%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM561+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 : n002.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 12:15:45 PM UTC 2026
% Result : Theorem 2.63s 1.32s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 130 ( 31 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 170 ( 69 ~; 65 |; 28 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 61 ( 50 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDomSet) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSImg) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2911) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2911_02) ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f73,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(flattening,[],[f72]) ).
fof(f80,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 ) ) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f86,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( aElementOf0(X5,X1)
& sdtlpdtrp0(X0,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6 ) )
& ( ? [X8] :
( aElementOf0(X8,X1)
& sdtlpdtrp0(X0,X8) = X6 )
| ~ aElementOf0(X6,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != sK0(X0,X1,X2) )
| ~ aElementOf0(sK0(X0,X1,X2),X2) )
& ( ( aElementOf0(sK1(X0,X1,X2),X1)
& sK0(X0,X1,X2) = sdtlpdtrp0(X0,sK1(X0,X1,X2)) )
| aElementOf0(sK0(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6 ) )
& ( ( aElementOf0(sK2(X0,X1,X6),X1)
& sdtlpdtrp0(X0,sK2(X0,X1,X6)) = X6 )
| ~ aElementOf0(X6,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f92]) ).
fof(f98,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f99,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f73]) ).
fof(f101,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X7] :
( aElementOf0(X6,X2)
| ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f111,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f118,plain,
! [X2,X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),X2)
| ~ aElementOf0(X7,X1)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f119,plain,
! [X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),sdtlcdtrc0(X0,X1))
| ~ aElementOf0(X7,X1)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f147,plain,
( ~ aElementOf0(xx,szDzozmdt0(xF))
| ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(resolution,[],[f119,f100]) ).
fof(f148,plain,
( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(forward_subsumption_resolution,[],[f147,f99]) ).
fof(f149,plain,
~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
inference(forward_subsumption_resolution,[],[f148,f98]) ).
fof(f150,plain,
~ aSet0(szDzozmdt0(xF)),
inference(resolution,[],[f149,f111]) ).
fof(f152,plain,
~ aFunction0(xF),
inference(resolution,[],[f150,f101]) ).
fof(f153,plain,
$false,
inference(forward_subsumption_resolution,[],[f152,f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM561+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:32:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.63/1.32 % (3856132)Detected formulas, will run a generic FOF schedule.
% 2.63/1.32 % (3856141)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2501824814:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.32 % (3856141)First to succeed.
% 2.63/1.32 % (3856141)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3856132"
% 2.63/1.32 % (3856143)dis-21_1_sil=8000:lcm=predicate:random_seed=178671462: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)
% 2.63/1.32 % (3856140)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3576969928:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.32 % (3856137)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=1613637178:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.32 % (3856138)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=2934253293:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.32 % (3856139)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=2520459361:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.32 % (3856140)Refutation not found, incomplete strategy
% 2.63/1.32 % (3856140)------------------------------
% 2.63/1.32 % (3856140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.32 % (3856140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.32 % (3856140)CaDiCaL version: 2.1.3
% 2.63/1.32 % (3856140)Termination reason: Refutation not found, incomplete strategy
% 2.63/1.32 % (3856140)Time elapsed: 0.001 s
% 2.63/1.32 % (3856140)Peak memory usage: 87 MB
% 2.63/1.32 % (3856142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2604286667:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.32 % (3856142)Also succeeded, but the first one will report.
% 2.63/1.32 % (3856143)Instruction limit reached!
% 2.63/1.32 % (3856143)------------------------------
% 2.63/1.32 % (3856143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.32 % (3856143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.32 % (3856143)CaDiCaL version: 2.1.3
% 2.63/1.32 % (3856143)Termination reason: Instruction limit
% 2.63/1.32 % (3856143)Termination phase: Saturation
% 2.63/1.32 % (3856143)Time elapsed: 0.055 s
% 2.63/1.32 % (3856143)Peak memory usage: 88 MB
% 2.63/1.32 % (3856143)Instructions burned: 129 (million)
% 2.63/1.32 % (3856141)Refutation found. Thanks to Tanya!
% 2.63/1.32 % SZS status Theorem for theBenchmark
% 2.63/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.32 % (3856141)------------------------------
% 2.63/1.32 % (3856141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.32 % (3856141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.32 % (3856141)CaDiCaL version: 2.1.3
% 2.63/1.32 % (3856141)Termination reason: Refutation
% 2.63/1.32 % (3856141)Time elapsed: 0.002 s
% 2.63/1.32 % (3856141)Peak memory usage: 88 MB
% 2.63/1.32 % (3856141)Instructions burned: 3 (million)
% 2.63/1.32 % (3856141)------------------------------
% 2.63/1.32 % (3856141)------------------------------
% 2.63/1.32 % (3856132)Success in time 0.288 s
% 2.63/1.32 % Vampire exiting
%------------------------------------------------------------------------------