%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM627+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 : 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 12:16:03 PM UTC 2026
% Result : ContradictoryAxioms 3.92s 1.54s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 12 unt; 2 def)
% Number of atoms : 112 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 53 ~; 39 |; 20 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).
fof(f111,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(f115,axiom,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
fof(f117,axiom,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5442) ).
fof(f118,axiom,
~ ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5461) ).
fof(f173,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f189,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f190,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f189]) ).
fof(f251,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f252,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f251]) ).
fof(f282,plain,
( ? [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(X0,sdtlpdtrp0(xN,xm)) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(ennf_transformation,[],[f117]) ).
fof(f283,plain,
( ? [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
& aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f118]) ).
fof(f469,plain,
( ~ aElementOf0(sK74,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aElementOf0(sK74,sdtlpdtrp0(xN,xm))
& ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(X0,sK74)],[f282]) ).
fof(f470,plain,
( ~ aElementOf0(sK75,sdtlpdtrp0(xN,xm))
& aElementOf0(sK75,sdtlpdtrp0(xN,xn))
& ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(X0,sK75)],[f283]) ).
fof(f520,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f533,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f693,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f898,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f911,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f913,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f469]) ).
fof(f916,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f470]) ).
fof(f1372,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[],[f693,f916]) ).
fof(f1373,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(resolution,[],[f693,f913]) ).
fof(f1378,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1373,f911]) ).
fof(f1379,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1372,f898]) ).
fof(f1382,definition,
( spl76_16
<=> aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl76_16])],[avatar_definition]) ).
fof(f1384,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl76_16 ),
inference(avatar_component_clause,[],[f1382]) ).
fof(f1386,definition,
( spl76_17
<=> sdtlseqdt0(szszuzczcdt0(xn),xm) ),
introduced(definition,[new_symbols(definition,[spl76_17])],[avatar_definition]) ).
fof(f1389,plain,
( ~ spl76_16
| ~ spl76_17 ),
inference(avatar_split_clause,[],[f1378,f1386,f1382]) ).
fof(f1390,plain,
~ sdtlseqdt0(xm,xn),
inference(forward_subsumption_resolution,[],[f1379,f911]) ).
fof(f1392,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1390,f533]) ).
fof(f1393,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1392,f911]) ).
fof(f1395,plain,
sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(forward_subsumption_resolution,[],[f1393,f898]) ).
fof(f1397,plain,
spl76_17,
inference(avatar_split_clause,[],[f1395,f1386]) ).
fof(f1398,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl76_16 ),
inference(resolution,[],[f1384,f520]) ).
fof(f1404,plain,
( $false
| spl76_16 ),
inference(forward_subsumption_resolution,[],[f1398,f898]) ).
fof(f1405,plain,
spl76_16,
inference(avatar_contradiction_clause,[],[f1404]) ).
cnf(s17,plain,
( ~ spl76_16
| ~ spl76_17 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s18,plain,
spl76_17,
inference(sat_conversion,[],[f1397]) ).
cnf(s19,plain,
spl76_16,
inference(sat_conversion,[],[f1405]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s17,s18,s19]) ).
fof(f1406,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM627+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:52:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 3.92/1.54 % (3193003)Detected formulas, will run a generic FOF schedule.
% 3.92/1.54 % (3193012)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=27192246:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.92/1.54 % (3193011)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2264186974:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.92/1.54 % (3193014)dis-21_1_sil=8000:lcm=predicate:random_seed=3073100761: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)
% 3.92/1.54 % (3193008)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=1361018781:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.92/1.54 % (3193010)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=3691987891:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.92/1.54 % (3193009)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=2218606321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.92/1.54 % (3193012)Instruction limit reached!
% 3.92/1.54 % (3193012)------------------------------
% 3.92/1.54 % (3193012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.54 % (3193012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.54 % (3193012)CaDiCaL version: 2.1.3
% 3.92/1.54 % (3193012)Termination reason: Instruction limit
% 3.92/1.54 % (3193012)Termination phase: Saturation
% 3.92/1.54 % (3193012)Time elapsed: 0.042 s
% 3.92/1.54 % (3193012)Peak memory usage: 89 MB
% 3.92/1.54 % (3193012)Instructions burned: 121 (million)
% 3.92/1.54 % (3193013)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1711014772:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.92/1.54 % (3193013)First to succeed.
% 3.92/1.54 % (3193013)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3193003"
% 3.92/1.54 % (3193011)Instruction limit reached!
% 3.92/1.54 % (3193011)------------------------------
% 3.92/1.54 % (3193011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.54 % (3193011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.54 % (3193011)CaDiCaL version: 2.1.3
% 3.92/1.54 % (3193011)Termination reason: Instruction limit
% 3.92/1.54 % (3193011)Termination phase: Saturation
% 3.92/1.54 % (3193011)Time elapsed: 0.070 s
% 3.92/1.54 % (3193011)Peak memory usage: 90 MB
% 3.92/1.54 % (3193011)Instructions burned: 110 (million)
% 3.92/1.54 % (3193014)Instruction limit reached!
% 3.92/1.54 % (3193014)------------------------------
% 3.92/1.54 % (3193014)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.54 % (3193014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.54 % (3193014)CaDiCaL version: 2.1.3
% 3.92/1.54 % (3193014)Termination reason: Instruction limit
% 3.92/1.54 % (3193014)Termination phase: Saturation
% 3.92/1.54 % (3193014)Time elapsed: 0.070 s
% 3.92/1.54 % (3193014)Peak memory usage: 90 MB
% 3.92/1.54 % (3193014)Instructions burned: 130 (million)
% 3.92/1.54 % (3193021)lrs+10_1_sil=8000:sp=occurrence:random_seed=1072185022:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.92/1.54 % (3193021)Also succeeded, but the first one will report.
% 3.92/1.54 % (3193024)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2909400614:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.92/1.54 % (3193023)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3005900798:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.92/1.54 % (3193023)Refutation not found, incomplete strategy
% 3.92/1.54 % (3193023)------------------------------
% 3.92/1.54 % (3193023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.54 % (3193023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.54 % (3193023)CaDiCaL version: 2.1.3
% 3.92/1.54 % (3193023)Termination reason: Refutation not found, incomplete strategy
% 3.92/1.54 % (3193023)Time elapsed: 0.006 s
% 3.92/1.54 % (3193023)Peak memory usage: 89 MB
% 3.92/1.54 % (3193023)Instructions burned: 7 (million)
% 3.92/1.54 % (3193024)Also succeeded, but the first one will report.
% 3.92/1.54 % (3193013)Refutation found. Thanks to Tanya!
% 3.92/1.54 % SZS status ContradictoryAxioms for theBenchmark
% 3.92/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.54 % (3193013)------------------------------
% 3.92/1.54 % (3193013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.54 % (3193013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.54 % (3193013)CaDiCaL version: 2.1.3
% 3.92/1.54 % (3193013)Termination reason: Refutation
% 3.92/1.54 % (3193013)Time elapsed: 0.028 s
% 3.92/1.54 % (3193013)Peak memory usage: 90 MB
% 3.92/1.54 % (3193013)Instructions burned: 41 (million)
% 3.92/1.54 % (3193013)------------------------------
% 3.92/1.54 % (3193013)------------------------------
% 3.92/1.54 % (3193003)Success in time 0.472 s
% 3.92/1.54 % Vampire exiting
%------------------------------------------------------------------------------