%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM633+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:25:05 PM UTC 2026
% Result : Theorem 0.10s 15.48s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 99 ( 25 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 122 ( 47 ~; 31 |; 35 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 23 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
fof(f96,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
fof(f98,axiom,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4998) ).
fof(f99,conjecture,
( ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xO,xK))
=> ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) ) )
=> ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( aSubsetOf0(X1,xS)
& isCountable0(X1)
& ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xK))
=> sdtlpdtrp0(xc,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f100,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xO,xK))
=> ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) ) )
=> ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( aSubsetOf0(X1,xS)
& isCountable0(X1)
& ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xK))
=> sdtlpdtrp0(xc,X2) = X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f99]) ).
fof(f108,plain,
~ ( ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xO,xK))
=> ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) ) )
=> ? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( aSubsetOf0(X2,xS)
& isCountable0(X2)
& ! [X3] :
( aElementOf0(X3,slbdtsldtrb0(X2,xK))
=> sdtlpdtrp0(xc,X3) = X1 ) ) ) ),
inference(rectify,[],[f100]) ).
fof(f232,plain,
( ! [X1] :
( ~ aElementOf0(X1,xT)
| ! [X2] :
( ~ aSubsetOf0(X2,xS)
| ~ isCountable0(X2)
| ? [X3] :
( sdtlpdtrp0(xc,X3) != X1
& aElementOf0(X3,slbdtsldtrb0(X2,xK)) ) ) )
& ! [X0] :
( ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0)
& aElementOf0(X0,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,slbdtsldtrb0(xO,xK)) ) ),
inference(ennf_transformation,[],[f108]) ).
fof(f302,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ? [X2] :
( sdtlpdtrp0(xc,X2) != X0
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) ) ) )
& ! [X3] :
( ( slcrc0 != X3
& aSubsetOf0(X3,szNzAzT0)
& aElementOf0(X3,szDzozmdt0(xc))
& szDzizrdt0(xd) = sdtlpdtrp0(xc,X3) )
| ~ aElementOf0(X3,slbdtsldtrb0(xO,xK)) ) ),
inference(rectify,[],[f232]) ).
fof(f303,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ( sdtlpdtrp0(xc,sK29(X0,X1)) != X0
& aElementOf0(sK29(X0,X1),slbdtsldtrb0(X1,xK)) ) ) )
& ! [X3] :
( ( slcrc0 != X3
& aSubsetOf0(X3,szNzAzT0)
& aElementOf0(X3,szDzozmdt0(xc))
& szDzizrdt0(xd) = sdtlpdtrp0(xc,X3) )
| ~ aElementOf0(X3,slbdtsldtrb0(xO,xK)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X2,sK29(X0,X1))],[f302]) ).
fof(f494,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f94]) ).
fof(f497,plain,
isCountable0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f502,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[],[f98]) ).
fof(f503,plain,
! [X3] :
( ~ aElementOf0(X3,slbdtsldtrb0(xO,xK))
| szDzizrdt0(xd) = sdtlpdtrp0(xc,X3) ),
inference(cnf_transformation,[],[f303]) ).
fof(f507,plain,
! [X0,X1] :
( aElementOf0(sK29(X0,X1),slbdtsldtrb0(X1,xK))
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f303]) ).
fof(f508,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK29(X0,X1)) != X0
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f303]) ).
fof(f649,plain,
! [X0] :
( szDzizrdt0(xd) = sdtlpdtrp0(xc,sK29(X0,xO))
| ~ aSubsetOf0(xO,xS)
| ~ isCountable0(xO)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f503,f507]) ).
fof(f650,plain,
! [X0] :
( szDzizrdt0(xd) = sdtlpdtrp0(xc,sK29(X0,xO))
| ~ isCountable0(xO)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f649,f502]) ).
fof(f651,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| szDzizrdt0(xd) = sdtlpdtrp0(xc,sK29(X0,xO)) ),
inference(forward_subsumption_resolution,[],[f650,f497]) ).
fof(f685,plain,
szDzizrdt0(xd) = sdtlpdtrp0(xc,sK29(szDzizrdt0(xd),xO)),
inference(resolution,[],[f494,f651]) ).
fof(f686,plain,
( szDzizrdt0(xd) != szDzizrdt0(xd)
| ~ aSubsetOf0(xO,xS)
| ~ isCountable0(xO)
| ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(superposition,[],[f508,f685]) ).
fof(f687,plain,
( ~ aSubsetOf0(xO,xS)
| ~ isCountable0(xO)
| ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(trivial_inequality_removal,[],[f686]) ).
fof(f688,plain,
( ~ isCountable0(xO)
| ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(forward_subsumption_resolution,[],[f687,f502]) ).
fof(f689,plain,
~ aElementOf0(szDzizrdt0(xd),xT),
inference(forward_subsumption_resolution,[],[f688,f497]) ).
fof(f690,plain,
$false,
inference(forward_subsumption_resolution,[],[f689,f494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM633+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/15.40 % Computer : n019.cluster.edu
% 0.10/15.40 % Model : x86_64 x86_64
% 0.10/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.40 % Memory : 8046.5625MB
% 0.10/15.40 % OS : Linux 6.8.0-71-generic
% 0.10/15.40 % CPULimit : 300
% 0.10/15.40 % WCLimit : 300
% 0.10/15.40 % DateTime : Sun Sep 27 20:51:54 UTC 2026
% 0.10/15.40 % CPUTime :
% 0.10/15.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/15.43 Running first-order model finding
% 0.10/15.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.48 % (3390627)Will run a generic schedule for satisfiability detection.
% 0.10/15.48 % (3390634)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3325858303:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/15.48 % (3390633)% WARNING: option uhcvi not known.
% 0.10/15.48 % (3390634) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3390627-3390634"...
% 0.10/15.48 % (3390632)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2074718627_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/15.48 % (3390637)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1384955230:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/15.48 % (3390633)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1052014744:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/15.48 % (3390635)dis+10_1_sil=32000:sp=arity:random_seed=3456746553:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/15.48 % (3390636)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=648158224:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/15.48 % (3390634)...printing done.
% 0.10/15.48 % (3390638)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3138081680:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/15.48 % (3390634)Refutation found. Thanks to Tanya!
% 0.10/15.48 % SZS status Theorem for theBenchmark
% 0.10/15.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/15.48 % (3390634)------------------------------
% 0.10/15.48 % (3390634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/15.48 % (3390634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/15.48 % (3390634)CaDiCaL version: 2.1.3
% 0.10/15.48 % (3390634)Termination reason: Refutation
% 0.10/15.48 % (3390634)Time elapsed: 0.007 s
% 0.10/15.48 % (3390634)Peak memory usage: 12 MB
% 0.10/15.48 % (3390634)Instructions burned: 17 (million)
% 0.10/15.48 % (3390627)Success in time 0.04 s
% 0.10/15.48 % Vampire exiting
%------------------------------------------------------------------------------