%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM309+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 : n013.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 6.36s 2.03s
% Output : Refutation 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 28 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 223 ( 114 ~; 95 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 157 ( 155 !; 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(f323,axiom,
rdn_digit_add(rdnn(n2),rdnn(n1),rdnn(n3),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n2_n1_n3_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(f333,axiom,
rdn_digit_add(rdnn(n3),rdnn(n1),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n3_n1_n4_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(n23,X0,n34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n23_something_n34) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(n23,X0,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(n23,X0,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(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(cnf_transformation,[],[f411]) ).
fof(f742,plain,
! [X2,X3,X0,X1,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(cnf_transformation,[],[f424]) ).
fof(f753,plain,
! [X2,X3,X0,X1,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(cnf_transformation,[],[f442]) ).
fof(f756,plain,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( 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(cnf_transformation,[],[f448]) ).
fof(f758,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f779,plain,
rdn_digit_add(rdnn(n2),rdnn(n1),rdnn(n3),rdnn(n0)),
inference(cnf_transformation,[],[f323]) ).
fof(f788,plain,
rdn_digit_add(rdnn(n3),rdnn(n0),rdnn(n3),rdnn(n0)),
inference(cnf_transformation,[],[f332]) ).
fof(f789,plain,
rdn_digit_add(rdnn(n3),rdnn(n1),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[],[f333]) ).
fof(f798,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[],[f342]) ).
fof(f858,plain,
! [X0] : ~ sum(n23,X0,n34),
inference(cnf_transformation,[],[f450]) ).
fof(f863,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(n34,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X0,X2,X3)
| ~ rdn_translate(n23,rdn_pos(X0)) ),
inference(resolution,[],[f858,f742]) ).
fof(f865,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n23,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X2,X1,rdn(rdnn(n4),rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f863,f488]) ).
fof(f870,plain,
! [X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),rdn(rdnn(n3),rdnn(n2)),X0,rdn(rdnn(n4),rdnn(n3)))
| ~ rdn_translate(X1,rdn_pos(X0)) ),
inference(resolution,[],[f865,f477]) ).
fof(f875,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_non_zero(rdnn(n3))
| ~ rdn_digit_add(rdnn(n3),rdnn(X1),rdnn(X3),rdnn(X4))
| ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n4),rdnn(X5))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(X6),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X6),rdnn(n2),X2,rdnn(n3))
| ~ rdn_non_zero(rdnn(n2))
| ~ rdn_non_zero(X2)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) ),
inference(resolution,[],[f870,f756]) ).
fof(f885,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_non_zero(rdnn(n2))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n4),rdnn(X3))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X4),rdnn(n2),X5,rdnn(n3))
| ~ rdn_digit_add(rdnn(n3),rdnn(X0),rdnn(X1),rdnn(X2))
| ~ rdn_non_zero(X5)
| ~ rdn_translate(X6,rdn_pos(rdn(rdnn(X0),X5)))
| ~ rdn_non_zero_digit(rdnn(n3)) ),
inference(resolution,[],[f875,f732]) ).
fof(f895,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_non_zero_digit(rdnn(n3))
| ~ rdn_digit_add(rdnn(X2),rdnn(X1),rdnn(X3),rdnn(n0))
| ~ rdn_add_with_carry(rdnn(X3),rdnn(n2),X4,rdnn(n3))
| ~ rdn_digit_add(rdnn(n3),rdnn(X5),rdnn(X0),rdnn(X2))
| ~ rdn_non_zero(X4)
| ~ rdn_translate(X6,rdn_pos(rdn(rdnn(X5),X4)))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n4),rdnn(X1))
| ~ rdn_non_zero_digit(rdnn(n2)) ),
inference(resolution,[],[f885,f732]) ).
fof(f910,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_non_zero_digit(rdnn(n2))
| ~ rdn_add_with_carry(rdnn(X2),rdnn(n2),X3,rdnn(n3))
| ~ rdn_digit_add(rdnn(n3),rdnn(X4),rdnn(X5),rdnn(X0))
| ~ rdn_non_zero(X3)
| ~ rdn_translate(X6,rdn_pos(rdn(rdnn(X4),X3)))
| ~ rdn_digit_add(rdnn(X5),rdnn(n0),rdnn(n4),rdnn(X1))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[],[f895,f712]) ).
