%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM547+3 : 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 12:15:41 PM UTC 2026
% Result : Theorem 2.74s 1.37s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 285 ( 46 equ)
% Maximal formula atoms : 43 ( 21 avg)
% Number of connectives : 368 ( 96 ~; 80 |; 162 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 53 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f63,axiom,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSubsetOf0(X0,xT)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) ) )
| aSubsetOf0(X0,xT) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) ) )
& ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(f65,conjecture,
? [X0] :
( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f66,negated_conjecture,
~ ? [X0] :
( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f73,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,xT) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk ) )
& ( ( ( ( aSet0(X3)
& ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,xT) ) )
| aSubsetOf0(X3,xT) )
& sbrdtbr0(X3) = xk )
=> aElementOf0(X3,slbdtsldtrb0(xT,xk)) ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xS,xk))
=> aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [X7] :
( ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
=> ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,xS) )
& aSubsetOf0(X7,xS)
& xk = sbrdtbr0(X7) ) )
& ( ( ( ( aSet0(X7)
& ! [X9] :
( aElementOf0(X9,X7)
=> aElementOf0(X9,xS) ) )
| aSubsetOf0(X7,xS) )
& xk = sbrdtbr0(X7) )
=> aElementOf0(X7,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
inference(rectify,[],[f63]) ).
fof(f156,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X7] :
( ( ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X7) )
& aSubsetOf0(X7,xS)
& xk = sbrdtbr0(X7) )
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X7)
| ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X7) ) )
& ~ aSubsetOf0(X7,xS) )
| xk != sbrdtbr0(X7) ) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f157,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X7] :
( ( ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X7) )
& aSubsetOf0(X7,xS)
& xk = sbrdtbr0(X7) )
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X7)
| ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X7) ) )
& ~ aSubsetOf0(X7,xS) )
| xk != sbrdtbr0(X7) ) ) ),
inference(flattening,[],[f156]) ).
fof(f158,plain,
! [X0] :
( ( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xS)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk )
& ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f66]) ).
fof(f210,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ? [X7] : aElementOf0(X7,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X8] :
( ( ( aSet0(X8)
& ! [X9] :
( aElementOf0(X9,xS)
| ~ aElementOf0(X9,X8) )
& aSubsetOf0(X8,xS)
& xk = sbrdtbr0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X8)
| ? [X10] :
( ~ aElementOf0(X10,xS)
& aElementOf0(X10,X8) ) )
& ~ aSubsetOf0(X8,xS) )
| xk != sbrdtbr0(X8) ) ) ),
inference(rectify,[],[f157]) ).
fof(f211,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK15(X0),xS)
& aElementOf0(sK15(X0),X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ( ~ aElementOf0(sK16(X3),xT)
& aElementOf0(sK16(X3),X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& aElementOf0(sK17,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X8] :
( ( ( aSet0(X8)
& ! [X9] :
( aElementOf0(X9,xS)
| ~ aElementOf0(X9,X8) )
& aSubsetOf0(X8,xS)
& xk = sbrdtbr0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X8)
| ( ~ aElementOf0(sK18(X8),xS)
& aElementOf0(sK18(X8),X8) ) )
& ~ aSubsetOf0(X8,xS) )
| xk != sbrdtbr0(X8) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18]),skolemize(X2,sK15(X0)),skolemize(X5,sK16(X3)),skolemize(X7,sK17),skolemize(X10,sK18(X8))],[f210]) ).
fof(f212,plain,
! [X0] :
( ( ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK19(X0),xS)
& aElementOf0(sK19(X0),X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk )
& ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X1,sK19(X0))],[f158]) ).
fof(f334,plain,
aElementOf0(sK17,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f211]) ).
fof(f354,plain,
! [X0] : ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f212]) ).
fof(f458,plain,
$false,
inference(resolution,[],[f334,f354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM547+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:26:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.74/1.37 % (138573)Detected formulas, will run a generic FOF schedule.
% 2.74/1.37 % (138584)dis-21_1_sil=8000:lcm=predicate:random_seed=4100754279: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)
% 2.74/1.37 % (138584)First to succeed.
% 2.74/1.37 % (138584)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-138573"
% 2.74/1.37 % (138582)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=130949301:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.37 % (138581)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1081202706:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.37 % (138578)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=3249580547:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.37 % (138580)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=1768500331:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.37 % (138579)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=841503318:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.37 % (138583)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2606856119:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.37 % (138582)Also succeeded, but the first one will report.
% 2.74/1.37 % (138581)Also succeeded, but the first one will report.
% 2.74/1.37 % (138583)Also succeeded, but the first one will report.
% 2.74/1.37 % (138584)Refutation found. Thanks to Tanya!
% 2.74/1.37 % SZS status Theorem for theBenchmark
% 2.74/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.37 % (138584)------------------------------
% 2.74/1.37 % (138584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.37 % (138584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.37 % (138584)CaDiCaL version: 2.1.3
% 2.74/1.37 % (138584)Termination reason: Refutation
% 2.74/1.37 % (138584)Time elapsed: 0.004 s
% 2.74/1.37 % (138584)Peak memory usage: 88 MB
% 2.74/1.37 % (138584)Instructions burned: 8 (million)
% 2.74/1.37 % (138584)------------------------------
% 2.74/1.37 % (138584)------------------------------
% 2.74/1.37 % (138573)Success in time 0.303 s
% 2.74/1.37 % Vampire exiting
%------------------------------------------------------------------------------