%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM290+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:12:05 PM UTC 2026
% Result : Theorem 3.64s 1.49s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 12 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn3) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less23) ).
fof(f281,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_pos(X2))
& rdn_translate(X1,rdn_pos(X3))
& rdn_positive_less(X2,X3) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).
fof(f402,conjecture,
less(n2,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n2_less_n3) ).
fof(f403,negated_conjecture,
~ less(n2,n3),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ less(n2,n3),
inference(flattening,[],[f403]) ).
fof(f509,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(ennf_transformation,[],[f281]) ).
fof(f510,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(flattening,[],[f509]) ).
fof(f514,plain,
~ less(n2,n3),
inference(cnf_transformation,[],[f404]) ).
fof(f515,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f518,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| less(X0,X1)
| ~ rdn_positive_less(X2,X3) ),
inference(cnf_transformation,[],[f510]) ).
fof(f519,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f530,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f553,plain,
! [X0,X1] :
( ~ rdn_positive_less(X1,rdnn(n3))
| less(X0,n3)
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f518,f519]) ).
fof(f583,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| less(X0,n3) ),
inference(resolution,[],[f553,f530]) ).
fof(f600,plain,
less(n2,n3),
inference(resolution,[],[f583,f515]) ).
fof(f601,plain,
$false,
inference(forward_subsumption_resolution,[],[f600,f514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM290+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.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 19:28:31 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.64/1.49 % (1118207)Detected formulas, will run a generic FOF schedule.
% 3.64/1.49 % (1118212)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=4154437482:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/1.49 % (1118218)dis-21_1_sil=8000:lcm=predicate:random_seed=1233021001: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)
% 3.64/1.49 % (1118213)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=2319651367:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/1.49 % (1118214)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=2593761391:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/1.49 % (1118216)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1075623613:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/1.49 % (1118215)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1005587204:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/1.49 % (1118217)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2323664416:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.64/1.49 % (1118215)Refutation not found, incomplete strategy
% 3.64/1.49 % (1118215)------------------------------
% 3.64/1.49 % (1118215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.49 % (1118215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.49 % (1118215)CaDiCaL version: 2.1.3
% 3.64/1.49 % (1118215)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.49 % (1118215)Time elapsed: 0.002 s
% 3.64/1.49 % (1118215)Peak memory usage: 87 MB
% 3.64/1.49 % (1118215)Instructions burned: 1 (million)
% 3.64/1.49 % (1118216)First to succeed.
% 3.64/1.49 % (1118216)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1118207"
% 3.64/1.49 % (1118218)Also succeeded, but the first one will report.
% 3.64/1.49 % (1118217)Also succeeded, but the first one will report.
% 3.64/1.49 % (1118215)------------------------------
% 3.64/1.49 % (1118215)------------------------------
% 3.64/1.49 % (1118216)Refutation found. Thanks to Tanya!
% 3.64/1.49 % SZS status Theorem for theBenchmark
% 3.64/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.49 % (1118216)------------------------------
% 3.64/1.49 % (1118216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.49 % (1118216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.49 % (1118216)CaDiCaL version: 2.1.3
% 3.64/1.49 % (1118216)Termination reason: Refutation
% 3.64/1.49 % (1118216)Time elapsed: 0.004 s
% 3.64/1.49 % (1118216)Peak memory usage: 88 MB
% 3.64/1.49 % (1118216)Instructions burned: 5 (million)
% 3.64/1.49 % (1118216)------------------------------
% 3.64/1.49 % (1118216)------------------------------
% 3.64/1.49 % (1118207)Success in time 0.445 s
% 3.64/1.49 % Vampire exiting
%------------------------------------------------------------------------------