%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM624+3 : 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 : 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 12:16:02 PM UTC 2026
% Result : Theorem 4.02s 1.55s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 101 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 43 ~; 27 |; 29 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 34 ( 25 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f103,axiom,
( aElementOf0(xp,xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f113,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).
fof(f114,axiom,
( aElementOf0(xx,szNzAzT0)
& ? [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X0) = xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
fof(f116,axiom,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f119,axiom,
( aElementOf0(xp,sdtlpdtrp0(xN,xm))
& aElementOf0(xx,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5481) ).
fof(f120,axiom,
( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) )
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> aElementOf0(X0,szNzAzT0) )
& ~ ~ ? [X0] : aElementOf0(X0,xQ)
& ~ ~ ? [X0] : aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5518) ).
fof(f121,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f122,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f121]) ).
fof(f138,plain,
( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) )
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,szNzAzT0) )
& ~ ~ ? [X2] : aElementOf0(X2,xQ)
& ~ ~ ? [X3] : aElementOf0(X3,sdtlpdtrp0(xN,xm)) ),
inference(rectify,[],[f120]) ).
fof(f139,plain,
( ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,szNzAzT0) )
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xm))
=> aElementOf0(X1,szNzAzT0) )
& ? [X2] : aElementOf0(X2,xQ)
& ? [X3] : aElementOf0(X3,sdtlpdtrp0(xN,xm)) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
xp != xx,
inference(flattening,[],[f122]) ).
fof(f182,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f186,plain,
! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f116]) ).
fof(f189,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xm)) )
& ? [X2] : aElementOf0(X2,xQ)
& ? [X3] : aElementOf0(X3,sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f139]) ).
fof(f245,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f246,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f245]) ).
fof(f402,plain,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(sK54,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& xx = sdtlpdtrp0(xe,sK54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X0,sK54)],[f114]) ).
fof(f404,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xm)) )
& aElementOf0(sK56,xQ)
& aElementOf0(sK57,sdtlpdtrp0(xN,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57]),skolemize(X2,sK56),skolemize(X3,sK57)],[f189]) ).
fof(f713,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f182]) ).
fof(f739,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f743,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f402]) ).
fof(f746,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f753,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f119]) ).
fof(f756,plain,
! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f404]) ).
fof(f758,plain,
xp != xx,
inference(cnf_transformation,[],[f140]) ).
fof(f833,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f1125,plain,
sdtlseqdt0(xx,xp),
inference(resolution,[],[f746,f753]) ).
fof(f1128,plain,
aElementOf0(xp,szNzAzT0),
inference(resolution,[],[f756,f753]) ).
fof(f2959,plain,
( ~ sdtlseqdt0(xp,xx)
| xp = xx
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(resolution,[],[f833,f1125]) ).
fof(f2972,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2959,f758]) ).
fof(f2985,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2972,f1128]) ).
fof(f2991,plain,
~ sdtlseqdt0(xp,xx),
inference(forward_subsumption_resolution,[],[f2985,f743]) ).
fof(f2993,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[],[f2991,f713]) ).
fof(f2994,plain,
$false,
inference(forward_subsumption_resolution,[],[f2993,f739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM624+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:55:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 4.02/1.55 % (3938918)Detected formulas, will run a generic FOF schedule.
% 4.02/1.55 % (3938928)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=3576009248:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.02/1.55 % (3938932)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3449685553:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.02/1.55 % (3938927)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=405028424:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.02/1.55 % (3938930)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=151236615:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.02/1.55 % (3938931)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=800317838:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.02/1.55 % (3938929)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=2195804748:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.02/1.55 % (3938933)dis-21_1_sil=8000:lcm=predicate:random_seed=3418384130: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)
% 4.02/1.55 % (3938931)First to succeed.
% 4.02/1.55 % (3938931)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3938918"
% 4.02/1.55 % (3938932)Also succeeded, but the first one will report.
% 4.02/1.55 % (3938930)Instruction limit reached!
% 4.02/1.55 % (3938930)------------------------------
% 4.02/1.55 % (3938930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (3938930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (3938930)CaDiCaL version: 2.1.3
% 4.02/1.55 % (3938930)Termination reason: Instruction limit
% 4.02/1.55 % (3938930)Termination phase: Saturation
% 4.02/1.55 % (3938930)Time elapsed: 0.068 s
% 4.02/1.55 % (3938930)Peak memory usage: 90 MB
% 4.02/1.55 % (3938930)Instructions burned: 110 (million)
% 4.02/1.55 % (3938933)Instruction limit reached!
% 4.02/1.55 % (3938933)------------------------------
% 4.02/1.55 % (3938933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (3938933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (3938933)CaDiCaL version: 2.1.3
% 4.02/1.55 % (3938933)Termination reason: Instruction limit
% 4.02/1.55 % (3938933)Termination phase: Saturation
% 4.02/1.55 % (3938933)Time elapsed: 0.069 s
% 4.02/1.55 % (3938933)Peak memory usage: 90 MB
% 4.02/1.55 % (3938933)Instructions burned: 130 (million)
% 4.02/1.55 % (3938941)lrs+10_1_sil=8000:sp=occurrence:random_seed=794369236:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.02/1.55 % (3938942)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1536704414:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.02/1.55 % (3938942)Refutation not found, incomplete strategy
% 4.02/1.55 % (3938942)------------------------------
% 4.02/1.55 % (3938942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (3938942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (3938942)CaDiCaL version: 2.1.3
% 4.02/1.55 % (3938942)Termination reason: Refutation not found, incomplete strategy
% 4.02/1.55 % (3938942)Time elapsed: 0.003 s
% 4.02/1.55 % (3938942)Peak memory usage: 88 MB
% 4.02/1.55 % (3938942)Instructions burned: 3 (million)
% 4.02/1.55 % (3938941)Also succeeded, but the first one will report.
% 4.02/1.55 % (3938931)Refutation found. Thanks to Tanya!
% 4.02/1.55 % SZS status Theorem for theBenchmark
% 4.02/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.55 % (3938931)------------------------------
% 4.02/1.55 % (3938931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.55 % (3938931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.55 % (3938931)CaDiCaL version: 2.1.3
% 4.02/1.55 % (3938931)Termination reason: Refutation
% 4.02/1.55 % (3938931)Time elapsed: 0.055 s
% 4.02/1.55 % (3938931)Peak memory usage: 89 MB
% 4.02/1.55 % (3938931)Instructions burned: 87 (million)
% 4.02/1.55 % (3938931)------------------------------
% 4.02/1.55 % (3938931)------------------------------
% 4.02/1.55 % (3938918)Success in time 0.491 s
% 4.02/1.55 % Vampire exiting
%------------------------------------------------------------------------------