%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM308+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 : n011.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 12:12:08 PM UTC 2026
% Result : Theorem 5.93s 1.92s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 68 ( 36 unt; 1 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 218 ( 104 ~; 99 |; 10 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 138 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn11) ).
fof(f24,axiom,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn23) ).
fof(f35,axiom,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn34) ).
fof(f257,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit1) ).
fof(f258,axiom,
rdn_non_zero_digit(rdnn(n2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit2) ).
fof(f259,axiom,
rdn_non_zero_digit(rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit3) ).
fof(f279,axiom,
! [X0] :
( rdn_non_zero_digit(rdnn(X0))
=> rdn_non_zero(rdnn(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_non_zero_by_digit) ).
fof(f287,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X0,rdn_pos(X3))
& rdn_translate(X1,rdn_pos(X4))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X2,rdn_pos(X5)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).
fof(f297,axiom,
! [X0,X1,X2,X3,X4] :
( ( rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
& rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f300,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ( rdn_digit_add(rdnn(X1),rdnn(X3),rdnn(X7),rdnn(X8))
& rdn_digit_add(rdnn(X7),rdnn(X0),rdnn(X5),rdnn(X9))
& rdn_digit_add(rdnn(X8),rdnn(X9),rdnn(X10),rdnn(n0))
& rdn_add_with_carry(rdnn(X10),X2,X4,X6)
& rdn_non_zero(X2)
& rdn_non_zero(X4)
& rdn_non_zero(X6) )
=> rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdn(rdnn(X3),X4),rdn(rdnn(X5),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_rdn_rdn_rdn) ).
fof(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n0_n0_n0) ).
fof(f314,axiom,
rdn_digit_add(rdnn(n1),rdnn(n2),rdnn(n3),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n1_n2_n3_n0) ).
fof(f315,axiom,
rdn_digit_add(rdnn(n1),rdnn(n3),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n1_n3_n4_n0) ).
fof(f332,axiom,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n3_n0_n3_n0) ).
fof(f342,axiom,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n4_n0_n4_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,n23,n34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_something_n23_n34) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,n23,n34),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f411,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(ennf_transformation,[],[f279]) ).
fof(f423,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(ennf_transformation,[],[f287]) ).
fof(f424,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(flattening,[],[f423]) ).
fof(f441,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) ),
inference(ennf_transformation,[],[f297]) ).
fof(f442,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) ),
inference(flattening,[],[f441]) ).
fof(f447,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdn(rdnn(X3),X4),rdn(rdnn(X5),X6))
| ~ rdn_digit_add(rdnn(X1),rdnn(X3),rdnn(X7),rdnn(X8))
| ~ rdn_digit_add(rdnn(X7),rdnn(X0),rdnn(X5),rdnn(X9))
| ~ rdn_digit_add(rdnn(X8),rdnn(X9),rdnn(X10),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X10),X2,X4,X6)
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(X4)
| ~ rdn_non_zero(X6) ),
inference(ennf_transformation,[],[f300]) ).
fof(f448,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdn(rdnn(X3),X4),rdn(rdnn(X5),X6))
| ~ rdn_digit_add(rdnn(X1),rdnn(X3),rdnn(X7),rdnn(X8))
| ~ rdn_digit_add(rdnn(X7),rdnn(X0),rdnn(X5),rdnn(X9))
| ~ rdn_digit_add(rdnn(X8),rdnn(X9),rdnn(X10),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X10),X2,X4,X6)
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(X4)
| ~ rdn_non_zero(X6) ),
inference(flattening,[],[f447]) ).
fof(f450,plain,
! [X0] : ~ sum(X0,n23,n34),
inference(ennf_transformation,[],[f403]) ).
fof(f465,plain,
rdn_translate(n11,rdn_pos(rdn(rdnn(n1),rdnn(n1)))),
inference(cnf_transformation,[],[f12]) ).
fof(f477,plain,
rdn_translate(n23,rdn_pos(rdn(rdnn(n3),rdnn(n2)))),
inference(cnf_transformation,[],[f24]) ).
fof(f488,plain,
rdn_translate(n34,rdn_pos(rdn(rdnn(n4),rdnn(n3)))),
inference(cnf_transformation,[],[f35]) ).
fof(f710,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[],[f257]) ).
