%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM540+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 : n005.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 12:15:39 PM UTC 2026
% Result : Theorem 2.68s 1.39s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 155 ( 29 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 202 ( 82 ~; 74 |; 38 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 49 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f31,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNoScLessZr) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f52,conjecture,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
slbdtrb0(sz00) != slcrc0,
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f54,plain,
slcrc0 != slbdtrb0(sz00),
inference(flattening,[],[f53]) ).
fof(f61,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f96,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f97,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK0(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f98]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ( ( ~ aElementOf0(sK2(X0,X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK2(X0,X1)),X0)
| ~ aElementOf0(sK2(X0,X1),X1) )
& ( ( aElementOf0(sK2(X0,X1),szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(sK2(X0,X1)),X0) )
| aElementOf0(sK2(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f104]) ).
fof(f113,plain,
slcrc0 != slbdtrb0(sz00),
inference(cnf_transformation,[],[f54]) ).
fof(f117,plain,
! [X0] :
( aElementOf0(sK0(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f120,plain,
! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f126,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f128,plain,
! [X3,X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f129,plain,
! [X3,X0,X1] :
( aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X3,X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f131,plain,
! [X0,X1] :
( aSet0(X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f160,plain,
! [X0] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f131]) ).
fof(f162,plain,
! [X3,X0] :
( ~ aElementOf0(X3,slbdtrb0(X0))
| aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f129]) ).
fof(f163,plain,
! [X3,X0] :
( sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f128]) ).
fof(f190,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtrb0(sz00))
| ~ aElementOf0(sz00,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f163,f120]) ).
fof(f192,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtrb0(sz00))
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f190,f162]) ).
fof(f193,plain,
! [X0] : ~ aElementOf0(X0,slbdtrb0(sz00)),
inference(forward_subsumption_resolution,[],[f192,f126]) ).
fof(f194,plain,
( ~ aSet0(slbdtrb0(sz00))
| slcrc0 = slbdtrb0(sz00) ),
inference(resolution,[],[f193,f117]) ).
fof(f196,plain,
~ aSet0(slbdtrb0(sz00)),
inference(forward_subsumption_resolution,[],[f194,f113]) ).
fof(f197,plain,
~ aElementOf0(sz00,szNzAzT0),
inference(resolution,[],[f196,f160]) ).
fof(f198,plain,
$false,
inference(forward_subsumption_resolution,[],[f197,f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM540+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n005.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 20:24:17 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 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
% 2.68/1.39 % (136782)Detected formulas, will run a generic FOF schedule.
% 2.68/1.39 % (136791)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4288065750:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.39 % (136791)First to succeed.
% 2.68/1.39 % (136791)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-136782"
% 2.68/1.39 % (136789)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=1425162294:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.39 % (136788)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=3357842104:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.39 % (136792)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1654708224:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.39 % (136787)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=4144777469:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.39 % (136793)dis-21_1_sil=8000:lcm=predicate:random_seed=3954158010: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)
% 2.68/1.39 % (136790)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2733444439:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.39 % (136790)Refutation not found, incomplete strategy
% 2.68/1.39 % (136790)------------------------------
% 2.68/1.39 % (136790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.39 % (136790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.39 % (136790)CaDiCaL version: 2.1.3
% 2.68/1.39 % (136790)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.39 % (136790)Time elapsed: 0.002 s
% 2.68/1.39 % (136790)Peak memory usage: 88 MB
% 2.68/1.39 % (136790)Instructions burned: 1 (million)
% 2.68/1.39 % (136792)Also succeeded, but the first one will report.
% 2.68/1.39 % (136793)Instruction limit reached!
% 2.68/1.39 % (136793)------------------------------
% 2.68/1.39 % (136793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.39 % (136793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.39 % (136793)CaDiCaL version: 2.1.3
% 2.68/1.39 % (136793)Termination reason: Instruction limit
% 2.68/1.39 % (136793)Termination phase: Saturation
% 2.68/1.39 % (136793)Time elapsed: 0.055 s
% 2.68/1.39 % (136793)Peak memory usage: 88 MB
% 2.68/1.39 % (136793)Instructions burned: 131 (million)
% 2.68/1.39 % (136791)Refutation found. Thanks to Tanya!
% 2.68/1.39 % SZS status Theorem for theBenchmark
% 2.68/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.39 % (136791)------------------------------
% 2.68/1.39 % (136791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.39 % (136791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.39 % (136791)CaDiCaL version: 2.1.3
% 2.68/1.39 % (136791)Termination reason: Refutation
% 2.68/1.39 % (136791)Time elapsed: 0.002 s
% 2.68/1.39 % (136791)Peak memory usage: 88 MB
% 2.68/1.39 % (136791)Instructions burned: 4 (million)
% 2.68/1.39 % (136791)------------------------------
% 2.68/1.39 % (136791)------------------------------
% 2.68/1.39 % (136782)Success in time 0.301 s
% 2.68/1.39 % Vampire exiting
%------------------------------------------------------------------------------