%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU143+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:47:23 PM UTC 2026
% Result : Theorem 2.66s 1.32s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 63 ( 36 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 74 ( 31 ~; 28 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f7,conjecture,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] : singleton(X0) != empty_set,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
? [X0] : singleton(X0) = empty_set,
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
empty_set = singleton(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11]) ).
fof(f14,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0] :
( ( X0 = empty_set
| in(sK1(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK2(X0,X1) != X0
| ~ in(sK2(X0,X1),X1) )
& ( sK2(X0,X1) = X0
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f18]) ).
fof(f22,plain,
empty_set = singleton(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f23]) ).
fof(f34,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f26]) ).
fof(f35,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f34]) ).
fof(f37,plain,
in(sK0,empty_set),
inference(superposition,[],[f35,f22]) ).
fof(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU143+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:43:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.66/1.32 % (2997465)Detected formulas, will run a generic FOF schedule.
% 2.66/1.32 % (2997474)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=284331974:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.32 % (2997474)First to succeed.
% 2.66/1.32 % (2997474)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2997465"
% 2.66/1.32 % (2997473)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=535264764:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.32 % (2997471)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=984102232:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.32 % (2997472)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=1835241353:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.32 % (2997470)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=934145177:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.32 % (2997473)Also succeeded, but the first one will report.
% 2.66/1.32 % (2997476)dis-21_1_sil=8000:lcm=predicate:random_seed=568133321: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)
% 2.66/1.32 % (2997475)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=220369865:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.32 % (2997475)Also succeeded, but the first one will report.
% 2.66/1.32 % (2997476)Instruction limit reached!
% 2.66/1.32 % (2997476)------------------------------
% 2.66/1.32 % (2997476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.32 % (2997476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.32 % (2997476)CaDiCaL version: 2.1.3
% 2.66/1.32 % (2997476)Termination reason: Instruction limit
% 2.66/1.32 % (2997476)Termination phase: Saturation
% 2.66/1.32 % (2997476)Time elapsed: 0.058 s
% 2.66/1.32 % (2997476)Peak memory usage: 88 MB
% 2.66/1.32 % (2997476)Instructions burned: 130 (million)
% 2.66/1.32 % (2997474)Refutation found. Thanks to Tanya!
% 2.66/1.32 % SZS status Theorem for theBenchmark
% 2.66/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.32 % (2997474)------------------------------
% 2.66/1.32 % (2997474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.32 % (2997474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.32 % (2997474)CaDiCaL version: 2.1.3
% 2.66/1.32 % (2997474)Termination reason: Refutation
% 2.66/1.32 % (2997474)Time elapsed: 0.001 s
% 2.66/1.32 % (2997474)Peak memory usage: 88 MB
% 2.66/1.32 % (2997474)Instructions burned: 1 (million)
% 2.66/1.32 % (2997474)------------------------------
% 2.66/1.32 % (2997474)------------------------------
% 2.66/1.32 % (2997465)Success in time 0.288 s
% 2.66/1.32 % Vampire exiting
%------------------------------------------------------------------------------