sK2) != set_intersection2(sK3,singleton(sK2))
& in(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11]) ).
fof(f21,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
singleton(sK2) != set_intersection2(sK3,singleton(sK2)),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( singleton(X0) = set_intersection2(X1,singleton(X0))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f27,plain,
~ sQ4_eqProxy(singleton(sK2),set_intersection2(sK3,singleton(sK2))),
inference(equality_proxy_replacement,[],[f22,f24]) ).
fof(f28,plain,
! [X0,X1] :
( sQ4_eqProxy(singleton(X0),set_intersection2(X1,singleton(X0)))
| ~ in(X0,X1) ),
inference(equality_proxy_replacement,[],[f23,f24]) ).
fof(f34,plain,
~ in(sK2,sK3),
inference(resolution,[],[f28,f27]) ).
fof(f35,plain,
$false,
inference(resolution,[],[f34,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n026.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:12:27 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.53/1.48 % (3431877)Detected formulas, will run a generic FOF schedule.
% 3.53/1.48 % (3431882)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=2326271472:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.48 % (3431884)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=2639891040:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.48 % (3431883)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=765524581:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.48 % (3431885)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1635615231:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.48 % (3431886)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1243957101:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.48 % (3431888)dis-21_1_sil=8000:lcm=predicate:random_seed=538190220: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)
% 3.53/1.48 % (3431887)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1009097094:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.48 % (3431885)Refutation not found, incomplete strategy
% 3.53/1.48 % (3431885)------------------------------
% 3.53/1.48 % (3431885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.48 % (3431885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.48 % (3431888)First to succeed.
% 3.53/1.48 % (3431885)CaDiCaL version: 2.1.3
% 3.53/1.48 % (3431885)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.48 % (3431885)Time elapsed: 0.001 s
% 3.53/1.48 % (3431885)Peak memory usage: 88 MB
% 3.53/1.48 % (3431886)Also succeeded, but the first one will report.
% 3.53/1.48 % (3431887)Also succeeded, but the first one will report.
% 3.53/1.48 % (3431888)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3431877"
% 3.53/1.48 % (3431885)------------------------------
% 3.53/1.48 % (3431885)------------------------------
% 3.53/1.48 % (3431888)Refutation found. Thanks to Tanya!
% 3.53/1.48 % SZS status Theorem for theBenchmark
% 3.53/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.48 % (3431888)------------------------------
% 3.53/1.48 % (3431888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.48 % (3431888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.48 % (3431888)CaDiCaL version: 2.1.3
% 3.53/1.48 % (3431888)Termination reason: Refutation
% 3.53/1.48 % (3431888)Time elapsed: 0.002 s
% 3.53/1.48 % (3431888)Peak memory usage: 88 MB
% 3.53/1.48 % (3431888)------------------------------
% 3.53/1.48 % (3431888)------------------------------
% 3.53/1.48 % (3431877)Success in time 0.413 s
% 3.53/1.48 % Vampire exiting
%------------------------------------------------------------------------------