%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM299+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 12:12:07 PM UTC 2026
% Result : Theorem 0.19s 1.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 20 unt; 3 def)
% Number of atoms : 107 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 59 ~; 44 |; 8 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 48 ( 0 sgn 48 !; 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(f284,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( ~ less(X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
fof(f402,conjecture,
~ less(nn2,nn4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nn2_not_less_nn4) ).
fof(f403,negated_conjecture,
~ ~ less(nn2,nn4),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
less(nn2,nn4),
inference(flattening,[],[f403]) ).
fof(f411,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(f412,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,[],[f411]) ).
fof(f439,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(f440,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,[],[f439]) ).
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(nn2,nn4),
inference(cnf_transformation,[],[f404]) ).
fof(f457,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f452]) ).
fof(f459,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_neg(X3))
| ~ rdn_positive_less(X3,X2) ),
inference(cnf_transformation,[],[f412]) ).
fof(f462,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f463,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(cnf_transformation,[],[f132]) ).
fof(f548,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,[],[f440]) ).
fof(f554,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f555,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f629,plain,
! [X2,X3,X0,X1] :
( ~ less(X2,X0)
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_positive_less(X3,X1)
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(resolution,[],[f459,f457]) ).
fof(f683,plain,
! [X0,X1] :
( ~ rdn_positive_less(X0,X1)
| ~ rdn_translate(nn2,rdn_neg(X0))
| ~ rdn_translate(nn4,rdn_neg(X1)) ),
inference(resolution,[],[f629,f453]) ).
fof(f687,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X2),rdnn(X1))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X0)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(X1))) ),
inference(resolution,[],[f683,f548]) ).
fof(f734,definition,
( spl1_11
<=> rdn_translate(nn4,rdn_neg(rdnn(n4))) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f735,plain,
( ~ rdn_translate(nn4,rdn_neg(rdnn(n4)))
| spl1_11 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f744,definition,
( spl1_14
<=> rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f745,plain,
( ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| spl1_14 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f754,plain,
( $false
| spl1_11 ),
inference(resolution,[],[f735,f463]) ).
fof(f755,plain,
spl1_11,
inference(avatar_contradiction_clause,[],[f754]) ).
fof(f756,plain,
( $false
| spl1_14 ),
inference(resolution,[],[f745,f462]) ).
fof(f757,plain,
spl1_14,
inference(avatar_contradiction_clause,[],[f756]) ).
fof(f842,plain,
! [X0] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n3))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X0)))
| ~ rdn_translate(nn4,rdn_neg(rdnn(n4))) ),
inference(resolution,[],[f687,f554]) ).
fof(f858,definition,
( spl1_37
<=> ! [X0] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n3))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl1_37])],[avatar_definition]) ).
fof(f859,plain,
( ! [X0] :
( ~ rdn_positive_less(rdnn(X0),rdnn(n3))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X0))) )
| ~ spl1_37 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f860,plain,
( ~ spl1_11
| spl1_37 ),
inference(avatar_split_clause,[],[f842,f858,f734]) ).
fof(f873,plain,
( ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ spl1_37 ),
inference(resolution,[],[f859,f555]) ).
fof(f874,plain,
( ~ spl1_14
| ~ spl1_37 ),
inference(avatar_split_clause,[],[f873,f858,f744]) ).
cnf(s9,plain,
spl1_11,
inference(sat_conversion,[],[f755]) ).
cnf(s10,plain,
spl1_14,
inference(sat_conversion,[],[f757]) ).
cnf(s22,plain,
( ~ spl1_11
| spl1_37 ),
inference(sat_conversion,[],[f860]) ).
cnf(s25,plain,
( ~ spl1_14
| ~ spl1_37 ),
inference(sat_conversion,[],[f874]) ).
cnf(s26,plain,
~ spl1_37,
inference(rat,[],[s25,s10]) ).
cnf(s27,plain,
~ spl1_11,
inference(rat,[],[s22,s26]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s9,s27]) ).
fof(f875,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM299+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n026.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 19:31:57 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 0.19/1.50 % (3162073)Detected formulas, will run a generic FOF schedule.
% 0.19/1.50 % (3162082)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1810278132:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.50 % (3162082)Refutation not found, incomplete strategy
% 0.19/1.50 % (3162082)------------------------------
% 0.19/1.50 % (3162082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3162082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3162082)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3162082)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.50 % (3162082)Time elapsed: 0.001 s
% 0.19/1.50 % (3162082)Peak memory usage: 87 MB
% 0.19/1.50 % (3162082)Instructions burned: 2 (million)
% 0.19/1.50 % (3162080)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=2954883324:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.50 % (3162078)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=1178712492:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.50 % (3162084)dis-21_1_sil=8000:lcm=predicate:random_seed=1838452919: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)
% 0.19/1.50 % (3162079)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=4055568532:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.50 % (3162083)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1458689079:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.50 % (3162081)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1347255721:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.50 % (3162084)First to succeed.
% 0.19/1.50 % (3162084)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3162073"
% 0.19/1.50 % (3162081)Refutation not found, incomplete strategy
% 0.19/1.50 % (3162081)------------------------------
% 0.19/1.50 % (3162081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3162081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3162081)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3162081)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.50 % (3162081)Time elapsed: 0.001 s
% 0.19/1.50 % (3162081)Peak memory usage: 87 MB
% 0.19/1.50 % (3162081)Instructions burned: 1 (million)
% 0.19/1.50 % (3162083)Also succeeded, but the first one will report.
% 0.19/1.50 % (3162082)------------------------------
% 0.19/1.50 % (3162082)------------------------------
% 0.19/1.50 % (3162092)lrs+10_1_sil=8000:sp=occurrence:random_seed=2076675795:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.19/1.50 % (3162092)Also succeeded, but the first one will report.
% 0.19/1.50 % (3162081)------------------------------
% 0.19/1.50 % (3162081)------------------------------
% 0.19/1.50 % (3162084)Refutation found. Thanks to Tanya!
% 0.19/1.50 % SZS status Theorem for theBenchmark
% 0.19/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50 % (3162084)------------------------------
% 0.19/1.50 % (3162084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3162084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3162084)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3162084)Termination reason: Refutation
% 0.19/1.50 % (3162084)Time elapsed: 0.010 s
% 0.19/1.50 % (3162084)Peak memory usage: 89 MB
% 0.19/1.50 % (3162084)Instructions burned: 17 (million)
% 0.19/1.50 % (3162084)------------------------------
% 0.19/1.50 % (3162084)------------------------------
% 0.19/1.50 % (3162073)Success in time 0.42 s
% 0.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------