fof(f923,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n4),rdnn(X6))
| ~ rdn_digit_add(rdnn(n3),rdnn(X2),rdnn(X3),rdnn(X4))
| ~ rdn_non_zero(X1)
| ~ rdn_translate(X5,rdn_pos(rdn(rdnn(X2),X1)))
| ~ rdn_add_with_carry(rdnn(X0),rdnn(n2),X1,rdnn(n3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X6),rdnn(X0),rdnn(n0)) ),
inference(resolution,[],[f910,f711]) ).
fof(f926,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(n3),rdnn(X0),rdnn(n4),rdnn(X1))
| ~ rdn_non_zero(X2)
| ~ rdn_translate(X3,rdn_pos(rdn(rdnn(X0),X2)))
| ~ rdn_add_with_carry(rdnn(X4),rdnn(n2),X2,rdnn(n3))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X4),rdnn(n0)) ),
inference(resolution,[],[f923,f798]) ).
fof(f929,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X1,rdn_pos(rdn(rdnn(n1),X0)))
| ~ rdn_add_with_carry(rdnn(X2),rdnn(n2),X0,rdnn(n3))
| ~ rdn_non_zero(X0) ),
inference(resolution,[],[f926,f789]) ).
fof(f931,plain,
! [X0,X1] :
( ~ rdn_add_with_carry(rdnn(n0),rdnn(n2),X1,rdnn(n3))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),X1)))
| ~ rdn_non_zero(X1) ),
inference(resolution,[],[f929,f758]) ).
fof(f933,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n3),rdnn(n0))
| ~ rdn_non_zero(rdnn(X1))
| ~ rdn_digit_add(rdnn(n2),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(X1)))) ),
inference(resolution,[],[f931,f753]) ).
fof(f935,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(n3),rdnn(n0))
| ~ rdn_non_zero(rdnn(X0))
| ~ rdn_translate(X1,rdn_pos(rdn(rdnn(n1),rdnn(X0)))) ),
inference(resolution,[],[f933,f788]) ).
fof(f937,plain,
! [X0] :
( ~ rdn_non_zero(rdnn(n1))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) ),
inference(resolution,[],[f935,f779]) ).
fof(f939,plain,
! [X0] :
( ~ rdn_non_zero_digit(rdnn(n1))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1)))) ),
inference(resolution,[],[f937,f732]) ).
fof(f941,plain,
! [X0] : ~ rdn_translate(X0,rdn_pos(rdn(rdnn(n1),rdnn(n1)))),
inference(resolution,[],[f939,f710]) ).
fof(f943,plain,
$false,
inference(resolution,[],[f941,f465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM309+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n013.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 19:29:52 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 5.22/1.73 % (506382)Detected formulas, will run a generic FOF schedule.
% 5.22/1.73 % (506388)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=2093698618:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.22/1.73 % (506393)dis-21_1_sil=8000:lcm=predicate:random_seed=3687917182: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)
% 5.22/1.73 % (506392)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1973556184:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.22/1.73 % (506387)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=382329569:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.22/1.73 % (506390)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=611652235:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.22/1.73 % (506389)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=2560460588:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.22/1.73 % (506391)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1908737531:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.22/1.73 % (506390)Refutation not found, incomplete strategy
% 5.22/1.73 % (506390)------------------------------
% 5.22/1.73 % (506390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.22/1.73 % (506390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.73 % (506390)CaDiCaL version: 2.1.3
% 5.22/1.73 % (506390)Termination reason: Refutation not found, incomplete strategy
% 5.22/1.73 % (506390)Time elapsed: 0.002 s
% 5.22/1.73 % (506390)Peak memory usage: 87 MB
% 5.22/1.73 % (506390)Instructions burned: 1 (million)
% 5.22/1.73 % (506391)Refutation not found, incomplete strategy
% 5.22/1.73 % (506391)------------------------------
% 5.22/1.73 % (506391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.22/1.73 % (506391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.73 % (506391)CaDiCaL version: 2.1.3
% 5.22/1.73 % (506391)Termination reason: Refutation not found, incomplete strategy
% 5.22/1.73 % (506391)Time elapsed: 0.002 s
% 5.22/1.73 % (506391)Peak memory usage: 87 MB
% 5.22/1.73 % (506391)Instructions burned: 2 (million)
% 5.22/1.73 % (506393)Instruction limit reached!
