%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU501_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:49:20 PM UTC 2026
% Result : Theorem 1.98s 0.88s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 4 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 29 ( 13 ~; 2 |; 4 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 26 ( 21 fml; 5 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 16 ( 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK1: $o ).
tff(f1,axiom,
( emptysetAx
= ( ! [X0: $i] : ~ in(X0,emptyset) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
tff(f2,conjecture,
( emptysetAx
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
tff(f3,negated_conjecture,
~ ( emptysetAx
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( emptysetAx
<=> ! [X0: $i] : ~ in(X0,emptyset) ),
inference(fool_elimination,[],[f1]) ).
tff(f5,plain,
~ ( emptysetAx
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ),
inference(rectify,[],[f3]) ).
tff(f6,plain,
~ ( emptysetAx
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( emptysetAx
=> ! [X0: $i] : ~ in(X0,emptyset) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
tff(f8,plain,
( ? [X0: $i] :
( ? [X1: $o] : ( $true != (X1) )
& in(X0,emptyset) )
& emptysetAx ),
inference(ennf_transformation,[],[f6]) ).
tff(f9,plain,
( ! [X0: $i] : ~ in(X0,emptyset)
| ~ emptysetAx ),
inference(ennf_transformation,[],[f7]) ).
tff(f10,plain,
( ( $true != sK1 )
& in(sK0,emptyset)
& emptysetAx ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
tff(f11,plain,
emptysetAx,
inference(cnf_transformation,[],[f10]) ).
tff(f12,plain,
in(sK0,emptyset),
inference(cnf_transformation,[],[f10]) ).
tff(f14,plain,
! [X0: $i] :
( ~ in(X0,emptyset)
| ~ emptysetAx ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
! [X0: $i] : ~ in(X0,emptyset),
inference(forward_subsumption_resolution,[],[f14,f11]) ).
tff(f18,plain,
$false,
inference(resolution,[],[f17,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU501_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Mon Sep 28 05:40:34 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 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
% 1.98/0.88 % (3071363)Detected formulas, will run a generic FOF schedule.
% 1.98/0.88 % (3071372)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3992690529:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.98/0.88 % (3071369)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=1020884468:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.98/0.88 % (3071371)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=649372427:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.98/0.88 % (3071374)dis-21_1_sil=8000:lcm=predicate:random_seed=1630652559: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)
% 1.98/0.88 % (3071370)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=2324047020:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.98/0.88 % (3071373)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2288862967:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.98/0.88 % (3071368)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=2857200261:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.98/0.88 % (3071372)First to succeed.
% 1.98/0.88 % (3071371)Also succeeded, but the first one will report.
% 1.98/0.88 % (3071373)Also succeeded, but the first one will report.
% 1.98/0.88 % (3071374)Also succeeded, but the first one will report.
% 1.98/0.88 % (3071372)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3071363"
% 1.98/0.88 % (3071372)Refutation found. Thanks to Tanya!
% 1.98/0.88 % SZS status Theorem for theBenchmark
% 1.98/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 1.98/0.88 % (3071372)------------------------------
% 1.98/0.88 % (3071372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.98/0.88 % (3071372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.88 % (3071372)CaDiCaL version: 2.1.3
% 1.98/0.88 % (3071372)Termination reason: Refutation
% 1.98/0.88 % (3071372)Time elapsed: 0.001 s
% 1.98/0.88 % (3071372)Peak memory usage: 88 MB
% 1.98/0.88 % (3071372)------------------------------
% 1.98/0.88 % (3071372)------------------------------
% 1.98/0.88 % (3071363)Success in time 0.257 s
% 1.98/0.88 % Vampire exiting
%------------------------------------------------------------------------------