%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET876+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:42:13 PM UTC 2026
% Result : Theorem 3.41s 1.25s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 57 ( 29 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 67 ( 28 ~; 23 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 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 : 31 ( 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1] :
( ~ disjoint(singleton(X0),singleton(X1))
& X0 != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
( ~ disjoint(singleton(sK0),singleton(sK1))
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f14,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(f15,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,[],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f17,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
~ disjoint(singleton(sK0),singleton(sK1)),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f19]) ).
fof(f33,plain,
in(sK0,singleton(sK1)),
inference(resolution,[],[f23,f18]) ).
fof(f37,plain,
sK0 = sK1,
inference(resolution,[],[f28,f33]) ).
fof(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET876+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:05:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.41/1.25 % (1525996)Detected formulas, will run a generic FOF schedule.
% 3.41/1.25 % (1526001)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=1367781665:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.25 % (1526003)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=4053859393:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.25 % (1526004)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3067574119:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.25 % (1526007)dis-21_1_sil=8000:lcm=predicate:random_seed=2308057065: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)
% 3.41/1.25 % (1526002)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=1699277085:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.25 % (1526005)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1750375901:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.25 % (1526006)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1418730742:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.25 % (1526004)Also succeeded, but the first one will report.
% 3.41/1.25 % (1526005)First to succeed.
% 3.41/1.25 % (1526007)Also succeeded, but the first one will report.
% 3.41/1.25 % (1526006)Also succeeded, but the first one will report.
% 3.41/1.25 % (1526005)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1525996"
% 3.41/1.25 % (1526005)Refutation found. Thanks to Tanya!
% 3.41/1.25 % SZS status Theorem for theBenchmark
% 3.41/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.26 % (1526005)------------------------------
% 3.41/1.26 % (1526005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.26 % (1526005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.26 % (1526005)CaDiCaL version: 2.1.3
% 3.41/1.26 % (1526005)Termination reason: Refutation
% 3.41/1.26 % (1526005)Time elapsed: 0.002 s
% 3.41/1.26 % (1526005)Peak memory usage: 88 MB
% 3.41/1.26 % (1526005)Instructions burned: 1 (million)
% 3.41/1.26 % (1526005)------------------------------
% 3.41/1.26 % (1526005)------------------------------
% 3.41/1.26 % (1525996)Success in time 0.426 s
% 3.41/1.26 % Vampire exiting
%------------------------------------------------------------------------------