%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM292+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:18:15 PM UTC 2026
% Result : Theorem 0.31s 0.67s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 18 unt; 2 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 83 ( 44 ~; 32 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f14,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn13) ).
fof(f257,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_digit1) ).
fof(f278,axiom,
! [X0,X1,X2] :
( rdn_non_zero(X2)
=> rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_extra_digits_positive_less) ).
fof(f279,axiom,
! [X0] :
( rdn_non_zero_digit(rdnn(X0))
=> rdn_non_zero(rdnn(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_non_zero_by_digit) ).
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/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(f402,conjecture,
less(n2,n13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n2_less_n13) ).
fof(f403,negated_conjecture,
~ less(n2,n13),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ less(n2,n13),
inference(flattening,[],[f403]) ).
fof(f411,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2) ),
inference(ennf_transformation,[],[f278]) ).
fof(f412,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(ennf_transformation,[],[f279]) ).
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(f456,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f467,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(cnf_transformation,[],[f14]) ).
fof(f710,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[],[f257]) ).
fof(f731,plain,
! [X2,X0,X1] :
( rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2) ),
inference(cnf_transformation,[],[f411]) ).
fof(f732,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(cnf_transformation,[],[f412]) ).
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(f858,plain,
~ less(n2,n13),
inference(cnf_transformation,[],[f404]) ).
fof(f860,plain,
~ rdn_non_zero_digit(rdnn(n1)),
inference(consistent_polarity_flipping,[],[f710]) ).
fof(f881,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2) ),
inference(consistent_polarity_flipping,[],[f731]) ).
fof(f882,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| rdn_non_zero_digit(rdnn(X0)) ),
inference(consistent_polarity_flipping,[],[f732]) ).
fof(f883,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(consistent_polarity_flipping,[],[f734]) ).
fof(f907,plain,
less(n2,n13),
inference(consistent_polarity_flipping,[],[f858]) ).
fof(f1172,plain,
! [X0,X1] :
( rdn_positive_less(X0,X1)
| ~ rdn_translate(n13,rdn_pos(X1))
| ~ rdn_translate(n2,rdn_pos(X0)) ),
inference(resolution,[],[f883,f907]) ).
fof(f1184,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n13,rdn_pos(rdn(rdnn(X0),X1)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X2)))
| ~ rdn_non_zero(X1) ),
inference(resolution,[],[f1172,f881]) ).
fof(f1187,definition,
( spl0_3
<=> ! [X2] : ~ rdn_translate(n2,rdn_pos(rdnn(X2))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1188,plain,
( ! [X2] : ~ rdn_translate(n2,rdn_pos(rdnn(X2)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f1190,definition,
( spl0_4
<=> ! [X0,X1] :
( ~ rdn_translate(n13,rdn_pos(rdn(rdnn(X0),X1)))
| ~ rdn_non_zero(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f1191,plain,
( ! [X0,X1] :
( ~ rdn_translate(n13,rdn_pos(rdn(rdnn(X0),X1)))
| ~ rdn_non_zero(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f1190]) ).
fof(f1192,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f1184,f1190,f1187]) ).
fof(f1274,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f1188,f456]) ).
fof(f1275,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1274]) ).
fof(f1281,plain,
( ~ rdn_non_zero(rdnn(n1))
| ~ spl0_4 ),
inference(resolution,[],[f1191,f467]) ).
fof(f1282,plain,
( rdn_non_zero_digit(rdnn(n1))
| ~ spl0_4 ),
inference(resolution,[],[f1281,f882]) ).
fof(f1283,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f1282,f860]) ).
fof(f1284,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f1283]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f1192]) ).
cnf(s12,plain,
~ spl0_3,
inference(sat_conversion,[],[f1275]) ).
cnf(s14,plain,
~ spl0_4,
inference(sat_conversion,[],[f1284]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s14,s12]) ).
fof(f1285,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM292+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.20/0.47 % Computer : n019.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 27 19:28:48 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.53 Running first-order model finding
% 0.25/0.53 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.66 % (3354682)Will run a generic schedule for satisfiability detection.
% 0.31/0.66 % (3354692)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1376122685:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.66 % (3354688)% WARNING: option uhcvi not known.
% 0.31/0.66 % (3354693)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=675804389:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.66 % (3354691)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=958750449:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.66 % (3354688)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1674229578:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.66 % (3354687)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4141633325_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.66 % (3354689)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=313159581:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.66 % (3354690)dis+10_1_sil=32000:sp=arity:random_seed=1057778245:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.67 % (3354693) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3354682-3354693"...
% 0.31/0.67 % (3354693)...printing done.
% 0.31/0.67 % (3354692)Instruction limit reached!
% 0.31/0.67 % (3354692)------------------------------
% 0.31/0.67 % (3354692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.67 % (3354692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.67 % (3354692)CaDiCaL version: 2.1.3
% 0.31/0.67 % (3354692)Termination reason: Instruction limit
% 0.31/0.67 % (3354692)Termination phase: Saturation
% 0.31/0.67 % (3354692)Time elapsed: 0.057 s
% 0.31/0.67 % (3354692)Peak memory usage: 14 MB
% 0.31/0.67 % (3354692)Instructions burned: 132 (million)
% 0.31/0.67 % (3354693)Refutation found. Thanks to Tanya!
% 0.31/0.67 % SZS status Theorem for theBenchmark
% 0.31/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.67 % (3354693)------------------------------
% 0.31/0.67 % (3354693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.67 % (3354693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.67 % (3354693)CaDiCaL version: 2.1.3
% 0.31/0.67 % (3354693)Termination reason: Refutation
% 0.31/0.67 % (3354693)Time elapsed: 0.040 s
% 0.31/0.67 % (3354693)Peak memory usage: 13 MB
% 0.31/0.67 % (3354693)Instructions burned: 46 (million)
% 0.31/0.67 % (3354682)Success in time 0.119 s
% 0.31/0.67 % Vampire exiting
%------------------------------------------------------------------------------