%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM544+2 : 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 : n020.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 12:15:40 PM UTC 2026
% Result : Theorem 4.54s 1.63s
% Output : Refutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 6 unt; 0 def)
% Number of atoms : 179 ( 9 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 226 ( 77 ~; 49 |; 75 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-1 aty)
% Number of variables : 49 ( 36 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(f55,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(f56,conjecture,
( ~ ( ~ ? [X0] : aElementOf0(X0,xS)
| xS = slcrc0 )
=> ( ( aElementOf0(szmzazxdt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(X0,szmzazxdt0(xS)) ) )
=> ( ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(szmzazxdt0(xS))) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( ~ ( ~ ? [X0] : aElementOf0(X0,xS)
| xS = slcrc0 )
=> ( ( aElementOf0(szmzazxdt0(xS),xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(X0,szmzazxdt0(xS)) ) )
=> ( ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(szmzazxdt0(xS))) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f58,plain,
~ ( ~ ( ~ ? [X0] : aElementOf0(X0,xS)
| xS = slcrc0 )
=> ( ( aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,szmzazxdt0(xS)) ) )
=> ( ( aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,xS)
=> aElementOf0(X3,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) )
| aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) ) ) ),
inference(rectify,[],[f57]) ).
fof(f65,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
inference(ennf_transformation,[],[f55]) ).
fof(f66,plain,
( ? [X3] :
( ~ aElementOf0(X3,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aElementOf0(X3,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) ) )
& aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(X1,szmzazxdt0(xS))
| ~ aElementOf0(X1,xS) )
& ? [X0] : aElementOf0(X0,xS)
& slcrc0 != xS ),
inference(ennf_transformation,[],[f58]) ).
fof(f67,plain,
( ? [X3] :
( ~ aElementOf0(X3,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aElementOf0(X3,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X2] :
( aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) ) )
& aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(X1,szmzazxdt0(xS))
| ~ aElementOf0(X1,xS) )
& ? [X0] : aElementOf0(X0,xS)
& slcrc0 != xS ),
inference(flattening,[],[f66]) ).
fof(f80,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f81,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f80]) ).
fof(f109,plain,
( ? [X3] :
( ~ aElementOf0(X3,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aElementOf0(X3,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X2] :
( ( aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) )
| ~ aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) )
& aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(X1,szmzazxdt0(xS))
| ~ aElementOf0(X1,xS) )
& ? [X0] : aElementOf0(X0,xS)
& slcrc0 != xS ),
inference(nnf_transformation,[],[f67]) ).
fof(f110,plain,
( ? [X3] :
( ~ aElementOf0(X3,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aElementOf0(X3,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X2] :
( ( aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),szszuzczcdt0(szmzazxdt0(xS))) )
| ~ aElementOf0(X2,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) )
& aElementOf0(szmzazxdt0(xS),xS)
& ! [X1] :
( sdtlseqdt0(X1,szmzazxdt0(xS))
| ~ aElementOf0(X1,xS) )
& ? [X0] : aElementOf0(X0,xS)
& slcrc0 != xS ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
( ? [X0] :
( ~ aElementOf0(X0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aElementOf0(X0,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) )
| ~ aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) )
& aElementOf0(szmzazxdt0(xS),xS)
& ! [X2] :
( sdtlseqdt0(X2,szmzazxdt0(xS))
| ~ aElementOf0(X2,xS) )
& ? [X3] : aElementOf0(X3,xS)
& slcrc0 != xS ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
( ~ aElementOf0(sK0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aElementOf0(sK0,xS)
& ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& aSet0(slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) )
| ~ aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ) )
& aElementOf0(szmzazxdt0(xS),xS)
& ! [X2] :
( sdtlseqdt0(X2,szmzazxdt0(xS))
| ~ aElementOf0(X2,xS) )
& aElementOf0(sK1,xS)
& slcrc0 != xS ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1)],[f111]) ).
fof(f121,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
& ( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f139,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f65]) ).
fof(f143,plain,
! [X2] :
( sdtlseqdt0(X2,szmzazxdt0(xS))
| ~ aElementOf0(X2,xS) ),
inference(cnf_transformation,[],[f112]) ).
fof(f144,plain,
aElementOf0(szmzazxdt0(xS),xS),
inference(cnf_transformation,[],[f112]) ).
