%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM291+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 : 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 12:12:05 PM UTC 2026
% Result : Theorem 0.18s 1.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 51 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 57 ( 29 ~; 19 |; 7 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn3) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',less_entry_point_pos_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(n3,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n3_not_less_n2) ).
fof(f403,negated_conjecture,
~ ~ less(n3,n2),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
less(n3,n2),
inference(flattening,[],[f403]) ).
fof(f414,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(f415,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,[],[f414]) ).
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(f456,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f457,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f721,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f734,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(cnf_transformation,[],[f415]) ).
fof(f738,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f452]) ).
fof(f858,plain,
less(n3,n2),
inference(cnf_transformation,[],[f404]) ).
fof(f860,plain,
~ less(n2,n3),
inference(resolution,[],[f738,f858]) ).
fof(f867,plain,
! [X0,X1] :
( ~ rdn_translate(n3,rdn_pos(X1))
| ~ rdn_translate(n2,rdn_pos(X0))
| ~ rdn_positive_less(X0,X1) ),
inference(resolution,[],[f734,f860]) ).
fof(f868,plain,
! [X0] :
( ~ rdn_translate(n2,rdn_pos(X0))
| ~ rdn_positive_less(X0,rdnn(n3)) ),
inference(resolution,[],[f867,f457]) ).
fof(f871,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(resolution,[],[f868,f456]) ).
fof(f872,plain,
$false,
inference(forward_subsumption_resolution,[],[f871,f721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM291+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 19:31:26 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.18/1.51 % (3160777)Detected formulas, will run a generic FOF schedule.
% 0.18/1.51 % (3160849)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1712922147:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.51 % (3160849)Refutation not found, incomplete strategy
% 0.18/1.51 % (3160849)------------------------------
% 0.18/1.51 % (3160849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3160849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3160849)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3160849)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.51 % (3160849)Time elapsed: 0.001 s
% 0.18/1.51 % (3160849)Peak memory usage: 87 MB
% 0.18/1.51 % (3160849)Instructions burned: 2 (million)
% 0.18/1.51 % (3160843)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=971332074:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.51 % (3160845)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=1793343022:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.51 % (3160841)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=1297139881:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.51 % (3160850)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=103494268:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.51 % (3160847)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3172186390:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.51 % (3160847)Refutation not found, incomplete strategy
% 0.18/1.51 % (3160847)------------------------------
% 0.18/1.51 % (3160847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3160847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3160847)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3160847)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.51 % (3160847)Time elapsed: 0.002 s
% 0.18/1.51 % (3160847)Peak memory usage: 87 MB
% 0.18/1.51 % (3160847)Instructions burned: 1 (million)
% 0.18/1.51 % (3160852)dis-21_1_sil=8000:lcm=predicate:random_seed=646906972: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)
% 0.18/1.51 % (3160850)First to succeed.
% 0.18/1.51 % (3160850)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3160777"
% 0.18/1.51 % (3160852)Also succeeded, but the first one will report.
% 0.18/1.51 % (3160849)------------------------------
% 0.18/1.51 % (3160849)------------------------------
% 0.18/1.51 % (3160928)lrs+10_1_sil=8000:sp=occurrence:random_seed=2644853060:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.18/1.51 % (3160928)Also succeeded, but the first one will report.
% 0.18/1.51 % (3160847)------------------------------
% 0.18/1.51 % (3160847)------------------------------
% 0.18/1.51 % (3160850)Refutation found. Thanks to Tanya!
% 0.18/1.51 % SZS status Theorem for theBenchmark
% 0.18/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (3160850)------------------------------
% 0.18/1.51 % (3160850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3160850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3160850)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3160850)Termination reason: Refutation
% 0.18/1.51 % (3160850)Time elapsed: 0.010 s
% 0.18/1.51 % (3160850)Peak memory usage: 89 MB
% 0.18/1.51 % (3160850)Instructions burned: 20 (million)
% 0.18/1.51 % (3160850)------------------------------
% 0.18/1.51 % (3160850)------------------------------
% 0.18/1.51 % (3160777)Success in time 0.426 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------