%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM613+1 : 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 : n020.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 12:15:59 PM UTC 2026
% Result : Theorem 0.18s 1.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 23 unt; 0 def)
% Number of atoms : 129 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 72 ~; 60 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> X0 != szszuzczcdt0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessSucc) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
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(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f109,axiom,
( sbrdtbr0(xQ) = szszuzczcdt0(xk)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5255) ).
fof(f110,conjecture,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f111,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negated_conjecture,[status(cth)],[f110]) ).
fof(f112,plain,
xk != sbrdtbr0(xP),
inference(flattening,[],[f111]) ).
fof(f171,plain,
! [X0] :
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f184,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f185,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f184]) ).
fof(f188,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f189,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f188]) ).
fof(f191,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f286,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f298,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f299,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f352,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(cnf_transformation,[],[f109]) ).
fof(f353,plain,
sbrdtbr0(xQ) = szszuzczcdt0(sbrdtbr0(xP)),
inference(cnf_transformation,[],[f109]) ).
fof(f354,plain,
szszuzczcdt0(xk) = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f109]) ).
fof(f355,plain,
xk != sbrdtbr0(xP),
inference(cnf_transformation,[],[f112]) ).
fof(f393,plain,
! [X0] :
( szszuzczcdt0(X0) != X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f414,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f416,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f418,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f499,plain,
xK = sbrdtbr0(xQ),
inference(forward_demodulation,[],[f354,f298]) ).
fof(f507,plain,
xK = szszuzczcdt0(sbrdtbr0(xP)),
inference(forward_demodulation,[],[f353,f499]) ).
fof(f547,plain,
( xK != xk
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f393,f298]) ).
fof(f548,plain,
( xK != sbrdtbr0(xP)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[],[f393,f507]) ).
fof(f549,plain,
xK != sbrdtbr0(xP),
inference(forward_subsumption_resolution,[],[f548,f352]) ).
fof(f550,plain,
xK != xk,
inference(forward_subsumption_resolution,[],[f547,f299]) ).
fof(f551,plain,
( sdtlseqdt0(xk,xK)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f418,f298]) ).
fof(f552,plain,
( sdtlseqdt0(sbrdtbr0(xP),xK)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[],[f418,f507]) ).
fof(f553,plain,
sdtlseqdt0(sbrdtbr0(xP),xK),
inference(forward_subsumption_resolution,[],[f552,f352]) ).
fof(f554,plain,
sdtlseqdt0(xk,xK),
inference(forward_subsumption_resolution,[],[f551,f299]) ).
fof(f889,plain,
! [X0] :
( sdtlseqdt0(xK,X0)
| sdtlseqdt0(X0,xk)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f414,f298]) ).
fof(f890,plain,
! [X0] :
( sdtlseqdt0(xK,X0)
| sdtlseqdt0(X0,sbrdtbr0(xP))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(superposition,[],[f414,f507]) ).
fof(f894,plain,
! [X0] :
( sdtlseqdt0(X0,sbrdtbr0(xP))
| sdtlseqdt0(xK,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f890,f352]) ).
fof(f895,plain,
! [X0] :
( sdtlseqdt0(xK,X0)
| sdtlseqdt0(X0,xk)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f889,f299]) ).
fof(f1147,plain,
( ~ sdtlseqdt0(xK,sbrdtbr0(xP))
| xK = sbrdtbr0(xP)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(resolution,[],[f416,f553]) ).
fof(f1150,plain,
( ~ sdtlseqdt0(xK,xk)
| xK = xk
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f416,f554]) ).
fof(f1160,plain,
( ~ sdtlseqdt0(xK,xk)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1150,f550]) ).
fof(f1162,plain,
( ~ sdtlseqdt0(xK,sbrdtbr0(xP))
| ~ aElementOf0(xK,szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1147,f549]) ).
fof(f1170,plain,
( ~ sdtlseqdt0(xK,xk)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1160,f286]) ).
fof(f1171,plain,
( ~ sdtlseqdt0(xK,sbrdtbr0(xP))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1162,f286]) ).
