%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM297+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 : n026.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 12:12:06 PM UTC 2026
% Result : Theorem 3.40s 1.38s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 23 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn2) ).
fof(f132,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn4) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less23) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less34) ).
fof(f275,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X0),rdnn(X1))
& rdn_positive_less(rdnn(X1),rdnn(X2)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).
fof(f283,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_neg(X2))
& rdn_translate(X1,rdn_neg(X3))
& rdn_positive_less(X3,X2) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_neg_neg) ).
fof(f402,conjecture,
less(nn4,nn2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nn4_less_nn2) ).
fof(f403,negated_conjecture,
~ less(nn4,nn2),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ less(nn4,nn2),
inference(flattening,[],[f403]) ).
fof(f505,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_neg(X3))
| ~ rdn_positive_less(X3,X2) ),
inference(ennf_transformation,[],[f283]) ).
fof(f506,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_neg(X3))
| ~ rdn_positive_less(X3,X2) ),
inference(flattening,[],[f505]) ).
fof(f512,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f513,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(flattening,[],[f512]) ).
fof(f514,plain,
~ less(nn4,nn2),
inference(cnf_transformation,[],[f404]) ).
fof(f515,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(X1,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_neg(X2))
| less(X0,X1)
| ~ rdn_positive_less(X3,X2) ),
inference(cnf_transformation,[],[f506]) ).
fof(f518,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f519,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(cnf_transformation,[],[f132]) ).
fof(f521,plain,
! [X2,X0,X1] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(cnf_transformation,[],[f513]) ).
fof(f527,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f528,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f553,plain,
! [X0,X1] :
( ~ rdn_positive_less(rdnn(n2),X1)
| less(X0,nn2)
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(resolution,[],[f515,f518]) ).
fof(f598,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(n2),rdnn(X2))
| ~ rdn_translate(X0,rdn_neg(rdnn(X1)))
| less(X0,nn2)
| ~ rdn_positive_less(rdnn(X2),rdnn(X1)) ),
inference(resolution,[],[f553,f521]) ).
fof(f641,plain,
! [X0,X1] :
( ~ rdn_positive_less(rdnn(n3),rdnn(X1))
| less(X0,nn2)
| ~ rdn_translate(X0,rdn_neg(rdnn(X1))) ),
inference(resolution,[],[f598,f528]) ).
fof(f722,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_neg(rdnn(n4)))
| less(X0,nn2) ),
inference(resolution,[],[f641,f527]) ).
fof(f724,plain,
less(nn4,nn2),
inference(resolution,[],[f722,f519]) ).
fof(f725,plain,
$false,
inference(forward_subsumption_resolution,[],[f724,f514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM297+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:31:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.40/1.38 % (3161655)Detected formulas, will run a generic FOF schedule.
% 3.40/1.38 % (3161660)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=2830611680:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.38 % (3161663)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3458150829:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.38 % (3161664)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=664416138:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.38 % (3161662)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=737886611:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.38 % (3161661)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=2511063366:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.38 % (3161666)dis-21_1_sil=8000:lcm=predicate:random_seed=41124935: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)
% 3.40/1.38 % (3161665)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=771190135:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.38 % (3161663)Refutation not found, incomplete strategy
% 3.40/1.38 % (3161663)------------------------------
% 3.40/1.38 % (3161663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (3161663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (3161663)CaDiCaL version: 2.1.3
% 3.40/1.38 % (3161663)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.38 % (3161663)Time elapsed: 0.002 s
% 3.40/1.38 % (3161663)Peak memory usage: 88 MB
% 3.40/1.38 % (3161663)Instructions burned: 1 (million)
% 3.40/1.38 % (3161664)First to succeed.
% 3.40/1.38 % (3161664)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3161655"
% 3.40/1.38 % (3161666)Also succeeded, but the first one will report.
% 3.40/1.38 % (3161665)Also succeeded, but the first one will report.
% 3.40/1.38 % (3161663)------------------------------
% 3.40/1.38 % (3161663)------------------------------
% 3.40/1.38 % (3161664)Refutation found. Thanks to Tanya!
% 3.40/1.38 % SZS status Theorem for theBenchmark
% 3.40/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.38 % (3161664)------------------------------
% 3.40/1.38 % (3161664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.38 % (3161664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.38 % (3161664)CaDiCaL version: 2.1.3
% 3.40/1.38 % (3161664)Termination reason: Refutation
% 3.40/1.38 % (3161664)Time elapsed: 0.007 s
% 3.40/1.38 % (3161664)Peak memory usage: 88 MB
% 3.40/1.38 % (3161664)Instructions burned: 9 (million)
% 3.40/1.38 % (3161664)------------------------------
% 3.40/1.38 % (3161664)------------------------------
% 3.40/1.38 % (3161655)Success in time 0.426 s
% 3.40/1.38 % Vampire exiting
%------------------------------------------------------------------------------