fof(f711,plain,
rdn_non_zero_digit(rdnn(n2)),
inference(cnf_transformation,[],[f258]) ).
fof(f712,plain,
rdn_non_zero_digit(rdnn(n3)),
inference(cnf_transformation,[],[f259]) ).
fof(f732,plain,
! [X0] :
( ~ rdn_non_zero_digit(rdnn(X0))
| rdn_non_zero(rdnn(X0)) ),
inference(cnf_transformation,[],[f411]) ).
fof(f742,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(cnf_transformation,[],[f424]) ).
fof(f753,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
inference(cnf_transformation,[],[f442]) ).
fof(f756,plain,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ rdn_digit_add(rdnn(X8),rdnn(X9),rdnn(X10),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X3),rdnn(X7),rdnn(X8))
| ~ rdn_digit_add(rdnn(X7),rdnn(X0),rdnn(X5),rdnn(X9))
| rdn_add_with_carry(rdnn(X0),rdn(rdnn(X1),X2),rdn(rdnn(X3),X4),rdn(rdnn(X5),X6))
| ~ rdn_add_with_carry(rdnn(X10),X2,X4,X6)
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(X4)
| ~ rdn_non_zero(X6) ),
inference(cnf_transformation,[],[f448]) ).
fof(f758,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f770,plain,
rdn_digit_add(rdnn(n1),rdnn(n2),rdnn(n3),rdnn(n0)),
inference(cnf_transformation,[],[f314]) ).
fof(f771,plain,
rdn_digit_add(rdnn(n1),rdnn(n3),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[],[f315]) ).
fof(f788,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(cnf_transformation,[],[f332]) ).
fof(f798,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[],[f342]) ).
fof(f858,plain,
! [X0] : ~ sum(X0,n23,n34),
inference(cnf_transformation,[],[f450]) ).
fof(f873,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| rdn_add_with_carry(rdnn(X3),rdn(rdnn(X0),X5),rdn(rdnn(X1),X6),rdn(rdnn(X4),X7))
| ~ rdn_add_with_carry(rdnn(n0),X5,X6,X7)
| ~ rdn_non_zero(X5)
| ~ rdn_non_zero(X6)
| ~ rdn_non_zero(X7) ),
inference(resolution,[],[f756,f758]) ).
fof(f879,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n3),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n3)) ),
inference(resolution,[],[f788,f753]) ).
fof(f901,plain,
! [X2,X3,X0,X1,X4] :
( rdn_add_with_carry(rdnn(n0),rdn(rdnn(X0),X2),rdn(rdnn(X1),X3),rdn(rdnn(n4),X4))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n4),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(n0),X2,X3,X4)
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(X3)
| ~ rdn_non_zero(X4) ),
inference(resolution,[],[f873,f798]) ).
fof(f906,plain,
rdn_non_zero(rdnn(n1)),
inference(resolution,[],[f732,f710]) ).
fof(f1046,plain,
rdn_non_zero(rdnn(n2)),
inference(resolution,[],[f711,f732]) ).
fof(f1195,definition,
( spl0_25
<=> rdn_non_zero(rdnn(n3)) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f1196,plain,
( rdn_non_zero(rdnn(n3))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1197,plain,
( ~ rdn_non_zero(rdnn(n3))
| spl0_25 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1486,plain,
rdn_non_zero(rdnn(n3)),
inference(resolution,[],[f712,f732]) ).
fof(f1487,plain,
( $false
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f1486,f1197]) ).
fof(f1488,plain,
spl0_25,
inference(avatar_contradiction_clause,[],[f1487]) ).
fof(f1627,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n4),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(n0),X2,X3,X4)
| ~ rdn_non_zero(X2)
| ~ rdn_non_zero(X3)
| ~ rdn_non_zero(X4)
| ~ rdn_translate(X5,rdn_pos(rdn(rdnn(X0),X2)))
| ~ rdn_translate(X6,rdn_pos(rdn(rdnn(X1),X3)))
| sum(X5,X6,X7)
| ~ rdn_translate(X7,rdn_pos(rdn(rdnn(n4),X4))) ),
inference(resolution,[],[f901,f742]) ).
