%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM592+1 : 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 : n012.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 12:15:54 PM UTC 2026
% Result : Theorem 2.04s 0.89s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 115 ( 24 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 150 ( 67 ~; 55 |; 25 &)
% ( 0 <=>; 3 =>; 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; 9 con; 0-2 aty)
% Number of variables : 39 ( 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,axiom,
( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
fof(f93,axiom,
( aElementOf0(xu,xT)
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X0] :
( ( aSet0(X0)
& aElementOf0(X0,slbdtsldtrb0(xX,xk)) )
=> sdtlpdtrp0(xd,X0) = xu ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4545) ).
fof(f94,conjecture,
? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f95,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f119,plain,
( aElementOf0(xu,xT)
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X0] :
( sdtlpdtrp0(xd,X0) = xu
| ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xX,xk)) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f120,plain,
( aElementOf0(xu,xT)
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X0] :
( sdtlpdtrp0(xd,X0) = xu
| ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xX,xk)) ) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X1)
| ? [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
& aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) ) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f122,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X1)
| ? [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
& aSet0(X2)
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) ) ) ),
inference(flattening,[],[f121]) ).
fof(f211,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK6(X0,X1)) != X0
& aSet0(sK6(X0,X1))
& aElementOf0(sK6(X0,X1),slbdtsldtrb0(X1,xk)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f122]) ).
fof(f286,plain,
xd = sdtlpdtrp0(xC,xi),
inference(cnf_transformation,[],[f91]) ).
fof(f287,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cnf_transformation,[],[f91]) ).
fof(f293,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
| ~ aSet0(X0)
| xu = sdtlpdtrp0(xd,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f294,plain,
isCountable0(xX),
inference(cnf_transformation,[],[f120]) ).
fof(f295,plain,
aSubsetOf0(xX,xY),
inference(cnf_transformation,[],[f120]) ).
fof(f296,plain,
aElementOf0(xu,xT),
inference(cnf_transformation,[],[f120]) ).
fof(f297,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| aElementOf0(sK6(X0,X1),slbdtsldtrb0(X1,xk)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f298,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| aSet0(sK6(X0,X1)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f299,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK6(X0,X1)) != X0
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f211]) ).
fof(f428,plain,
! [X0,X1] :
( sdtlpdtrp0(xd,sK6(X0,X1)) != X0
| ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f299,f286]) ).
fof(f517,plain,
! [X0,X1] :
( aElementOf0(sK6(X1,X0),slbdtsldtrb0(X0,xk))
| ~ aElementOf0(X1,xT)
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,xY) ),
inference(superposition,[],[f297,f287]) ).
fof(f518,plain,
! [X0,X1] :
( aSet0(sK6(X1,X0))
| ~ aElementOf0(X1,xT)
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,xY) ),
inference(superposition,[],[f298,f287]) ).
fof(f597,plain,
! [X0] :
( ~ aSet0(sK6(X0,xX))
| xu = sdtlpdtrp0(xd,sK6(X0,xX))
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xX)
| ~ aSubsetOf0(xX,xY) ),
inference(resolution,[],[f293,f517]) ).
fof(f601,plain,
! [X0] :
( xu = sdtlpdtrp0(xd,sK6(X0,xX))
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xX)
| ~ aSubsetOf0(xX,xY) ),
inference(forward_subsumption_resolution,[],[f597,f518]) ).
fof(f602,plain,
! [X0] :
( xu = sdtlpdtrp0(xd,sK6(X0,xX))
| ~ aElementOf0(X0,xT)
| ~ aSubsetOf0(xX,xY) ),
inference(forward_subsumption_resolution,[],[f601,f294]) ).
fof(f603,plain,
! [X0] :
( xu = sdtlpdtrp0(xd,sK6(X0,xX))
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f602,f295]) ).
fof(f604,plain,
! [X0] :
( xu != X0
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f428,f603]) ).
fof(f606,plain,
! [X0] :
( xu != X0
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT) ),
inference(duplicate_literal_removal,[],[f604]) ).
fof(f607,plain,
! [X0] :
( xu != X0
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f606,f294]) ).
fof(f608,plain,
! [X0] :
( ~ aSubsetOf0(xX,xY)
| xu != X0
| ~ aElementOf0(X0,xT) ),
inference(forward_demodulation,[],[f607,f287]) ).
fof(f609,plain,
! [X0] :
( xu != X0
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f608,f295]) ).
fof(f610,plain,
~ aElementOf0(xu,xT),
inference(equality_resolution,[],[f609]) ).
fof(f611,plain,
$false,
inference(forward_subsumption_resolution,[],[f610,f296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM592+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:39:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.33 Running first-order theorem proving
% 0.06/0.33 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
% 2.04/0.89 % (2717159)Detected formulas, will run a generic FOF schedule.