fof(f1176,plain,
~ sdtlseqdt0(xK,xk),
inference(forward_subsumption_resolution,[],[f1170,f299]) ).
fof(f1177,plain,
~ sdtlseqdt0(xK,sbrdtbr0(xP)),
inference(forward_subsumption_resolution,[],[f1171,f352]) ).
fof(f1360,plain,
( sdtlseqdt0(sbrdtbr0(xP),xk)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(resolution,[],[f895,f1177]) ).
fof(f1363,plain,
sdtlseqdt0(sbrdtbr0(xP),xk),
inference(forward_subsumption_resolution,[],[f1360,f352]) ).
fof(f1392,plain,
( ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| xk = sbrdtbr0(xP)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(resolution,[],[f1363,f416]) ).
fof(f1393,plain,
( ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1392,f355]) ).
fof(f1394,plain,
( ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1393,f299]) ).
fof(f1395,plain,
~ sdtlseqdt0(xk,sbrdtbr0(xP)),
inference(forward_subsumption_resolution,[],[f1394,f352]) ).
fof(f2712,plain,
( sdtlseqdt0(xK,xk)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f894,f1395]) ).
fof(f2738,plain,
~ aElementOf0(xk,szNzAzT0),
inference(forward_subsumption_resolution,[],[f2712,f1176]) ).
fof(f2744,plain,
$false,
inference(forward_subsumption_resolution,[],[f2738,f299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.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 20:46:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.18/1.41 % (3730389)Detected formulas, will run a generic FOF schedule.
% 0.18/1.41 % (3730398)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3776554570:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.41 % (3730398)First to succeed.
% 0.18/1.41 % (3730398)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3730389"
% 0.18/1.41 % (3730400)dis-21_1_sil=8000:lcm=predicate:random_seed=1572890330: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)
% 0.18/1.41 % (3730397)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3885733994:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.41 % (3730395)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=3687365161:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.41 % (3730399)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1757227387:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.41 % (3730394)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=989197244:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.41 % (3730396)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=3317871667:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.41 % (3730399)Also succeeded, but the first one will report.
% 0.18/1.41 % (3730397)Instruction limit reached!
% 0.18/1.41 % (3730397)------------------------------
% 0.18/1.41 % (3730397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.41 % (3730397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.41 % (3730397)CaDiCaL version: 2.1.3
% 0.18/1.41 % (3730397)Termination reason: Instruction limit
% 0.18/1.41 % (3730397)Termination phase: Saturation
% 0.18/1.41 % (3730397)Time elapsed: 0.067 s
% 0.18/1.41 % (3730397)Peak memory usage: 89 MB
% 0.18/1.41 % (3730397)Instructions burned: 109 (million)
% 0.18/1.41 % (3730400)Instruction limit reached!
% 0.18/1.41 % (3730400)------------------------------
% 0.18/1.41 % (3730400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.41 % (3730400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.41 % (3730400)CaDiCaL version: 2.1.3
% 0.18/1.41 % (3730400)Termination reason: Instruction limit
% 0.18/1.41 % (3730400)Termination phase: Saturation
% 0.18/1.41 % (3730400)Time elapsed: 0.073 s
% 0.18/1.41 % (3730400)Peak memory usage: 91 MB
% 0.18/1.41 % (3730400)Instructions burned: 129 (million)
% 0.18/1.41 % (3730398)Refutation found. Thanks to Tanya!
% 0.18/1.41 % SZS status Theorem for theBenchmark
% 0.18/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.41 % (3730398)------------------------------
% 0.18/1.41 % (3730398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.41 % (3730398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.41 % (3730398)CaDiCaL version: 2.1.3
% 0.18/1.41 % (3730398)Termination reason: Refutation
% 0.18/1.41 % (3730398)Time elapsed: 0.037 s
% 0.18/1.41 % (3730398)Peak memory usage: 89 MB
% 0.18/1.41 % (3730398)Instructions burned: 108 (million)
% 0.18/1.41 % (3730398)------------------------------
% 0.18/1.41 % (3730398)------------------------------
% 0.18/1.41 % (3730389)Success in time 0.322 s
% 0.18/1.41 % Vampire exiting
%------------------------------------------------------------------------------