fof(f1779,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_translate(X5,rdn_pos(rdn(rdnn(n4),X2)))
| ~ rdn_non_zero(X0)
| ~ rdn_non_zero(X1)
| ~ rdn_non_zero(X2)
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(n1),X0)))
| ~ rdn_translate(X4,rdn_pos(rdn(rdnn(n3),X1)))
| sum(X3,X4,X5)
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2) ),
inference(resolution,[],[f771,f1627]) ).
fof(f1810,plain,
! [X2,X3,X0,X1] :
( ~ rdn_non_zero(X0)
| ~ rdn_non_zero(X1)
| ~ rdn_non_zero(rdnn(n3))
| ~ rdn_translate(X2,rdn_pos(rdn(rdnn(n1),X0)))
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(n3),X1)))
| sum(X2,X3,n34)
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,rdnn(n3)) ),
inference(resolution,[],[f1779,f488]) ).
fof(f1811,plain,
( ! [X2,X3,X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),X0,X1,rdnn(n3))
| ~ rdn_non_zero(X1)
| ~ rdn_translate(X2,rdn_pos(rdn(rdnn(n1),X0)))
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(n3),X1)))
| sum(X2,X3,n34)
| ~ rdn_non_zero(X0) )
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1810,f1196]) ).
fof(f1841,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n1),rdnn(n2),rdnn(n3)),
inference(resolution,[],[f770,f879]) ).
fof(f1863,plain,
( ! [X0,X1] :
( ~ rdn_non_zero(rdnn(n2))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| ~ rdn_translate(X1,rdn_pos(rdn(rdnn(n3),rdnn(n2))))
| sum(X0,X1,n34)
| ~ rdn_non_zero(rdnn(n1)) )
| ~ spl0_25 ),
inference(resolution,[],[f1841,f1811]) ).
fof(f1870,plain,
( ! [X0,X1] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| ~ rdn_translate(X1,rdn_pos(rdn(rdnn(n3),rdnn(n2))))
| sum(X0,X1,n34)
| ~ rdn_non_zero(rdnn(n1)) )
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1863,f1046]) ).
fof(f1871,plain,
( ! [X0,X1] :
( ~ rdn_translate(X1,rdn_pos(rdn(rdnn(n3),rdnn(n2))))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X0,X1,n34) )
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1870,f906]) ).
fof(f1872,plain,
( ! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| sum(X0,n23,n34) )
| ~ spl0_25 ),
inference(resolution,[],[f1871,f477]) ).
fof(f1873,plain,
( ! [X0] : ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1))))
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1872,f858]) ).
fof(f1874,plain,
( $false
| ~ spl0_25 ),
inference(resolution,[],[f1873,f465]) ).
fof(f1875,plain,
~ spl0_25,
inference(avatar_contradiction_clause,[],[f1874]) ).
cnf(s28,plain,
spl0_25,
inference(sat_conversion,[],[f1488]) ).
cnf(s39,plain,
~ spl0_25,
inference(sat_conversion,[],[f1875]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s28,s39]) ).
fof(f1876,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM308+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.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 19:30:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 4.92/1.63 % (2705737)Detected formulas, will run a generic FOF schedule.
% 4.92/1.63 % (2705742)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=1089249508:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.92/1.63 % (2705744)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=2439314259:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.92/1.63 % (2705748)dis-21_1_sil=8000:lcm=predicate:random_seed=2425139472: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)
% 4.92/1.63 % (2705745)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=60207810:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.92/1.63 % (2705746)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1653836825:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.92/1.63 % (2705743)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=770751273:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.92/1.63 % (2705747)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=392957199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.92/1.63 % (2705745)Refutation not found, incomplete strategy
% 4.92/1.63 % (2705745)------------------------------
% 4.92/1.63 % (2705745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.63 % (2705745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.63 % (2705745)CaDiCaL version: 2.1.3
% 4.92/1.63 % (2705745)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.63 % (2705745)Time elapsed: 0.002 s
% 4.92/1.63 % (2705745)Peak memory usage: 87 MB
% 4.92/1.63 % (2705745)Instructions burned: 1 (million)
% 4.92/1.63 % (2705746)Refutation not found, incomplete strategy
% 4.92/1.63 % (2705746)------------------------------
% 4.92/1.63 % (2705746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.63 % (2705746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.63 % (2705746)CaDiCaL version: 2.1.3
% 4.92/1.63 % (2705746)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.63 % (2705746)Time elapsed: 0.002 s
% 4.92/1.63 % (2705746)Peak memory usage: 88 MB
% 4.92/1.63 % (2705746)Instructions burned: 2 (million)
% 4.92/1.63 % (2705748)Instruction limit reached!