% 2.04/0.89 % (2717166)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=2970983028:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.04/0.89 % (2717165)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=2336579837:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.04/0.89 % (2717164)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=833395072:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.04/0.89 % (2717168)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=419076916:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.04/0.89 % (2717167)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2452849127:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.04/0.89 % (2717169)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1618680257:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.04/0.89 % (2717168)First to succeed.
% 2.04/0.89 % (2717168)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2717159"
% 2.04/0.89 % (2717170)dis-21_1_sil=8000:lcm=predicate:random_seed=2164145123: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)
% 2.04/0.89 % (2717167)Instruction limit reached!
% 2.04/0.89 % (2717167)------------------------------
% 2.04/0.89 % (2717167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/0.89 % (2717167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.89 % (2717167)CaDiCaL version: 2.1.3
% 2.04/0.89 % (2717167)Termination reason: Instruction limit
% 2.04/0.89 % (2717167)Termination phase: Saturation
% 2.04/0.89 % (2717167)Time elapsed: 0.039 s
% 2.04/0.89 % (2717167)Peak memory usage: 89 MB
% 2.04/0.89 % (2717167)Instructions burned: 110 (million)
% 2.04/0.89 % (2717170)Instruction limit reached!
% 2.04/0.89 % (2717170)------------------------------
% 2.04/0.89 % (2717170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/0.89 % (2717170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.89 % (2717170)CaDiCaL version: 2.1.3
% 2.04/0.89 % (2717170)Termination reason: Instruction limit
% 2.04/0.89 % (2717170)Termination phase: Saturation
% 2.04/0.89 % (2717170)Time elapsed: 0.039 s
% 2.04/0.89 % (2717170)Peak memory usage: 90 MB
% 2.04/0.89 % (2717170)Instructions burned: 130 (million)
% 2.04/0.89 % (2717169)Instruction limit reached!
% 2.04/0.89 % (2717169)------------------------------
% 2.04/0.89 % (2717169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/0.89 % (2717169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.89 % (2717169)CaDiCaL version: 2.1.3
% 2.04/0.89 % (2717169)Termination reason: Instruction limit
% 2.04/0.89 % (2717169)Termination phase: Saturation
% 2.04/0.89 % (2717169)Time elapsed: 0.055 s
% 2.04/0.89 % (2717169)Peak memory usage: 90 MB
% 2.04/0.89 % (2717169)Instructions burned: 140 (million)
% 2.04/0.89 % (2717178)lrs+10_1_sil=8000:sp=occurrence:random_seed=3016342493:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.04/0.89 % (2717178)Also succeeded, but the first one will report.
% 2.04/0.89 % (2717180)lrs+1011_1_sil=32000:sp=occurrence:random_seed=819894952:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 2.04/0.89 % (2717179)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1846092811:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.04/0.89 % (2717179)Also succeeded, but the first one will report.
% 2.04/0.89 % (2717180)Also succeeded, but the first one will report.
% 2.04/0.89 % (2717168)Refutation found. Thanks to Tanya!
% 2.04/0.89 % SZS status Theorem for theBenchmark
% 2.04/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.04/0.89 % (2717168)------------------------------
% 2.04/0.89 % (2717168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/0.89 % (2717168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.89 % (2717168)CaDiCaL version: 2.1.3
% 2.04/0.89 % (2717168)Termination reason: Refutation
% 2.04/0.89 % (2717168)Time elapsed: 0.006 s
% 2.04/0.89 % (2717168)Peak memory usage: 88 MB
% 2.04/0.89 % (2717168)Instructions burned: 15 (million)
% 2.04/0.89 % (2717168)------------------------------
% 2.04/0.89 % (2717168)------------------------------
% 2.04/0.89 % (2717159)Success in time 0.267 s
% 2.04/0.89 % Vampire exiting
%------------------------------------------------------------------------------