%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV521+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:57:52 PM UTC 2026
% Result : Theorem 1.15s 1.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 6 unt; 1 def)
% Number of atoms : 221 ( 29 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 244 ( 78 ~; 92 |; 52 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 132 ( 103 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f13,axiom,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X1) )
& ! [X2] :
( member(X2,X1)
=> ? [X3] :
( member(X3,X0)
& member(X2,X3) ) )
& ! [X2,X3] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( ? [X4] :
( member(X4,X2)
& member(X4,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition) ).
fof(f20,conjecture,
! [X0] :
( X0 != empty_set
=> partition(singleton(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_partitions_itself) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( X0 != empty_set
=> partition(singleton(X0),X0) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( partition(X0,X1)
<=> ( ! [X2] :
( member(X2,X0)
=> subset(X2,X1) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X0)
& member(X3,X4) ) )
& ! [X5,X6] :
( ( member(X5,X0)
& member(X6,X0) )
=> ( ? [X7] :
( member(X7,X5)
& member(X7,X6) )
=> X5 = X6 ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
=> subset(X2,X1) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X0)
& member(X3,X4) ) )
& ! [X5,X6] :
( ( member(X5,X0)
& member(X6,X0) )
=> ( ? [X7] :
( member(X7,X5)
& member(X7,X6) )
=> X5 = X6 ) ) )
=> partition(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f25,plain,
? [X0] :
( ~ partition(singleton(X0),X0)
& X0 != empty_set ),
inference(ennf_transformation,[],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( partition(X0,X1)
| ? [X2] :
( ~ subset(X2,X1)
& member(X2,X0) )
| ? [X3] :
( ! [X4] :
( ~ member(X4,X0)
| ~ member(X3,X4) )
& member(X3,X1) )
| ? [X5,X6] :
( X5 != X6
& ? [X7] :
( member(X7,X5)
& member(X7,X6) )
& member(X5,X0)
& member(X6,X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( partition(X0,X1)
| ? [X2] :
( ~ subset(X2,X1)
& member(X2,X0) )
| ? [X3] :
( ! [X4] :
( ~ member(X4,X0)
| ~ member(X3,X4) )
& member(X3,X1) )
| ? [X5,X6] :
( X5 != X6
& ? [X7] :
( member(X7,X5)
& member(X7,X6) )
& member(X5,X0)
& member(X6,X0) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f29,definition,
! [X0] :
( ? [X5,X6] :
( X5 != X6
& ? [X7] :
( member(X7,X5)
& member(X7,X6) )
& member(X5,X0)
& member(X6,X0) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f30,plain,
! [X0,X1] :
( partition(X0,X1)
| ? [X2] :
( ~ subset(X2,X1)
& member(X2,X0) )
| ? [X3] :
( ! [X4] :
( ~ member(X4,X0)
| ~ member(X3,X4) )
& member(X3,X1) )
| sP0(X0) ),
inference(definition_folding,[],[f27,f29]) ).
fof(f31,plain,
( ~ partition(singleton(sK1),sK1)
& empty_set != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f25]) ).
fof(f32,plain,
! [X0] :
( ? [X5,X6] :
( X5 != X6
& ? [X7] :
( member(X7,X5)
& member(X7,X6) )
& member(X5,X0)
& member(X6,X0) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f33,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& ? [X3] :
( member(X3,X1)
& member(X3,X2) )
& member(X1,X0)
& member(X2,X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ( sK2(X0) != sK3(X0)
& member(sK4(X0),sK2(X0))
& member(sK4(X0),sK3(X0))
& member(sK2(X0),X0)
& member(sK3(X0),X0) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0)),skolemize(X3,sK4(X0))],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( partition(X0,X1)
| ( ~ subset(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) )
| ( ! [X4] :
( ~ member(X4,X0)
| ~ member(sK6(X0,X1),X4) )
& member(sK6(X0,X1),X1) )
| sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1))],[f30]) ).
fof(f36,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f28]) ).
fof(f39,plain,
~ partition(singleton(sK1),sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f41,plain,
! [X0] :
( member(sK3(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f42,plain,
! [X0] :
( member(sK2(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f45,plain,
! [X0] :
( sK2(X0) != sK3(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| member(sK5(X0,X1),X0)
| partition(X0,X1)
| sP0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0,X1,X4] :
( member(sK5(X0,X1),X0)
| partition(X0,X1)
| ~ member(X4,X0)
| ~ member(sK6(X0,X1),X4)
| sP0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f48,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| ~ subset(sK5(X0,X1),X1)
| partition(X0,X1)
| sP0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f49,plain,
! [X0,X1,X4] :
( ~ member(sK6(X0,X1),X4)
| ~ subset(sK5(X0,X1),X1)
| ~ member(X4,X0)
| partition(X0,X1)
| sP0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f50,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f51]) ).
fof(f58,plain,
! [X0] :
( sK2(singleton(X0)) = X0
| ~ sP0(singleton(X0)) ),
inference(resolution,[],[f50,f42]) ).
fof(f59,plain,
! [X0] :
( sK3(singleton(X0)) = X0
| ~ sP0(singleton(X0)) ),
inference(resolution,[],[f50,f41]) ).
fof(f62,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[],[f53,f52]) ).
fof(f63,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literal_removal,[],[f62]) ).
fof(f70,plain,
! [X0] :
( sK2(singleton(X0)) != X0
| ~ sP0(singleton(X0))
| ~ sP0(singleton(X0)) ),
inference(superposition,[],[f45,f59]) ).
