%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM298+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.15s 1.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 14 unt; 2 def)
% Number of atoms : 64 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 36 ~; 22 |; 6 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn2) ).
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn2) ).
fof(f282,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_neg(X2))
& rdn_translate(X1,rdn_pos(X3)) )
=> less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_neg_pos) ).
fof(f284,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( ~ less(X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
fof(f402,conjecture,
~ less(n2,nn2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n2_not_less_nn2) ).
fof(f403,negated_conjecture,
~ ~ less(n2,nn2),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
less(n2,nn2),
inference(flattening,[],[f403]) ).
fof(f413,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f282]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(flattening,[],[f413]) ).
fof(f451,plain,
! [X0,X1] :
( ( less(X0,X1)
| less(X1,X0)
| X0 = X1 )
& ( ( ~ less(X1,X0)
& X1 != X0 )
| ~ less(X0,X1) ) ),
inference(nnf_transformation,[],[f284]) ).
fof(f452,plain,
! [X0,X1] :
( ( less(X0,X1)
| less(X1,X0)
| X0 = X1 )
& ( ( ~ less(X1,X0)
& X1 != X0 )
| ~ less(X0,X1) ) ),
inference(flattening,[],[f451]) ).
fof(f453,plain,
less(n2,nn2),
inference(cnf_transformation,[],[f404]) ).
fof(f481,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f485,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f452]) ).
fof(f488,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f414]) ).
fof(f490,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f613,plain,
! [X2,X3,X0,X1] :
( ~ less(X2,X0)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(resolution,[],[f488,f485]) ).
fof(f633,plain,
! [X0,X1] :
( ~ rdn_translate(n2,rdn_pos(X0))
| ~ rdn_translate(nn2,rdn_neg(X1)) ),
inference(resolution,[],[f613,f453]) ).
fof(f638,definition,
( spl1_1
<=> ! [X1] : ~ rdn_translate(nn2,rdn_neg(X1)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f639,plain,
( ! [X1] : ~ rdn_translate(nn2,rdn_neg(X1))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f641,definition,
( spl1_2
<=> ! [X0] : ~ rdn_translate(n2,rdn_pos(X0)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f642,plain,
( ! [X0] : ~ rdn_translate(n2,rdn_pos(X0))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f643,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f633,f641,f638]) ).
fof(f644,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f642,f481]) ).
fof(f645,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f644]) ).
fof(f646,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f639,f490]) ).
fof(f647,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f646]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f643]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f645]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f647]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f648,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM298+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 19:30:56 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.67/1.50 % (877093)Detected formulas, will run a generic FOF schedule.
% 3.67/1.50 % (877102)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1595868560:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.50 % (877102)Refutation not found, incomplete strategy
% 3.67/1.50 % (877102)------------------------------
% 3.67/1.50 % (877102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.50 % (877102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.50 % (877102)CaDiCaL version: 2.1.3
% 3.67/1.50 % (877102)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.50 % (877102)Time elapsed: 0.001 s
% 3.67/1.50 % (877102)Peak memory usage: 87 MB
% 3.67/1.50 % (877102)Instructions burned: 2 (million)
% 3.67/1.50 % (877100)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=3096286515:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.50 % (877101)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1759044545:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.50 % (877099)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=4207056613:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.50 % (877098)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=3885980622:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.50 % (877101)Refutation not found, incomplete strategy
% 0.15/1.50 % (877101)------------------------------
% 0.15/1.50 % (877101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (877101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (877101)CaDiCaL version: 2.1.3
% 0.15/1.50 % (877101)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.50 % (877101)Time elapsed: 0.002 s
% 0.15/1.50 % (877101)Peak memory usage: 87 MB
% 0.15/1.50 % (877101)Instructions burned: 1 (million)
% 0.15/1.50 % (877104)dis-21_1_sil=8000:lcm=predicate:random_seed=4262245995: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)
% 0.15/1.50 % (877103)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=239595876:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.50 % (877104)First to succeed.
% 0.15/1.50 % (877104)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-877093"
% 0.15/1.50 % (877103)Also succeeded, but the first one will report.
% 0.15/1.50 % (877102)------------------------------
% 0.15/1.50 % (877102)------------------------------
% 0.15/1.50 % (877112)lrs+10_1_sil=8000:sp=occurrence:random_seed=3393434401:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.15/1.50 % (877112)Also succeeded, but the first one will report.
% 0.15/1.50 % (877101)------------------------------
% 0.15/1.50 % (877101)------------------------------
% 0.15/1.50 % (877104)Refutation found. Thanks to Tanya!
% 0.15/1.50 % SZS status Theorem for theBenchmark
% 0.15/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (877104)------------------------------
% 0.15/1.50 % (877104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (877104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (877104)CaDiCaL version: 2.1.3
% 0.15/1.50 % (877104)Termination reason: Refutation
% 0.15/1.50 % (877104)Time elapsed: 0.008 s
% 0.15/1.50 % (877104)Peak memory usage: 89 MB
% 0.15/1.50 % (877104)Instructions burned: 12 (million)
% 0.15/1.50 % (877104)------------------------------
% 0.15/1.50 % (877104)------------------------------
% 0.15/1.50 % (877093)Success in time 0.45 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------