% 5.22/1.73 % (506393)------------------------------
% 5.22/1.73 % (506393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.22/1.73 % (506393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.73 % (506393)CaDiCaL version: 2.1.3
% 5.22/1.73 % (506393)Termination reason: Instruction limit
% 5.22/1.73 % (506393)Termination phase: Saturation
% 5.22/1.73 % (506393)Time elapsed: 0.065 s
% 5.22/1.73 % (506393)Peak memory usage: 88 MB
% 5.22/1.73 % (506393)Instructions burned: 129 (million)
% 5.22/1.73 % (506392)Instruction limit reached!
% 5.22/1.73 % (506392)------------------------------
% 5.22/1.73 % (506392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.22/1.73 % (506392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.73 % (506392)CaDiCaL version: 2.1.3
% 5.22/1.73 % (506392)Termination reason: Instruction limit
% 5.22/1.73 % (506392)Termination phase: Saturation
% 5.22/1.73 % (506392)Time elapsed: 0.081 s
% 5.22/1.73 % (506392)Peak memory usage: 89 MB
% 5.22/1.73 % (506392)Instructions burned: 140 (million)
% 5.22/1.73 [W927 19:29:53.048584687 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.
% 5.22/1.73 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.22/1.73 [W927 19:29:53.048621534 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.
% 5.22/1.73 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.22/1.73 [W927 19:29:53.048643630 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048649913 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048663457 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048680230 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048693304 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048698756 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048711664 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048723932 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048737780 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 [W927 19:29:53.048743209 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.
% 6.36/2.03 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 6.36/2.03 % (506401)lrs+10_1_sil=8000:sp=occurrence:random_seed=787295935:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.36/2.03 % (506401)Refutation not found, incomplete strategy
% 6.36/2.03 % (506401)------------------------------
% 6.36/2.03 % (506401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506401)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506401)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506401)Time elapsed: 0.002 s
% 6.36/2.03 % (506401)Peak memory usage: 88 MB
% 6.36/2.03 % (506401)Instructions burned: 2 (million)
% 6.36/2.03 % (506391)------------------------------
% 6.36/2.03 % (506391)------------------------------
% 6.36/2.03 % (506390)------------------------------
% 6.36/2.03 % (506390)------------------------------
% 6.36/2.03 % (506402)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3925951876:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.36/2.03 % (506402)Refutation not found, incomplete strategy
% 6.36/2.03 % (506402)------------------------------
% 6.36/2.03 % (506402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506402)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506402)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506402)Time elapsed: 0.003 s
% 6.36/2.03 % (506402)Peak memory usage: 88 MB
% 6.36/2.03 % (506402)Instructions burned: 5 (million)
% 6.36/2.03 % (506388)Refutation not found, incomplete strategy
% 6.36/2.03 % (506388)------------------------------
% 6.36/2.03 % (506388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506388)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506388)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506388)Time elapsed: 0.311 s
% 6.36/2.03 % (506388)Peak memory usage: 127 MB
% 6.36/2.03 % (506388)Instructions burned: 835 (million)
% 6.36/2.03 % (506406)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=2589534888:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.36/2.03 % (506388)------------------------------
% 6.36/2.03 % (506388)------------------------------
% 6.36/2.03 % (506405)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1973148326:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.36/2.03 % (506405)Refutation not found, incomplete strategy
% 6.36/2.03 % (506405)------------------------------
% 6.36/2.03 % (506405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506405)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506405)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506405)Time elapsed: 0.002 s
% 6.36/2.03 % (506405)Peak memory usage: 88 MB
% 6.36/2.03 % (506405)Instructions burned: 2 (million)
% 6.36/2.03 % (506401)------------------------------
% 6.36/2.03 % (506401)------------------------------
% 6.36/2.03 % (506402)------------------------------
% 6.36/2.03 % (506402)------------------------------
% 6.36/2.03 % (506406)Instruction limit reached!
