%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM294+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:18:16 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 16 unt; 2 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 34 ~; 22 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn12) ).
fof(f21,axiom,
rdn_translate(n20,rdn_pos(rdn(rdnn(n0),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn20) ).
fof(f267,axiom,
rdn_positive_less(rdnn(n1),rdnn(n2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less12) ).
fof(f276,axiom,
! [X0,X1,X2,X3] :
( rdn_positive_less(X1,X3)
=> rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_multi_digit_high) ).
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/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(f402,conjecture,
? [X0] : less(n12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n12_less_something) ).
fof(f403,negated_conjecture,
~ ? [X0] : less(n12,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f407,plain,
! [X0,X1,X2,X3] :
( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3))
| ~ rdn_positive_less(X1,X3) ),
inference(ennf_transformation,[],[f276]) ).
fof(f413,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(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(flattening,[],[f413]) ).
fof(f450,plain,
! [X0] : ~ less(n12,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f463,plain,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
inference(cnf_transformation,[],[f13]) ).
fof(f471,plain,
rdn_translate(n20,rdn_pos(rdn(rdnn(n0),rdnn(n2)))),
inference(cnf_transformation,[],[f21]) ).
fof(f717,plain,
rdn_positive_less(rdnn(n1),rdnn(n2)),
inference(cnf_transformation,[],[f267]) ).
fof(f726,plain,
! [X2,X3,X0,X1] :
( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3))
| ~ rdn_positive_less(X1,X3) ),
inference(cnf_transformation,[],[f407]) ).
fof(f731,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_positive_less(X2,X3) ),
inference(cnf_transformation,[],[f414]) ).
fof(f855,plain,
! [X0] : ~ less(n12,X0),
inference(cnf_transformation,[],[f450]) ).
fof(f1144,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(X2,X1)
| ~ rdn_translate(n12,rdn_pos(X2))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f731,f855]) ).
fof(f1157,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_positive_less(X1,X4)
| ~ rdn_translate(X2,rdn_pos(rdn(rdnn(X3),X4)))
| ~ rdn_translate(n12,rdn_pos(rdn(rdnn(X0),X1))) ),
inference(resolution,[],[f1144,f726]) ).
fof(f1270,plain,
! [X2,X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2))))
| ~ rdn_translate(n12,rdn_pos(rdn(rdnn(X2),rdnn(n1)))) ),
inference(resolution,[],[f1157,f717]) ).
fof(f1329,definition,
( spl0_35
<=> ! [X2] : ~ rdn_translate(n12,rdn_pos(rdn(rdnn(X2),rdnn(n1)))) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f1330,plain,
( ! [X2] : ~ rdn_translate(n12,rdn_pos(rdn(rdnn(X2),rdnn(n1))))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f1332,definition,
( spl0_36
<=> ! [X0,X1] : ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2)))) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f1333,plain,
( ! [X0,X1] : ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2))))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1332]) ).
fof(f1334,plain,
( spl0_35
| spl0_36 ),
inference(avatar_split_clause,[],[f1270,f1332,f1329]) ).
fof(f1698,plain,
( $false
| ~ spl0_35 ),
inference(resolution,[],[f1330,f463]) ).
fof(f1699,plain,
~ spl0_35,
inference(avatar_contradiction_clause,[],[f1698]) ).
fof(f1702,plain,
( $false
| ~ spl0_36 ),
inference(resolution,[],[f1333,f471]) ).
fof(f1721,plain,
~ spl0_36,
inference(avatar_contradiction_clause,[],[f1702]) ).
cnf(s18,plain,
( spl0_35
| spl0_36 ),
inference(sat_conversion,[],[f1334]) ).
cnf(s113,plain,
~ spl0_35,
inference(sat_conversion,[],[f1699]) ).
cnf(s123,plain,
~ spl0_36,
inference(sat_conversion,[],[f1721]) ).
cnf(s139,plain,
$false,
inference(rat,[],[s18,s123,s113]) ).
fof(f1722,plain,
$false,
inference(avatar_sat_refutation,[],[s139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM294+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 19:28:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (3268046)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3268055)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3598112088:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3268052)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3268054)dis+10_1_sil=32000:sp=arity:random_seed=2699746745:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3268051)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3850257376_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3268052)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3255494109:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3268053)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2947782552:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3268056)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=453075392:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3268057)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1108668279:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3268055) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3268046-3268055"...
% 0.17/0.48 % (3268055)...printing done.
% 0.17/0.48 % (3268055)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3268055)------------------------------
% 0.17/0.48 % (3268055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3268055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3268055)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3268055)Termination reason: Refutation
% 0.17/0.48 % (3268055)Time elapsed: 0.019 s
% 0.17/0.48 % (3268055)Peak memory usage: 14 MB
% 0.17/0.48 % (3268055)Instructions burned: 64 (million)
% 0.17/0.48 % (3268046)Success in time 0.058 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------