%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM302+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 : n008.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 2.66s 1.34s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 14 unt; 2 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 23 ~; 13 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 29 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn0) ).
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',less_entry_point_neg_pos) ).
fof(f402,conjecture,
? [X0] : less(nn2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nn2_less_something) ).
fof(f403,negated_conjecture,
~ ? [X0] : less(nn2,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
! [X0] : ~ less(nn2,X0),
inference(ennf_transformation,[],[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(f453,plain,
! [X0] : ~ less(nn2,X0),
inference(cnf_transformation,[],[f406]) ).
fof(f460,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(f462,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f543,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f612,plain,
! [X2,X0,X1] :
( ~ rdn_translate(nn2,rdn_neg(X0))
| ~ rdn_translate(X1,rdn_pos(X2)) ),
inference(resolution,[],[f460,f453]) ).
fof(f617,definition,
( spl1_1
<=> ! [X2,X1] : ~ rdn_translate(X1,rdn_pos(X2)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f618,plain,
( ! [X2,X1] : ~ rdn_translate(X1,rdn_pos(X2))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f620,definition,
( spl1_2
<=> ! [X0] : ~ rdn_translate(nn2,rdn_neg(X0)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f621,plain,
( ! [X0] : ~ rdn_translate(nn2,rdn_neg(X0))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f622,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f612,f620,f617]) ).
fof(f623,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f621,f462]) ).
fof(f624,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f623]) ).
fof(f625,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f618,f543]) ).
fof(f644,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f625]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f622]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f624]) ).
cnf(s12,plain,
~ spl1_1,
inference(sat_conversion,[],[f644]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s2,s12]) ).
fof(f645,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM302+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 19:30:25 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.66/1.34 % (1544874)Detected formulas, will run a generic FOF schedule.
% 2.66/1.34 % (1544885)dis-21_1_sil=8000:lcm=predicate:random_seed=3577294268: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)
% 2.66/1.34 % (1544885)First to succeed.
% 2.66/1.34 % (1544885)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1544874"
% 2.66/1.34 % (1544880)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=2952467002:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.34 % (1544879)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=3706916925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.34 % (1544881)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=3370433647:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.34 % (1544882)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2192187754:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.34 % (1544883)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1324616931:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.34 % (1544884)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2950252128:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.34 % (1544882)Refutation not found, incomplete strategy
% 2.66/1.34 % (1544882)------------------------------
% 2.66/1.34 % (1544882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.34 % (1544882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.34 % (1544882)CaDiCaL version: 2.1.3
% 2.66/1.34 % (1544882)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.34 % (1544882)Time elapsed: 0.002 s
% 2.66/1.34 % (1544882)Peak memory usage: 88 MB
% 2.66/1.34 % (1544882)Instructions burned: 1 (million)
% 2.66/1.34 % (1544883)Also succeeded, but the first one will report.
% 2.66/1.34 % (1544884)Also succeeded, but the first one will report.
% 2.66/1.34 % (1544885)Refutation found. Thanks to Tanya!
% 2.66/1.34 % SZS status Theorem for theBenchmark
% 2.66/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.35 % (1544885)------------------------------
% 2.66/1.35 % (1544885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (1544885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (1544885)CaDiCaL version: 2.1.3
% 2.66/1.35 % (1544885)Termination reason: Refutation
% 2.66/1.35 % (1544885)Time elapsed: 0.004 s
% 2.66/1.35 % (1544885)Peak memory usage: 90 MB
% 2.66/1.35 % (1544885)Instructions burned: 10 (million)
% 2.66/1.35 % (1544885)------------------------------
% 2.66/1.35 % (1544885)------------------------------
% 2.66/1.35 % (1544874)Success in time 0.299 s
% 2.66/1.35 % Vampire exiting
%------------------------------------------------------------------------------