%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM303+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 : n015.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 2.72s 1.37s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 61 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 34 ~; 23 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn21) ).
fof(f32,axiom,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn31) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less23) ).
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/theBenchmark.p',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/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,
n31 != n21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n31_not_n12) ).
fof(f403,negated_conjecture,
~ ( n31 != n21 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
n21 = n31,
inference(flattening,[],[f403]) ).
fof(f436,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(f437,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,[],[f436]) ).
fof(f438,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(f446,plain,
! [X0,X1] :
( ( less(X0,X1)
| less(X1,X0)
| X0 = X1 )
& ( ( ~ less(X1,X0)
& X1 != X0 )
| ~ less(X0,X1) ) ),
inference(nnf_transformation,[],[f284]) ).
fof(f447,plain,
! [X0,X1] :
( ( less(X0,X1)
| less(X1,X0)
| X0 = X1 )
& ( ( ~ less(X1,X0)
& X1 != X0 )
| ~ less(X0,X1) ) ),
inference(flattening,[],[f446]) ).
fof(f448,plain,
n21 = n31,
inference(cnf_transformation,[],[f404]) ).
fof(f453,plain,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f447]) ).
fof(f456,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(cnf_transformation,[],[f22]) ).
fof(f457,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(cnf_transformation,[],[f32]) ).
fof(f467,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,[],[f437]) ).
fof(f564,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f580,plain,
! [X2,X3,X0,X1] :
( rdn_positive_less(rdn(rdnn(X0),X1),rdn(rdnn(X2),X3))
| ~ rdn_positive_less(X1,X3) ),
inference(cnf_transformation,[],[f438]) ).
fof(f592,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(definition_unfolding,[],[f456,f448]) ).
fof(f593,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f453]) ).
fof(f621,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(X1,X2)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f467,f593]) ).
fof(f660,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_positive_less(X4,X2)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X3),X4)))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) ),
inference(resolution,[],[f621,f580]) ).
fof(f690,plain,
! [X2,X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2))))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X2),rdnn(n3)))) ),
inference(resolution,[],[f660,f564]) ).
fof(f815,plain,
! [X0] : ~ rdn_translate(n31,rdn_pos(rdn(rdnn(X0),rdnn(n3)))),
inference(resolution,[],[f690,f592]) ).
fof(f817,plain,
$false,
inference(resolution,[],[f815,f457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM303+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 19:32:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.72/1.37 % (1965122)Detected formulas, will run a generic FOF schedule.
% 2.72/1.37 % (1965133)dis-21_1_sil=8000:lcm=predicate:random_seed=1796516320: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)
% 2.72/1.37 % (1965133)First to succeed.
% 2.72/1.37 % (1965133)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1965122"
% 2.72/1.37 % (1965127)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=2246421413:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.37 % (1965132)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=561515175:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.37 % (1965129)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=951288257:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.37 % (1965128)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=3432652705:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.37 % (1965131)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1436286281:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.37 % (1965130)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3435643957:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.37 % (1965130)Refutation not found, incomplete strategy
% 2.72/1.37 % (1965130)------------------------------
% 2.72/1.37 % (1965130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.37 % (1965130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.37 % (1965130)CaDiCaL version: 2.1.3
% 2.72/1.37 % (1965130)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.37 % (1965130)Time elapsed: 0.002 s
% 2.72/1.37 % (1965130)Peak memory usage: 88 MB
% 2.72/1.37 % (1965130)Instructions burned: 1 (million)
% 2.72/1.37 % (1965131)Also succeeded, but the first one will report.
% 2.72/1.37 % (1965132)Also succeeded, but the first one will report.
% 2.72/1.37 % (1965133)Refutation found. Thanks to Tanya!
% 2.72/1.37 % SZS status Theorem for theBenchmark
% 2.72/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.37 % (1965133)------------------------------
% 2.72/1.37 % (1965133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.37 % (1965133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.37 % (1965133)CaDiCaL version: 2.1.3
% 2.72/1.37 % (1965133)Termination reason: Refutation
% 2.72/1.37 % (1965133)Time elapsed: 0.007 s
% 2.72/1.37 % (1965133)Peak memory usage: 89 MB
% 2.72/1.37 % (1965133)Instructions burned: 22 (million)
% 2.72/1.37 % (1965133)------------------------------
% 2.72/1.37 % (1965133)------------------------------
% 2.72/1.37 % (1965122)Success in time 0.315 s
% 2.72/1.37 % Vampire exiting
%------------------------------------------------------------------------------