% 4.92/1.63 % (2705748)------------------------------
% 4.92/1.63 % (2705748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.63 % (2705748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.63 % (2705748)CaDiCaL version: 2.1.3
% 4.92/1.63 % (2705748)Termination reason: Instruction limit
% 4.92/1.63 % (2705748)Termination phase: Saturation
% 4.92/1.63 % (2705748)Time elapsed: 0.063 s
% 4.92/1.63 % (2705748)Peak memory usage: 88 MB
% 4.92/1.63 % (2705748)Instructions burned: 130 (million)
% 4.92/1.63 % (2705747)Instruction limit reached!
% 4.92/1.63 % (2705747)------------------------------
% 4.92/1.63 % (2705747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.63 % (2705747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.63 % (2705747)CaDiCaL version: 2.1.3
% 4.92/1.63 % (2705747)Termination reason: Instruction limit
% 4.92/1.63 % (2705747)Termination phase: Saturation
% 4.92/1.63 % (2705747)Time elapsed: 0.084 s
% 4.92/1.63 % (2705747)Peak memory usage: 90 MB
% 4.92/1.63 % (2705747)Instructions burned: 140 (million)
% 4.92/1.63 % (2705756)lrs+10_1_sil=8000:sp=occurrence:random_seed=2681606218:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.92/1.63 % (2705756)Refutation not found, incomplete strategy
% 4.92/1.63 % (2705756)------------------------------
% 4.92/1.63 % (2705756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.92/1.63 % (2705756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.92/1.63 % (2705756)CaDiCaL version: 2.1.3
% 4.92/1.63 % (2705756)Termination reason: Refutation not found, incomplete strategy
% 4.92/1.63 % (2705756)Time elapsed: 0.002 s
% 4.92/1.63 % (2705756)Peak memory usage: 88 MB
% 4.92/1.63 % (2705756)Instructions burned: 2 (million)
% 4.92/1.63 % (2705757)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2902575631:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.93/1.92 % (2705757)Refutation not found, incomplete strategy
% 5.93/1.92 % (2705757)------------------------------
% 5.93/1.92 % (2705757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705757)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705757)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.92 % (2705757)Time elapsed: 0.003 s
% 5.93/1.92 % (2705757)Peak memory usage: 88 MB
% 5.93/1.92 % (2705757)Instructions burned: 5 (million)
% 5.93/1.92 % (2705745)------------------------------
% 5.93/1.92 % (2705745)------------------------------
% 5.93/1.92 % (2705746)------------------------------
% 5.93/1.92 % (2705746)------------------------------
% 5.93/1.92 % (2705761)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=748369054:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.93/1.92 [W927 19:30:17.069121741 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069152657 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069192274 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069206057 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069234094 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069258361 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069286147 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069297094 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069326017 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069336821 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069361728 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 [W927 19:30:17.069372828 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.93/1.92 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.93/1.92 % (2705760)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2270487349:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.93/1.92 % (2705760)Refutation not found, incomplete strategy
% 5.93/1.92 % (2705760)------------------------------
% 5.93/1.92 % (2705760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705760)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705760)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.92 % (2705760)Time elapsed: 0.002 s
% 5.93/1.92 % (2705760)Peak memory usage: 88 MB
% 5.93/1.92 % (2705760)Instructions burned: 2 (million)
% 5.93/1.92 % (2705761)Instruction limit reached!
