%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV517+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 4.00s 1.70s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 10 unt; 2 def)
% Number of atoms : 174 ( 11 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 194 ( 71 ~; 62 |; 40 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 84 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
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,X1,X2,X3] :
( ( member(X0,difference(X1,X2))
& partition(X3,X1) )
=> ? [X4] :
( member(X4,difference(X3,singleton(X2)))
& member(X0,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_elem_in_partition) ).
fof(f21,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( member(X0,difference(X1,X2))
& partition(X3,X1) )
=> ? [X4] :
( member(X4,difference(X3,singleton(X2)))
& member(X0,X4) ) ),
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(f25,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(unused_predicate_definition_removal,[],[f22]) ).
fof(f28,plain,
! [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) ) )
| ~ partition(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f29,plain,
! [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) ) )
| ~ partition(X0,X1) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
? [X0,X1,X2,X3] :
( ! [X4] :
( ~ member(X4,difference(X3,singleton(X2)))
| ~ member(X0,X4) )
& member(X0,difference(X1,X2))
& partition(X3,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f31,plain,
? [X0,X1,X2,X3] :
( ! [X4] :
( ~ member(X4,difference(X3,singleton(X2)))
| ~ member(X0,X4) )
& member(X0,difference(X1,X2))
& partition(X3,X1) ),
inference(flattening,[],[f30]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( ( ! [X2] :
( subset(X2,X1)
| ~ member(X2,X0) )
& ! [X3] :
( ( member(sK3(X0,X3),X0)
& member(X3,sK3(X0,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6] :
( X5 = X6
| ! [X7] :
( ~ member(X7,X5)
| ~ member(X7,X6) )
| ~ member(X5,X0)
| ~ member(X6,X0) ) )
| ~ partition(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X3))],[f29]) ).
fof(f57,plain,
( ! [X4] :
( ~ member(X4,difference(sK10,singleton(sK9)))
| ~ member(sK7,X4) )
& member(sK7,difference(sK8,sK9))
& partition(sK10,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f31]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f72,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f73,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
! [X3,X0,X1] :
( member(X3,sK3(X0,X3))
| ~ member(X3,X1)
| ~ partition(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f86,plain,
! [X3,X0,X1] :
( ~ partition(X0,X1)
| ~ member(X3,X1)
| member(sK3(X0,X3),X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f98,plain,
partition(sK10,sK8),
inference(cnf_transformation,[],[f57]) ).
fof(f99,plain,
member(sK7,difference(sK8,sK9)),
inference(cnf_transformation,[],[f57]) ).
fof(f100,plain,
! [X4] :
( ~ member(X4,difference(sK10,singleton(sK9)))
| ~ member(sK7,X4) ),
inference(cnf_transformation,[],[f57]) ).
fof(f111,plain,
~ member(sK7,sK9),
inference(resolution,[],[f70,f99]) ).
fof(f112,plain,
member(sK7,sK8),
inference(resolution,[],[f71,f99]) ).
fof(f128,plain,
! [X0] :
( ~ member(X0,sK10)
| member(X0,singleton(sK9))
| ~ member(sK7,X0) ),
inference(resolution,[],[f72,f100]) ).
fof(f134,plain,
! [X0] :
( ~ member(X0,sK8)
| member(sK3(sK10,X0),sK10) ),
inference(resolution,[],[f86,f98]) ).
fof(f135,plain,
member(sK3(sK10,sK7),sK10),
inference(resolution,[],[f134,f112]) ).
fof(f136,plain,
( member(sK3(sK10,sK7),singleton(sK9))
| ~ member(sK7,sK3(sK10,sK7)) ),
inference(resolution,[],[f135,f128]) ).
fof(f139,definition,
( spl11_1
<=> member(sK7,sK3(sK10,sK7)) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f140,plain,
( member(sK7,sK3(sK10,sK7))
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f141,plain,
( ~ member(sK7,sK3(sK10,sK7))
| spl11_1 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f143,definition,
( spl11_2
<=> member(sK3(sK10,sK7),singleton(sK9)) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f145,plain,
( member(sK3(sK10,sK7),singleton(sK9))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f136,f143,f139]) ).
