%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM627+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 4.33s 1.83s
% Output : Refutation 4.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 14 unt; 2 def)
% Number of atoms : 88 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 91 ( 43 ~; 35 |; 7 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f111,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f115,axiom,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(f117,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5442) ).
fof(f118,axiom,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5461) ).
fof(f158,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f174,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f175,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f174]) ).
fof(f233,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f234,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f233]) ).
fof(f370,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f383,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f487,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f535,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f542,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f544,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f117]) ).
fof(f545,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f118]) ).
fof(f775,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[],[f487,f545]) ).
fof(f776,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(resolution,[],[f487,f544]) ).
fof(f781,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f776,f542]) ).
fof(f782,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f775,f535]) ).
fof(f784,definition,
( spl29_9
<=> aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f786,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl29_9 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f788,definition,
( spl29_10
<=> sdtlseqdt0(szszuzczcdt0(xn),xm) ),
introduced(definition,[new_symbols(definition,[spl29_10])],[avatar_definition]) ).
fof(f791,plain,
( ~ spl29_9
| ~ spl29_10 ),
inference(avatar_split_clause,[],[f781,f788,f784]) ).
fof(f792,plain,
~ sdtlseqdt0(xm,xn),
inference(forward_subsumption_resolution,[],[f782,f542]) ).
fof(f794,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f792,f383]) ).
fof(f795,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f794,f542]) ).
fof(f797,plain,
sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(forward_subsumption_resolution,[],[f795,f535]) ).
fof(f799,plain,
spl29_10,
inference(avatar_split_clause,[],[f797,f788]) ).
fof(f815,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl29_9 ),
inference(resolution,[],[f786,f370]) ).
fof(f817,plain,
( $false
| spl29_9 ),
inference(forward_subsumption_resolution,[],[f815,f535]) ).
fof(f818,plain,
spl29_9,
inference(avatar_contradiction_clause,[],[f817]) ).
cnf(s9,plain,
( ~ spl29_9
| ~ spl29_10 ),
inference(sat_conversion,[],[f791]) ).
cnf(s10,plain,
spl29_10,
inference(sat_conversion,[],[f799]) ).
cnf(s11,plain,
spl29_9,
inference(sat_conversion,[],[f818]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s9,s10,s11]) ).
fof(f819,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM627+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.60 % Computer : n004.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Sun Sep 27 20:50:07 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.63 Running first-order theorem proving
% 0.17/0.63 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
% 4.33/1.83 % (3865673)Detected formulas, will run a generic FOF schedule.
% 4.33/1.83 % (3865704)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=690960795:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.33/1.83 % (3865701)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=4035750858:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.33/1.83 % (3865702)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=2072759701:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.33/1.83 % (3865703)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=979078269:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.33/1.83 % (3865704)Instruction limit reached!
% 4.33/1.83 % (3865704)------------------------------
% 4.33/1.83 % (3865704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.83 % (3865704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.83 % (3865704)CaDiCaL version: 2.1.3
% 4.33/1.83 % (3865704)Termination reason: Instruction limit
% 4.33/1.83 % (3865704)Termination phase: Saturation
% 4.33/1.83 % (3865704)Time elapsed: 0.038 s
% 4.33/1.83 % (3865704)Peak memory usage: 89 MB
% 4.33/1.83 % (3865704)Instructions burned: 112 (million)
% 4.33/1.83 % (3865705)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4157721374:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.33/1.83 % (3865706)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2634954507:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.33/1.83 % (3865707)dis-21_1_sil=8000:lcm=predicate:random_seed=348734783: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)
% 4.33/1.83 % (3865706)First to succeed.
% 4.33/1.83 % (3865706)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3865673"
% 4.33/1.83 % (3865705)Instruction limit reached!
% 4.33/1.83 % (3865705)------------------------------
% 4.33/1.83 % (3865705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.83 % (3865705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.83 % (3865705)CaDiCaL version: 2.1.3
% 4.33/1.83 % (3865705)Termination reason: Instruction limit
% 4.33/1.83 % (3865705)Termination phase: Saturation
% 4.33/1.83 % (3865705)Time elapsed: 0.073 s
% 4.33/1.83 % (3865705)Peak memory usage: 89 MB
% 4.33/1.83 % (3865705)Instructions burned: 119 (million)
% 4.33/1.83 % (3865707)Instruction limit reached!
% 4.33/1.83 % (3865707)------------------------------
% 4.33/1.83 % (3865707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.83 % (3865707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.83 % (3865707)CaDiCaL version: 2.1.3
% 4.33/1.83 % (3865707)Termination reason: Instruction limit
% 4.33/1.83 % (3865707)Termination phase: Saturation
% 4.33/1.83 % (3865707)Time elapsed: 0.074 s
% 4.33/1.83 % (3865707)Peak memory usage: 91 MB
% 4.33/1.83 % (3865707)Instructions burned: 130 (million)
% 4.33/1.83 % (3865715)lrs+10_1_sil=8000:sp=occurrence:random_seed=201200411:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.33/1.83 % (3865715)Also succeeded, but the first one will report.
% 4.33/1.83 % (3865716)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3205875143:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.33/1.83 % (3865716)Refutation not found, incomplete strategy
% 4.33/1.83 % (3865716)------------------------------
% 4.33/1.83 % (3865716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.83 % (3865716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.83 % (3865716)CaDiCaL version: 2.1.3
% 4.33/1.83 % (3865716)Termination reason: Refutation not found, incomplete strategy
% 4.33/1.83 % (3865716)Time elapsed: 0.005 s
% 4.33/1.83 % (3865716)Peak memory usage: 88 MB
% 4.33/1.83 % (3865716)Instructions burned: 3 (million)
% 4.33/1.83 % (3865717)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4158558677:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.33/1.83 % (3865706)Refutation found. Thanks to Tanya!
% 4.33/1.83 % SZS status ContradictoryAxioms for theBenchmark
% 4.33/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 4.33/1.83 % (3865706)------------------------------
% 4.33/1.83 % (3865706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.33/1.83 % (3865706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.33/1.83 % (3865706)CaDiCaL version: 2.1.3
% 4.33/1.83 % (3865706)Termination reason: Refutation
% 4.33/1.83 % (3865706)Time elapsed: 0.015 s
% 4.33/1.83 % (3865706)Peak memory usage: 90 MB
% 4.33/1.83 % (3865706)Instructions burned: 21 (million)
% 4.33/1.83 % (3865706)------------------------------
% 4.33/1.83 % (3865706)------------------------------
% 4.33/1.83 % (3865673)Success in time 0.532 s
% 4.33/1.83 % Vampire exiting
%------------------------------------------------------------------------------