%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n013.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 12:16:04 PM UTC 2026
% Result : Theorem 5.68s 1.96s
% Output : Refutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 100 ( 21 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 130 ( 52 ~; 34 |; 35 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 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(f101,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(f133,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,[],[f101]) ).
fof(f231,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,[],[f133]) ).
fof(f232,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ( sdtlpdtrp0(xc,sK10(X0,X1)) != X0
& aElementOf0(sK10(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,[sK10]),skolemize(X2,sK10(X0,X1))],[f231]) ).
fof(f323,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f94]) ).
fof(f326,plain,
isCountable0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f331,plain,
aSubsetOf0(xO,xS),
inference(cnf_transformation,[],[f98]) ).
fof(f332,plain,
! [X3] :
( szDzizrdt0(xd) = sdtlpdtrp0(xc,X3)
| ~ aElementOf0(X3,slbdtsldtrb0(xO,xK)) ),
inference(cnf_transformation,[],[f232]) ).
fof(f336,plain,
! [X0,X1] :
( aElementOf0(sK10(X0,X1),slbdtsldtrb0(X1,xK))
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f232]) ).
fof(f337,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK10(X0,X1)) != X0
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f232]) ).
fof(f483,plain,
! [X0,X1] :
( szDzizrdt0(xd) != X0
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT)
| ~ aElementOf0(sK10(X0,X1),slbdtsldtrb0(xO,xK)) ),
inference(superposition,[],[f337,f332]) ).
fof(f484,plain,
! [X0] :
( ~ aElementOf0(sK10(szDzizrdt0(xd),X0),slbdtsldtrb0(xO,xK))
| ~ isCountable0(X0)
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ~ aSubsetOf0(X0,xS) ),
inference(equality_resolution,[],[f483]) ).
fof(f485,plain,
( ~ isCountable0(xO)
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ~ aSubsetOf0(xO,xS)
| ~ aSubsetOf0(xO,xS)
| ~ isCountable0(xO)
| ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(resolution,[],[f484,f336]) ).
fof(f486,plain,
( ~ aElementOf0(szDzizrdt0(xd),xT)
| ~ isCountable0(xO)
| ~ aSubsetOf0(xO,xS) ),
inference(duplicate_literal_removal,[],[f485]) ).
fof(f487,plain,
( ~ isCountable0(xO)
| ~ aSubsetOf0(xO,xS) ),
inference(resolution,[],[f323,f486]) ).
fof(f488,plain,
~ aSubsetOf0(xO,xS),
inference(forward_subsumption_resolution,[],[f487,f326]) ).
fof(f489,plain,
$false,
inference(forward_subsumption_resolution,[],[f488,f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM633+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n013.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 20:51:10 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 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
% 5.68/1.96 % (536982)Detected formulas, will run a generic FOF schedule.
% 5.68/1.96 % (536989)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=1056151724:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.68/1.96 % (536990)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=1469003331:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.68/1.96 % (536992)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=590140423:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.68/1.96 % (536991)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=3650052339:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.68/1.96 % (536993)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1007121089:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.68/1.96 % (536993)First to succeed.
% 5.68/1.96 % (536993)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-536982"
% 5.68/1.96 % (536994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1800275439:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.68/1.96 % (536995)dis-21_1_sil=8000:lcm=predicate:random_seed=3058130255: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)
% 5.68/1.96 % (536994)Also succeeded, but the first one will report.
% 5.68/1.96 % (536995)Also succeeded, but the first one will report.
% 5.68/1.96 % (536992)Instruction limit reached!
% 5.68/1.96 % (536992)------------------------------
% 5.68/1.96 % (536992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.96 % (536992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.96 % (536992)CaDiCaL version: 2.1.3
% 5.68/1.96 % (536992)Termination reason: Instruction limit
% 5.68/1.96 % (536992)Termination phase: Saturation
% 5.68/1.96 % (536992)Time elapsed: 0.106 s
% 5.68/1.96 % (536992)Peak memory usage: 89 MB
% 5.68/1.96 % (536992)Instructions burned: 109 (million)
% 5.68/1.96 % (537003)lrs+10_1_sil=8000:sp=occurrence:random_seed=3123997236:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.68/1.96 % (537003)Also succeeded, but the first one will report.
% 5.68/1.96 % (536993)Refutation found. Thanks to Tanya!
% 5.68/1.96 % SZS status Theorem for theBenchmark
% 5.68/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 5.68/1.96 % (536993)------------------------------
% 5.68/1.96 % (536993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.96 % (536993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.96 % (536993)CaDiCaL version: 2.1.3
% 5.68/1.96 % (536993)Termination reason: Refutation
% 5.68/1.96 % (536993)Time elapsed: 0.011 s
% 5.68/1.96 % (536993)Peak memory usage: 89 MB
% 5.68/1.96 % (536993)Instructions burned: 9 (million)
% 5.68/1.96 % (536993)------------------------------
% 5.68/1.96 % (536993)------------------------------
% 5.68/1.96 % (536982)Success in time 0.699 s
% 5.68/1.96 % Vampire exiting
%------------------------------------------------------------------------------