%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM618+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 : n018.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 12:16:00 PM UTC 2026
% Result : Theorem 2.71s 1.26s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 3 unt; 0 def)
% Number of atoms : 34 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 34 ( 15 ~; 9 |; 9 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f97,axiom,
! [X0] :
( aElementOf0(X0,xO)
=> ? [X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).
fof(f114,axiom,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(xx,xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
fof(f115,conjecture,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& xx = sdtlpdtrp0(xe,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f116,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,szNzAzT0)
& xx = sdtlpdtrp0(xe,X0) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
fof(f147,plain,
! [X0] :
( ? [X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 )
| ~ aElementOf0(X0,xO) ),
inference(ennf_transformation,[],[f97]) ).
fof(f148,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,X0) != xx ),
inference(ennf_transformation,[],[f116]) ).
fof(f245,plain,
! [X0] :
( ( aElementOf0(sK9(X0),szNzAzT0)
& aElementOf0(sK9(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,sK9(X0)) = X0 )
| ~ aElementOf0(X0,xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f147]) ).
fof(f341,plain,
! [X0] :
( sdtlpdtrp0(xe,sK9(X0)) = X0
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f245]) ).
fof(f343,plain,
! [X0] :
( aElementOf0(sK9(X0),szNzAzT0)
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f245]) ).
fof(f364,plain,
aElementOf0(xx,xO),
inference(cnf_transformation,[],[f114]) ).
fof(f366,plain,
! [X0] :
( sdtlpdtrp0(xe,X0) != xx
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f599,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(sK9(X0),szNzAzT0)
| ~ aElementOf0(X0,xO) ),
inference(superposition,[],[f366,f341]) ).
fof(f600,plain,
! [X0] :
( xx != X0
| ~ aElementOf0(X0,xO) ),
inference(forward_subsumption_resolution,[],[f599,f343]) ).
fof(f601,plain,
~ aElementOf0(xx,xO),
inference(equality_resolution,[],[f600]) ).
fof(f602,plain,
$false,
inference(forward_subsumption_resolution,[],[f601,f364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM618+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:48:39 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.71/1.26 % (2708353)Detected formulas, will run a generic FOF schedule.
% 2.71/1.26 % (2708362)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2145620865:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.26 % (2708362)First to succeed.
% 2.71/1.26 % (2708362)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2708353"
% 2.71/1.26 % (2708364)dis-21_1_sil=8000:lcm=predicate:random_seed=423892220: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)
% 2.71/1.26 % (2708359)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=3128933743:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.26 % (2708360)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=3376644761:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.26 % (2708358)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=68512463:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.26 % (2708361)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=600695531:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.26 % (2708363)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3511571507:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.26 % (2708364)Also succeeded, but the first one will report.
% 2.71/1.26 % (2708363)Also succeeded, but the first one will report.
% 2.71/1.26 % (2708361)Instruction limit reached!
% 2.71/1.26 % (2708361)------------------------------
% 2.71/1.26 % (2708361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.26 % (2708361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.26 % (2708361)CaDiCaL version: 2.1.3
% 2.71/1.26 % (2708361)Termination reason: Instruction limit
% 2.71/1.26 % (2708361)Termination phase: Saturation
% 2.71/1.26 % (2708361)Time elapsed: 0.070 s
% 2.71/1.26 % (2708361)Peak memory usage: 90 MB
% 2.71/1.26 % (2708361)Instructions burned: 109 (million)
% 2.71/1.26 % (2708362)Refutation found. Thanks to Tanya!
% 2.71/1.26 % SZS status Theorem for theBenchmark
% 2.71/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.26 % (2708362)------------------------------
% 2.71/1.26 % (2708362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.26 % (2708362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.26 % (2708362)CaDiCaL version: 2.1.3
% 2.71/1.26 % (2708362)Termination reason: Refutation
% 2.71/1.26 % (2708362)Time elapsed: 0.005 s
% 2.71/1.26 % (2708362)Peak memory usage: 89 MB
% 2.71/1.26 % (2708362)Instructions burned: 12 (million)
% 2.71/1.26 % (2708362)------------------------------
% 2.71/1.26 % (2708362)------------------------------
% 2.71/1.26 % (2708353)Success in time 0.316 s
% 2.71/1.26 % Vampire exiting
%------------------------------------------------------------------------------