fof(f167,plain,
( ! [X0] :
( ~ partition(sK10,X0)
| ~ member(sK7,X0) )
| spl11_1 ),
inference(resolution,[],[f141,f85]) ).
fof(f180,plain,
( ~ member(sK7,sK8)
| spl11_1 ),
inference(resolution,[],[f167,f98]) ).
fof(f181,plain,
( $false
| spl11_1 ),
inference(forward_subsumption_resolution,[],[f180,f112]) ).
fof(f182,plain,
spl11_1,
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f351,plain,
( sK9 = sK3(sK10,sK7)
| ~ spl11_2 ),
inference(resolution,[],[f145,f73]) ).
fof(f355,plain,
( member(sK7,sK9)
| ~ spl11_1
| ~ spl11_2 ),
inference(superposition,[],[f140,f351]) ).
fof(f361,plain,
( $false
| ~ spl11_1
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f355,f111]) ).
fof(f362,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_contradiction_clause,[],[f361]) ).
cnf(s1,plain,
( ~ spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f146]) ).
cnf(s2,plain,
spl11_1,
inference(sat_conversion,[],[f182]) ).
cnf(s11,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f362]) ).
cnf(s15,plain,
~ spl11_2,
inference(rat,[],[s11,s2]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s15,s2]) ).
fof(f363,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV517+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n003.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 28 06:31:42 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 4.00/1.70 % (1378969)Detected formulas, will run a generic FOF schedule.
% 4.00/1.70 % (1378979)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1632560164:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.00/1.70 % (1378979)First to succeed.
% 4.00/1.70 % (1378979)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1378969"
% 4.00/1.70 % (1378977)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2277256998:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.00/1.70 % (1378976)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=1620198315:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.00/1.70 % (1378975)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=1508402679:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.00/1.70 % (1378974)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=1859301601:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.00/1.70 % (1378977)Also succeeded, but the first one will report.
% 4.00/1.70 % (1378980)dis-21_1_sil=8000:lcm=predicate:random_seed=1499460905: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)
% 4.00/1.70 % (1378978)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=132767893:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.00/1.70 % (1378978)Instruction limit reached!
% 4.00/1.70 % (1378978)------------------------------
% 4.00/1.70 % (1378978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.70 % (1378978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.70 % (1378978)CaDiCaL version: 2.1.3
% 4.00/1.70 % (1378978)Termination reason: Instruction limit
% 4.00/1.70 % (1378978)Termination phase: Saturation
% 4.00/1.70 % (1378978)Time elapsed: 0.064 s
% 4.00/1.70 % (1378978)Peak memory usage: 88 MB
% 4.00/1.70 % (1378978)Instructions burned: 119 (million)
% 4.00/1.70 % (1378980)Instruction limit reached!
% 4.00/1.70 % (1378980)------------------------------
% 4.00/1.70 % (1378980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.70 % (1378980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.70 % (1378980)CaDiCaL version: 2.1.3
% 4.00/1.70 % (1378980)Termination reason: Instruction limit
% 4.00/1.70 % (1378980)Termination phase: Saturation
% 4.00/1.70 % (1378980)Time elapsed: 0.128 s
% 4.00/1.70 % (1378980)Peak memory usage: 90 MB
% 4.00/1.70 % (1378980)Instructions burned: 129 (million)
% 4.00/1.70 % (1378979)Refutation found. Thanks to Tanya!
% 4.00/1.70 % SZS status Theorem for theBenchmark
% 4.00/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/1.70 % (1378979)------------------------------
% 4.00/1.70 % (1378979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.70 % (1378979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.70 % (1378979)CaDiCaL version: 2.1.3
% 4.00/1.70 % (1378979)Termination reason: Refutation
% 4.00/1.70 % (1378979)Time elapsed: 0.013 s
% 4.00/1.70 % (1378979)Peak memory usage: 90 MB
% 4.00/1.70 % (1378979)Instructions burned: 14 (million)
% 4.00/1.70 % (1378979)------------------------------
% 4.00/1.70 % (1378979)------------------------------
% 4.00/1.70 % (1378969)Success in time 0.466 s
% 4.00/1.70 % Vampire exiting
%------------------------------------------------------------------------------