% 5.93/1.92 % (2705761)------------------------------
% 5.93/1.92 % (2705761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705761)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705761)Termination reason: Instruction limit
% 5.93/1.92 % (2705761)Termination phase: Saturation
% 5.93/1.92 % (2705761)Time elapsed: 0.063 s
% 5.93/1.92 % (2705761)Peak memory usage: 91 MB
% 5.93/1.92 % (2705761)Instructions burned: 248 (million)
% 5.93/1.92 % (2705756)------------------------------
% 5.93/1.92 % (2705756)------------------------------
% 5.93/1.92 % (2705757)------------------------------
% 5.93/1.92 % (2705757)------------------------------
% 5.93/1.92 % (2705764)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=582032335:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.93/1.92 % (2705764)Refutation not found, incomplete strategy
% 5.93/1.92 % (2705764)------------------------------
% 5.93/1.92 % (2705764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705764)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705764)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.92 % (2705764)Time elapsed: 0.003 s
% 5.93/1.92 % (2705764)Peak memory usage: 89 MB
% 5.93/1.92 % (2705764)Instructions burned: 9 (million)
% 5.93/1.92 % (2705743)Refutation not found, incomplete strategy
% 5.93/1.92 % (2705743)------------------------------
% 5.93/1.92 % (2705743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705743)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705743)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.92 % (2705743)Time elapsed: 0.569 s
% 5.93/1.92 % (2705743)Peak memory usage: 127 MB
% 5.93/1.92 % (2705743)Instructions burned: 835 (million)
% 5.93/1.92 % (2705765)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2913412344:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 5.93/1.92 % (2705744)Refutation not found, incomplete strategy
% 5.93/1.92 % (2705744)------------------------------
% 5.93/1.92 % (2705744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705744)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705744)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.92 % (2705744)Time elapsed: 0.616 s
% 5.93/1.92 % (2705744)Peak memory usage: 128 MB
% 5.93/1.92 % (2705744)Instructions burned: 907 (million)
% 5.93/1.92 % (2705766)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2948467197:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.93/1.92 % (2705766)Refutation not found, incomplete strategy
% 5.93/1.92 % (2705766)------------------------------
% 5.93/1.92 % (2705766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705766)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705766)Termination reason: Refutation not found, incomplete strategy
% 5.93/1.92 % (2705766)Time elapsed: 0.002 s
% 5.93/1.92 % (2705766)Peak memory usage: 89 MB
% 5.93/1.92 % (2705766)Instructions burned: 2 (million)
% 5.93/1.92 % (2705760)------------------------------
% 5.93/1.92 % (2705760)------------------------------
% 5.93/1.92 % (2705742)First to succeed.
% 5.93/1.92 % (2705742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2705737"
% 5.93/1.92 % (2705764)------------------------------
% 5.93/1.92 % (2705764)------------------------------
% 5.93/1.92 % (2705771)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=128814110:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 5.93/1.92 % (2705770)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3936938685:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 5.93/1.92 % (2705771)Instruction limit reached!
% 5.93/1.92 % (2705771)------------------------------
% 5.93/1.92 % (2705771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.93/1.92 % (2705771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.93/1.92 % (2705771)CaDiCaL version: 2.1.3
% 5.93/1.92 % (2705771)Termination reason: Instruction limit
% 5.93/1.92 % (2705771)Termination phase: Saturation
% 5.93/1.92 % (2705771)Time elapsed: 0.031 s
% 5.93/1.92 % (2705771)Peak memory usage: 90 MB
% 5.93/1.92 % (2705771)Instructions burned: 118 (million)
% 5.93/1.92 % (2705770)Also succeeded, but the first one will report.
% 5.93/1.92 % (2705743)------------------------------
% 5.93/1.92 % (2705743)------------------------------
% 5.93/1.92 % (2705744)------------------------------
% 5.93/1.92 % (2705744)------------------------------
% 5.93/1.92 % (2705766)------------------------------
% 5.93/1.92 % (2705766)------------------------------
% 5.93/1.92 % (2705774)lrs+10_1_sil=8000:sp=occurrence:random_seed=2809867506:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 5.93/1.92 % (2705742)Refutation found. Thanks to Tanya!
% 5.93/1.92 % SZS status Theorem for theBenchmark
% 5.93/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.06 % (2705742)------------------------------
% 0.17/2.06 % (2705742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.06 % (2705742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.06 % (2705742)CaDiCaL version: 2.1.3
% 0.17/2.06 % (2705742)Termination reason: Refutation
% 0.17/2.06 % (2705742)Time elapsed: 0.686 s
% 0.17/2.06 % (2705742)Peak memory usage: 134 MB
% 0.17/2.06 % (2705742)Instructions burned: 1371 (million)
% 0.17/2.06 % (2705742)------------------------------
% 0.17/2.06 % (2705742)------------------------------
% 0.17/2.06 % (2705737)Success in time 1.068 s
% 0.17/2.06 % Vampire exiting
%------------------------------------------------------------------------------