fof(f75,plain,
! [X0] :
( sK2(singleton(X0)) != X0
| ~ sP0(singleton(X0)) ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f76,plain,
! [X0] : ~ sP0(singleton(X0)),
inference(forward_subsumption_resolution,[],[f75,f58]) ).
fof(f80,plain,
! [X2,X0,X1] :
( partition(singleton(X0),X1)
| ~ member(X2,singleton(X0))
| ~ member(sK6(singleton(X0),X1),X2)
| sP0(singleton(X0))
| sK5(singleton(X0),X1) = X0 ),
inference(resolution,[],[f47,f50]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ member(sK6(singleton(X0),X1),X2)
| ~ member(X2,singleton(X0))
| partition(singleton(X0),X1)
| sK5(singleton(X0),X1) = X0 ),
inference(forward_subsumption_resolution,[],[f80,f76]) ).
fof(f82,plain,
! [X0,X1] :
( ~ subset(sK5(X0,X1),X1)
| ~ member(X1,X0)
| partition(X0,X1)
| sP0(X0)
| ~ subset(sK5(X0,X1),X1)
| partition(X0,X1)
| sP0(X0) ),
inference(resolution,[],[f49,f48]) ).
fof(f86,plain,
! [X0,X1] :
( ~ subset(sK5(X0,X1),X1)
| ~ member(X1,X0)
| partition(X0,X1)
| sP0(X0) ),
inference(duplicate_literal_removal,[],[f82]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| partition(singleton(X1),X0)
| sK5(singleton(X1),X0) = X1
| member(sK5(singleton(X1),X0),singleton(X1))
| partition(singleton(X1),X0)
| sP0(singleton(X1)) ),
inference(resolution,[],[f81,f46]) ).
fof(f130,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| partition(singleton(X1),X0)
| sK5(singleton(X1),X0) = X1
| member(sK5(singleton(X1),X0),singleton(X1))
| sP0(singleton(X1)) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f132,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| partition(singleton(X1),X0)
| sK5(singleton(X1),X0) = X1
| sP0(singleton(X1)) ),
inference(forward_subsumption_resolution,[],[f130,f50]) ).
fof(f133,plain,
! [X0,X1] :
( sK5(singleton(X1),X0) = X1
| partition(singleton(X1),X0)
| ~ member(X0,singleton(X1)) ),
inference(forward_subsumption_resolution,[],[f132,f76]) ).
fof(f134,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ member(X1,singleton(X0))
| partition(singleton(X0),X1)
| sP0(singleton(X0))
| partition(singleton(X0),X1)
| ~ member(X1,singleton(X0)) ),
inference(superposition,[],[f86,f133]) ).
fof(f145,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ member(X1,singleton(X0))
| partition(singleton(X0),X1)
| sP0(singleton(X0)) ),
inference(duplicate_literal_removal,[],[f134]) ).
fof(f147,plain,
! [X0,X1] :
( partition(singleton(X0),X1)
| ~ member(X1,singleton(X0))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f145,f76]) ).
fof(f148,plain,
( ~ member(sK1,singleton(sK1))
| ~ subset(sK1,sK1) ),
inference(resolution,[],[f147,f39]) ).
fof(f149,plain,
~ subset(sK1,sK1),
inference(forward_subsumption_resolution,[],[f148,f54]) ).
fof(f150,plain,
$false,
inference(forward_subsumption_resolution,[],[f149,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV521+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.41 % Computer : n003.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Mon Sep 28 06:31:57 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 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
% 1.15/1.41 % (1379449)Detected formulas, will run a generic FOF schedule.
% 1.15/1.41 % (1379458)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3368360715:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.15/1.41 % (1379458)First to succeed.
% 1.15/1.41 % (1379458)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1379449"
% 1.15/1.41 % (1379459)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=98154888:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.15/1.41 % (1379460)dis-21_1_sil=8000:lcm=predicate:random_seed=2272919171: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)
% 1.15/1.41 % (1379454)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=3448233135:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.15/1.41 % (1379455)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=3007158011:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.15/1.41 % (1379457)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3773613152:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.15/1.41 % (1379456)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=2047857884:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.15/1.41 % (1379457)Refutation not found, incomplete strategy
% 1.15/1.41 % (1379457)------------------------------
% 1.15/1.41 % (1379457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.15/1.41 % (1379457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/1.41 % (1379457)CaDiCaL version: 2.1.3
% 1.15/1.41 % (1379457)Termination reason: Refutation not found, incomplete strategy
% 1.15/1.41 % (1379457)Time elapsed: 0.002 s
% 1.15/1.41 % (1379457)Peak memory usage: 88 MB
% 1.15/1.41 % (1379459)Also succeeded, but the first one will report.
% 1.15/1.41 % (1379458)Refutation found. Thanks to Tanya!
% 1.15/1.41 % SZS status Theorem for theBenchmark
% 1.15/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/1.60 % (1379458)------------------------------
% 0.22/1.60 % (1379458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.60 % (1379458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.60 % (1379458)CaDiCaL version: 2.1.3
% 0.22/1.60 % (1379458)Termination reason: Refutation
% 0.22/1.60 % (1379458)Time elapsed: 0.003 s
% 0.22/1.60 % (1379458)Peak memory usage: 88 MB
% 0.22/1.60 % (1379458)Instructions burned: 5 (million)
% 0.22/1.60 % (1379458)------------------------------
% 0.22/1.60 % (1379458)------------------------------
% 0.22/1.60 % (1379449)Success in time 0.396 s
% 0.22/1.60 % Vampire exiting
%------------------------------------------------------------------------------