%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM605+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:15:57 PM UTC 2026
% Result : Theorem 3.45s 1.46s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 12 unt; 2 def)
% Number of atoms : 94 ( 36 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 39 ~; 26 |; 23 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 19 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f78,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f99,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f100,conjecture,
~ ( ~ ? [X0] : aElementOf0(X0,xQ)
& xQ = slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f101,negated_conjecture,
~ ~ ( ~ ? [X0] : aElementOf0(X0,xQ)
& xQ = slcrc0 ),
inference(negated_conjecture,[status(cth)],[f100]) ).
fof(f121,plain,
( ~ ? [X0] : aElementOf0(X0,xQ)
& xQ = slcrc0 ),
inference(flattening,[],[f101]) ).
fof(f123,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f172,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f250,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(ennf_transformation,[],[f99]) ).
fof(f251,plain,
( ! [X0] : ~ aElementOf0(X0,xQ)
& xQ = slcrc0 ),
inference(ennf_transformation,[],[f121]) ).
fof(f285,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f286,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f285]) ).
fof(f287,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f286]) ).
fof(f288,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK25(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X1,sK25(X0))],[f287]) ).
fof(f308,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f172]) ).
fof(f434,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f288]) ).
fof(f500,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f308]) ).
fof(f628,plain,
sz00 != xK,
inference(cnf_transformation,[],[f78]) ).
fof(f825,plain,
xK = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f250]) ).
fof(f829,plain,
slcrc0 = xQ,
inference(cnf_transformation,[],[f251]) ).
fof(f831,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f434]) ).
fof(f838,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f500]) ).
fof(f891,definition,
( spl71_1
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl71_1])],[avatar_definition]) ).
fof(f895,definition,
( spl71_2
<=> sz00 = sbrdtbr0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl71_2])],[avatar_definition]) ).
fof(f897,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ spl71_2 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f898,plain,
( ~ spl71_1
| spl71_2 ),
inference(avatar_split_clause,[],[f838,f895,f891]) ).
fof(f904,plain,
spl71_1,
inference(avatar_split_clause,[],[f831,f891]) ).
fof(f908,plain,
xK = sbrdtbr0(slcrc0),
inference(forward_demodulation,[],[f825,f829]) ).
fof(f909,plain,
( sz00 = xK
| ~ spl71_2 ),
inference(forward_demodulation,[],[f897,f908]) ).
fof(f910,plain,
( $false
| ~ spl71_2 ),
inference(forward_subsumption_resolution,[],[f909,f628]) ).
fof(f911,plain,
~ spl71_2,
inference(avatar_contradiction_clause,[],[f910]) ).
cnf(s1,plain,
( ~ spl71_1
| spl71_2 ),
inference(sat_conversion,[],[f898]) ).
cnf(s3,plain,
spl71_1,
inference(sat_conversion,[],[f904]) ).
cnf(s5,plain,
~ spl71_2,
inference(sat_conversion,[],[f911]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f912,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM605+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:49:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.45/1.46 % (3936208)Detected formulas, will run a generic FOF schedule.
% 3.45/1.46 % (3936328)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=4090574853:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.46 % (3936330)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3731539651:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.46 % (3936331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2821582448:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.46 % (3936326)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=10885480:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.46 % (3936329)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4025617713:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.46 % (3936327)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=3472428499:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.46 % (3936331)First to succeed.
% 3.45/1.46 % (3936331)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3936208"
% 3.45/1.46 % (3936332)dis-21_1_sil=8000:lcm=predicate:random_seed=3222267510: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)
% 3.45/1.46 % (3936330)Also succeeded, but the first one will report.
% 3.45/1.46 % (3936329)Instruction limit reached!
% 3.45/1.46 % (3936329)------------------------------
% 3.45/1.46 % (3936329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.46 % (3936329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.46 % (3936329)CaDiCaL version: 2.1.3
% 3.45/1.46 % (3936329)Termination reason: Instruction limit
% 3.45/1.46 % (3936329)Termination phase: Saturation
% 3.45/1.46 % (3936329)Time elapsed: 0.058 s
% 3.45/1.46 % (3936329)Peak memory usage: 90 MB
% 3.45/1.46 % (3936329)Instructions burned: 110 (million)
% 3.45/1.46 % (3936332)Instruction limit reached!
% 3.45/1.46 % (3936332)------------------------------
% 3.45/1.46 % (3936332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.46 % (3936332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.46 % (3936332)CaDiCaL version: 2.1.3
% 3.45/1.46 % (3936332)Termination reason: Instruction limit
% 3.45/1.46 % (3936332)Termination phase: Saturation
% 3.45/1.46 % (3936332)Time elapsed: 0.072 s
% 3.45/1.46 % (3936332)Peak memory usage: 89 MB
% 3.45/1.46 % (3936332)Instructions burned: 131 (million)
% 3.45/1.46 % (3936340)lrs+10_1_sil=8000:sp=occurrence:random_seed=1562269074:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.45/1.46 % (3936340)Also succeeded, but the first one will report.
% 3.45/1.46 % (3936341)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4034923805:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.45/1.46 % (3936341)Refutation not found, incomplete strategy
% 3.45/1.46 % (3936341)------------------------------
% 3.45/1.46 % (3936341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.46 % (3936341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.46 % (3936341)CaDiCaL version: 2.1.3
% 3.45/1.46 % (3936341)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.46 % (3936341)Time elapsed: 0.003 s
% 3.45/1.46 % (3936341)Peak memory usage: 89 MB
% 3.45/1.46 % (3936341)Instructions burned: 3 (million)
% 3.45/1.46 % (3936331)Refutation found. Thanks to Tanya!
% 3.45/1.46 % SZS status Theorem for theBenchmark
% 3.45/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.46 % (3936331)------------------------------
% 3.45/1.46 % (3936331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.46 % (3936331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.46 % (3936331)CaDiCaL version: 2.1.3
% 3.45/1.46 % (3936331)Termination reason: Refutation
% 3.45/1.46 % (3936331)Time elapsed: 0.013 s
% 3.45/1.46 % (3936331)Peak memory usage: 90 MB
% 3.45/1.46 % (3936331)Instructions burned: 22 (million)
% 3.45/1.46 % (3936331)------------------------------
% 3.45/1.46 % (3936331)------------------------------
% 3.45/1.46 % (3936208)Success in time 0.419 s
% 3.45/1.46 % Vampire exiting
%------------------------------------------------------------------------------