% 6.36/2.03 % (506406)------------------------------
% 6.36/2.03 % (506406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506406)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506406)Termination reason: Instruction limit
% 6.36/2.03 % (506406)Termination phase: Saturation
% 6.36/2.03 % (506406)Time elapsed: 0.122 s
% 6.36/2.03 % (506406)Peak memory usage: 92 MB
% 6.36/2.03 % (506406)Instructions burned: 248 (million)
% 6.36/2.03 % (506409)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=844114218:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.36/2.03 % (506409)Refutation not found, incomplete strategy
% 6.36/2.03 % (506409)------------------------------
% 6.36/2.03 % (506409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506409)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506409)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506409)Time elapsed: 0.003 s
% 6.36/2.03 % (506409)Peak memory usage: 88 MB
% 6.36/2.03 % (506409)Instructions burned: 9 (million)
% 6.36/2.03 % (506389)Refutation not found, incomplete strategy
% 6.36/2.03 % (506389)------------------------------
% 6.36/2.03 % (506389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506389)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506389)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506389)Time elapsed: 0.622 s
% 6.36/2.03 % (506389)Peak memory usage: 128 MB
% 6.36/2.03 % (506389)Instructions burned: 905 (million)
% 6.36/2.03 % (506410)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1036872744:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.36/2.03 % (506411)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1531464952:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.36/2.03 % (506411)Refutation not found, incomplete strategy
% 6.36/2.03 % (506411)------------------------------
% 6.36/2.03 % (506411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506411)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506411)Termination reason: Refutation not found, incomplete strategy
% 6.36/2.03 % (506411)Time elapsed: 0.002 s
% 6.36/2.03 % (506411)Peak memory usage: 88 MB
% 6.36/2.03 % (506411)Instructions burned: 2 (million)
% 6.36/2.03 % (506405)------------------------------
% 6.36/2.03 % (506405)------------------------------
% 6.36/2.03 % (506412)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2682913769:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.36/2.03 % (506412)First to succeed.
% 6.36/2.03 % (506412)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-506382"
% 6.36/2.03 % (506409)------------------------------
% 6.36/2.03 % (506409)------------------------------
% 6.36/2.03 % (506416)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3268748650:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.36/2.03 % (506418)lrs+10_1_sil=8000:sp=occurrence:random_seed=3556880557:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 6.36/2.03 % (506389)------------------------------
% 6.36/2.03 % (506389)------------------------------
% 6.36/2.03 % (506416)Instruction limit reached!
% 6.36/2.03 % (506416)------------------------------
% 6.36/2.03 % (506416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.36/2.03 % (506416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.36/2.03 % (506416)CaDiCaL version: 2.1.3
% 6.36/2.03 % (506416)Termination reason: Instruction limit
% 6.36/2.03 % (506416)Termination phase: Saturation
% 6.36/2.03 % (506416)Time elapsed: 0.059 s
% 6.36/2.03 % (506416)Peak memory usage: 90 MB
% 6.36/2.03 % (506416)Instructions burned: 115 (million)
% 6.36/2.03 % (506411)------------------------------
% 6.36/2.03 % (506411)------------------------------
% 6.36/2.03 % (506412)Refutation found. Thanks to Tanya!
% 6.36/2.03 % SZS status Theorem for theBenchmark
% 6.36/2.03 % SZS output start Proof for theBenchmark
% See solution above
% 8.68/2.23 % (506412)------------------------------
% 8.68/2.23 % (506412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.23 % (506412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.23 % (506412)CaDiCaL version: 2.1.3
% 8.68/2.23 % (506412)Termination reason: Refutation
% 8.68/2.23 % (506412)Time elapsed: 0.011 s
% 8.68/2.23 % (506412)Peak memory usage: 88 MB
% 8.68/2.23 % (506412)Instructions burned: 20 (million)
% 8.68/2.23 % (506412)------------------------------
% 8.68/2.23 % (506412)------------------------------
% 8.68/2.23 % (506382)Success in time 1.147 s
% 8.68/2.23 % Vampire exiting
%------------------------------------------------------------------------------