%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM623+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 : n007.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 3.80s 1.49s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 89 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 35 ~; 27 |; 21 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 21 ( 20 !; 1 ?)
% 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(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
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(f115,axiom,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
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,conjecture,
xp = xx,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f121,negated_conjecture,
xp != xx,
inference(negated_conjecture,[status(cth)],[f120]) ).
fof(f137,plain,
xp != xx,
inference(flattening,[],[f121]) ).
fof(f152,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f179,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f183,plain,
! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f116]) ).
fof(f241,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f242,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f241]) ).
fof(f398,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(f520,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f708,plain,
! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f179]) ).
fof(f734,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f738,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f398]) ).
fof(f740,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f741,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f748,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f119]) ).
fof(f749,plain,
xp != xx,
inference(cnf_transformation,[],[f137]) ).
fof(f824,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f1108,plain,
sdtlseqdt0(xx,xp),
inference(resolution,[],[f741,f748]) ).
fof(f1494,plain,
( aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[],[f520,f748]) ).
fof(f1510,plain,
aElementOf0(xp,szNzAzT0),
inference(forward_subsumption_resolution,[],[f1494,f740]) ).
fof(f2923,plain,
( ~ sdtlseqdt0(xp,xx)
| xp = xx
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(resolution,[],[f824,f1108]) ).
fof(f2936,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2923,f749]) ).
fof(f2952,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xx,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2936,f1510]) ).
fof(f2959,plain,
~ sdtlseqdt0(xp,xx),
inference(forward_subsumption_resolution,[],[f2952,f738]) ).
fof(f2963,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[],[f2959,f708]) ).
fof(f2964,plain,
$false,
inference(forward_subsumption_resolution,[],[f2963,f734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM623+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:47:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.80/1.49 % (1763195)Detected formulas, will run a generic FOF schedule.
% 3.80/1.49 % (1763200)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=1261579640:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.80/1.49 % (1763204)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=218854924:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.80/1.49 % (1763206)dis-21_1_sil=8000:lcm=predicate:random_seed=2028778976: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)
% 3.80/1.49 % (1763201)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=566914349:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.80/1.49 % (1763202)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=46608972:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.80/1.49 % (1763203)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3151405110:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.80/1.49 % (1763205)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=531932619:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.80/1.49 % (1763204)First to succeed.
% 3.80/1.49 % (1763204)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1763195"
% 3.80/1.49 % (1763205)Also succeeded, but the first one will report.
% 3.80/1.49 % (1763203)Instruction limit reached!
% 3.80/1.49 % (1763203)------------------------------
% 3.80/1.49 % (1763203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.49 % (1763203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.49 % (1763203)CaDiCaL version: 2.1.3
% 3.80/1.49 % (1763203)Termination reason: Instruction limit
% 3.80/1.49 % (1763203)Termination phase: Saturation
% 3.80/1.49 % (1763203)Time elapsed: 0.067 s
% 3.80/1.49 % (1763203)Peak memory usage: 90 MB
% 3.80/1.49 % (1763203)Instructions burned: 110 (million)
% 3.80/1.49 % (1763206)Instruction limit reached!
% 3.80/1.49 % (1763206)------------------------------
% 3.80/1.49 % (1763206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.49 % (1763206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.49 % (1763206)CaDiCaL version: 2.1.3
% 3.80/1.49 % (1763206)Termination reason: Instruction limit
% 3.80/1.49 % (1763206)Termination phase: Saturation
% 3.80/1.49 % (1763206)Time elapsed: 0.069 s
% 3.80/1.49 % (1763206)Peak memory usage: 90 MB
% 3.80/1.49 % (1763206)Instructions burned: 131 (million)
% 3.80/1.49 % (1763214)lrs+10_1_sil=8000:sp=occurrence:random_seed=254566948:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.80/1.49 % (1763215)lrs+10_1_sil=32000:urr=on:br=off:random_seed=458678783:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.80/1.49 % (1763215)Refutation not found, incomplete strategy
% 3.80/1.49 % (1763215)------------------------------
% 3.80/1.49 % (1763215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.49 % (1763215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.49 % (1763215)CaDiCaL version: 2.1.3
% 3.80/1.49 % (1763215)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.49 % (1763215)Time elapsed: 0.003 s
% 3.80/1.49 % (1763215)Peak memory usage: 89 MB
% 3.80/1.49 % (1763215)Instructions burned: 3 (million)
% 3.80/1.49 % (1763214)Also succeeded, but the first one will report.
% 3.80/1.49 % (1763204)Refutation found. Thanks to Tanya!
% 3.80/1.49 % SZS status Theorem for theBenchmark
% 3.80/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.49 % (1763204)------------------------------
% 3.80/1.49 % (1763204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.49 % (1763204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.49 % (1763204)CaDiCaL version: 2.1.3
% 3.80/1.49 % (1763204)Termination reason: Refutation
% 3.80/1.49 % (1763204)Time elapsed: 0.055 s
% 3.80/1.49 % (1763204)Peak memory usage: 89 MB
% 3.80/1.49 % (1763204)Instructions burned: 87 (million)
% 3.80/1.49 % (1763204)------------------------------
% 3.80/1.49 % (1763204)------------------------------
% 3.80/1.49 % (1763195)Success in time 0.468 s
% 3.80/1.49 % Vampire exiting
%------------------------------------------------------------------------------