%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET880+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 : 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 12:42:13 PM UTC 2026
% Result : Theorem 2.64s 1.32s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 61 ( 39 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 68 ( 26 ~; 25 |; 12 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 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(f4,axiom,
! [X0,X1] :
( set_difference(singleton(X0),X1) = empty_set
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = empty_set
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = empty_set
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1] :
( X0 != X1
& set_difference(singleton(X0),singleton(X1)) = empty_set ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
( sK0 != sK1
& empty_set = set_difference(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,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,[],[f4]) ).
fof(f18,plain,
empty_set = set_difference(singleton(sK0),singleton(sK1)),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( empty_set != set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f20]) ).
fof(f36,plain,
( empty_set != empty_set
| in(sK0,singleton(sK1)) ),
inference(superposition,[],[f25,f18]) ).
fof(f37,plain,
in(sK0,singleton(sK1)),
inference(trivial_inequality_removal,[],[f36]) ).
fof(f39,plain,
sK0 = sK1,
inference(resolution,[],[f37,f32]) ).
fof(f41,plain,
$false,
inference(forward_subsumption_resolution,[],[f39,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:08:42 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 2.64/1.32 % (3429826)Detected formulas, will run a generic FOF schedule.
% 2.64/1.32 % (3429835)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3197187838:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.32 % (3429835)First to succeed.
% 2.64/1.32 % (3429835)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3429826"
% 2.64/1.32 % (3429832)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=1962991874:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.32 % (3429831)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=1175986553:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.32 % (3429834)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=966407:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.32 % (3429833)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=1821315578:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.32 % (3429834)Also succeeded, but the first one will report.
% 2.64/1.32 % (3429837)dis-21_1_sil=8000:lcm=predicate:random_seed=1837511936: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)
% 2.64/1.32 % (3429836)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3187494860:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.32 % (3429837)Also succeeded, but the first one will report.
% 2.64/1.32 % (3429836)Also succeeded, but the first one will report.
% 2.64/1.32 % (3429835)Refutation found. Thanks to Tanya!
% 2.64/1.32 % SZS status Theorem for theBenchmark
% 2.64/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.32 % (3429835)------------------------------
% 2.64/1.32 % (3429835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.32 % (3429835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.32 % (3429835)CaDiCaL version: 2.1.3
% 2.64/1.32 % (3429835)Termination reason: Refutation
% 2.64/1.32 % (3429835)Time elapsed: 0.001 s
% 2.64/1.33 % (3429835)Peak memory usage: 88 MB
% 2.64/1.33 % (3429835)Instructions burned: 1 (million)
% 2.64/1.33 % (3429835)------------------------------
% 2.64/1.33 % (3429835)------------------------------
% 2.64/1.33 % (3429826)Success in time 0.291 s
% 2.64/1.33 % Vampire exiting
%------------------------------------------------------------------------------