fof(f147,plain,
! [X1] :
( aElementOf0(X1,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),szszuzczcdt0(szmzazxdt0(xS))) ),
inference(cnf_transformation,[],[f112]) ).
fof(f150,plain,
aElementOf0(sK0,xS),
inference(cnf_transformation,[],[f112]) ).
fof(f151,plain,
~ aElementOf0(sK0,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(cnf_transformation,[],[f112]) ).
fof(f166,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f216,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK0),szszuzczcdt0(szmzazxdt0(xS)))
| ~ aElementOf0(sK0,szNzAzT0) ),
inference(resolution,[],[f147,f151]) ).
fof(f346,plain,
( ~ sdtlseqdt0(sK0,szmzazxdt0(xS))
| ~ aElementOf0(sK0,szNzAzT0)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ aElementOf0(sK0,szNzAzT0) ),
inference(resolution,[],[f166,f216]) ).
fof(f352,plain,
( ~ sdtlseqdt0(sK0,szmzazxdt0(xS))
| ~ aElementOf0(sK0,szNzAzT0)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
inference(duplicate_literal_removal,[],[f346]) ).
fof(f356,plain,
( ~ aElementOf0(sK0,szNzAzT0)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ aElementOf0(sK0,xS) ),
inference(resolution,[],[f352,f143]) ).
fof(f357,plain,
( ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ aElementOf0(sK0,xS) ),
inference(forward_subsumption_resolution,[],[f356,f139]) ).
fof(f358,plain,
~ aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(forward_subsumption_resolution,[],[f357,f150]) ).
fof(f359,plain,
~ aElementOf0(szmzazxdt0(xS),xS),
inference(resolution,[],[f358,f139]) ).
fof(f361,plain,
$false,
inference(forward_subsumption_resolution,[],[f359,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM544+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.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
% 0.11/0.37 % DateTime : Sun Sep 27 20:26:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 4.54/1.63 % (3720743)Detected formulas, will run a generic FOF schedule.
% 4.54/1.63 % (3720759)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=1676716276:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.54/1.63 % (3720762)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1990993400:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.54/1.63 % (3720762)First to succeed.
% 4.54/1.63 % (3720762)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3720743"
% 4.54/1.63 % (3720764)dis-21_1_sil=8000:lcm=predicate:random_seed=516395852: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)
% 4.54/1.63 % (3720761)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4163949228:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.54/1.63 % (3720760)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=3787275451:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.54/1.63 % (3720758)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=1779894412:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.54/1.63 % (3720763)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2698771301:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.54/1.63 % (3720761)Also succeeded, but the first one will report.
% 4.54/1.63 % (3720763)Also succeeded, but the first one will report.
% 4.54/1.63 % (3720764)Instruction limit reached!
% 4.54/1.63 % (3720764)------------------------------
% 4.54/1.63 % (3720764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.63 % (3720764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.63 % (3720764)CaDiCaL version: 2.1.3
% 4.54/1.63 % (3720764)Termination reason: Instruction limit
% 4.54/1.63 % (3720764)Termination phase: Saturation
% 4.54/1.63 % (3720764)Time elapsed: 0.073 s
% 4.54/1.63 % (3720764)Peak memory usage: 88 MB
% 4.54/1.63 % (3720764)Instructions burned: 129 (million)
% 4.54/1.63 % (3720762)Refutation found. Thanks to Tanya!
% 4.54/1.63 % SZS status Theorem for theBenchmark
% 4.54/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.54/1.63 % (3720762)------------------------------
% 4.54/1.63 % (3720762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.63 % (3720762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.63 % (3720762)CaDiCaL version: 2.1.3
% 4.54/1.63 % (3720762)Termination reason: Refutation
% 4.54/1.63 % (3720762)Time elapsed: 0.013 s
% 4.54/1.63 % (3720762)Peak memory usage: 89 MB
% 4.54/1.63 % (3720762)Instructions burned: 10 (million)
% 4.54/1.63 % (3720762)------------------------------
% 4.54/1.63 % (3720762)------------------------------
% 4.54/1.63 % (3720743)Success in time 0.554 s
% 4.54/1.63 % Vampire exiting
%------------------------------------------------------------------------------