%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM547+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 : n009.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 12:15:41 PM UTC 2026
% Result : Theorem 3.47s 1.49s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 206 ( 46 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 266 ( 101 ~; 94 |; 58 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 79 ( 67 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f65,conjecture,
? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f66,negated_conjecture,
~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f74,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(ennf_transformation,[],[f66]) ).
fof(f81,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f96]) ).
fof(f122,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f123,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK1(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f124]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f89]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK2(X0,X1),X0)
& aElementOf0(sK2(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f97]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK3(X0,X1,X2),X0)
| sbrdtbr0(sK3(X0,X1,X2)) != X1
| ~ aElementOf0(sK3(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK3(X0,X1,X2),X0)
& sbrdtbr0(sK3(X0,X1,X2)) = X1 )
| aElementOf0(sK3(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f132]) ).
fof(f137,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f139,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f141,plain,
slcrc0 != slbdtsldtrb0(xS,xk),
inference(cnf_transformation,[],[f63]) ).
fof(f142,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f144,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f74]) ).
fof(f157,plain,
! [X0] :
( aElementOf0(sK1(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f172,plain,
! [X2,X0,X1] :
( aSet0(X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f197,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f172]) ).
fof(f208,plain,
( aSet0(slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(resolution,[],[f163,f142]) ).
fof(f214,plain,
( ~ aSet0(slbdtsldtrb0(xS,xk))
| slcrc0 = slbdtsldtrb0(xS,xk) ),
inference(resolution,[],[f157,f144]) ).
fof(f216,plain,
~ aSet0(slbdtsldtrb0(xS,xk)),
inference(forward_subsumption_resolution,[],[f214,f141]) ).
fof(f217,plain,
~ aSet0(slbdtsldtrb0(xT,xk)),
inference(resolution,[],[f216,f208]) ).
fof(f222,plain,
( ~ aSet0(xT)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f197,f217]) ).
fof(f223,plain,
~ aElementOf0(xk,szNzAzT0),
inference(forward_subsumption_resolution,[],[f222,f139]) ).
fof(f225,plain,
$false,
inference(forward_subsumption_resolution,[],[f223,f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM547+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n009.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sun Sep 27 20:27:00 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 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
% 3.47/1.49 % (2371525)Detected formulas, will run a generic FOF schedule.
% 3.47/1.49 % (2371530)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=3257577284:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.49 % (2371531)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=467320828:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.49 % (2371534)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1129600280:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.49 % (2371533)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2070794634:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.49 % (2371535)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=503475752:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.49 % (2371532)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=3895166955:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.49 % (2371536)dis-21_1_sil=8000:lcm=predicate:random_seed=2263355242: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)
% 3.47/1.49 % (2371534)First to succeed.
% 3.47/1.49 % (2371533)Also succeeded, but the first one will report.
% 3.47/1.49 % (2371534)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2371525"
% 3.47/1.49 % (2371535)Also succeeded, but the first one will report.
% 3.47/1.49 % (2371536)Instruction limit reached!
% 3.47/1.49 % (2371536)------------------------------
% 3.47/1.49 % (2371536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.49 % (2371536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.49 % (2371536)CaDiCaL version: 2.1.3
% 3.47/1.49 % (2371536)Termination reason: Instruction limit
% 3.47/1.49 % (2371536)Termination phase: Saturation
% 3.47/1.49 % (2371536)Time elapsed: 0.059 s
% 3.47/1.49 % (2371536)Peak memory usage: 88 MB
% 3.47/1.49 % (2371536)Instructions burned: 131 (million)
% 3.47/1.49 % (2371544)lrs+10_1_sil=8000:sp=occurrence:random_seed=3981773263:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.47/1.49 % (2371544)Also succeeded, but the first one will report.
% 3.47/1.49 % (2371534)Refutation found. Thanks to Tanya!
% 3.47/1.49 % SZS status Theorem for theBenchmark
% 3.47/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.49 % (2371534)------------------------------
% 3.47/1.49 % (2371534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.49 % (2371534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.49 % (2371534)CaDiCaL version: 2.1.3
% 3.47/1.49 % (2371534)Termination reason: Refutation
% 3.47/1.49 % (2371534)Time elapsed: 0.004 s
% 3.47/1.49 % (2371534)Peak memory usage: 88 MB
% 3.47/1.49 % (2371534)Instructions burned: 5 (million)
% 3.47/1.49 % (2371534)------------------------------
% 3.47/1.49 % (2371534)------------------------------
% 3.47/1.49 % (2371525)Success in time 0.417 s
% 3.47/1.49 % Vampire exiting
%------------------------------------------------------------------------------