%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM320+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 : n004.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 12:18:19 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 22 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 138 ( 70 ~; 59 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 95 ( 93 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f131,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn3) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
fof(f275,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X0),rdnn(X1))
& rdn_positive_less(rdnn(X1),rdnn(X2)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(f289,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X0,rdn_pos(X3))
& rdn_translate(X1,rdn_neg(X4))
& rdn_positive_less(X3,X4)
& rdn_add_with_carry(rdnn(n0),X3,X5,X4)
& rdn_translate(X2,rdn_neg(X5)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_1) ).
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/sandbox2/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
? [X0] : sum(n2,nn5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n2_nn5_what) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(n2,nn5,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f405,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f406,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2)) ),
inference(flattening,[],[f405]) ).
fof(f427,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_positive_less(X3,X4)
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(ennf_transformation,[],[f289]) ).
fof(f428,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_positive_less(X3,X4)
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(flattening,[],[f427]) ).
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(f450,plain,
! [X0] : ~ sum(n2,nn5,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f453,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f581,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[],[f131]) ).
fof(f583,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f718,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f719,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f720,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f270]) ).
fof(f725,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| rdn_positive_less(rdnn(X0),rdnn(X2)) ),
inference(cnf_transformation,[],[f406]) ).
fof(f741,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f428]) ).
fof(f750,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(f778,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f805,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f855,plain,
! [X0] : ~ sum(n2,nn5,X0),
inference(cnf_transformation,[],[f450]) ).
fof(f1142,plain,
! [X0] :
( rdn_positive_less(rdnn(X0),rdnn(n4))
| ~ rdn_positive_less(rdnn(X0),rdnn(n3)) ),
inference(resolution,[],[f725,f719]) ).
fof(f1143,plain,
! [X0] :
( rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_positive_less(rdnn(X0),rdnn(n4)) ),
inference(resolution,[],[f725,f720]) ).
fof(f1168,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X6,X5,X4)
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_translate(X4,rdn_neg(rdnn(X1)))
| ~ rdn_positive_less(rdnn(X0),rdnn(X3))
| ~ rdn_translate(X5,rdn_neg(rdnn(X3)))
| ~ rdn_translate(X6,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[],[f750,f741]) ).
fof(f1572,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_positive_less(rdnn(X4),rdnn(X1))
| ~ rdn_translate(X2,rdn_neg(rdnn(X3)))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_translate(nn5,rdn_neg(rdnn(X1)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X4)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X3),rdnn(X0),rdnn(n0)) ),
inference(resolution,[],[f1168,f855]) ).
fof(f1700,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(X0,rdn_neg(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X3)))
| ~ rdn_digit_add(rdnn(X3),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_positive_less(rdnn(X3),rdnn(n4)) ),
inference(resolution,[],[f1572,f1143]) ).
fof(f1748,plain,
! [X2,X3,X0,X1] :
( ~ rdn_positive_less(rdnn(X3),rdnn(n4))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n2,rdn_pos(rdnn(X3)))
| ~ rdn_digit_add(rdnn(X3),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X0,rdn_neg(rdnn(X1))) ),
inference(forward_subsumption_resolution,[],[f1700,f583]) ).
fof(f1803,plain,
! [X2,X3,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(n3))
| ~ rdn_translate(n2,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X3,rdn_neg(rdnn(X2)))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n5),rdnn(n0)) ),
inference(resolution,[],[f1748,f1142]) ).
fof(f1812,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_translate(X2,rdn_neg(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0)) ),
inference(resolution,[],[f1803,f718]) ).
fof(f1813,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X2,rdn_neg(rdnn(X0))) ),
inference(forward_subsumption_resolution,[],[f1812,f453]) ).
fof(f1814,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X1,rdn_neg(rdnn(X0))) ),
inference(resolution,[],[f1813,f805]) ).
fof(f1815,plain,
! [X0] : ~ rdn_translate(X0,rdn_neg(rdnn(n3))),
inference(resolution,[],[f1814,f778]) ).
fof(f1816,plain,
$false,
inference(resolution,[],[f1815,f581]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM320+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 19:33:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.18/0.49 % (3827552)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (3827561)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2066947229:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (3827558)% WARNING: option uhcvi not known.
% 0.18/0.49 % (3827557)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=621717474_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (3827560)dis+10_1_sil=32000:sp=arity:random_seed=779522105:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (3827558)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1615800178:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (3827559)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3769957736:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (3827562)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2596512054:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (3827563)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2926090348:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % (3827561) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3827552-3827561"...
% 0.18/0.49 % (3827561)...printing done.
% 0.18/0.49 % (3827561)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (3827561)------------------------------
% 0.18/0.49 % (3827561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (3827561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (3827561)CaDiCaL version: 2.1.3
% 0.18/0.49 % (3827561)Termination reason: Refutation
% 0.18/0.49 % (3827561)Time elapsed: 0.029 s
% 0.18/0.49 % (3827561)Peak memory usage: 13 MB
% 0.18/0.49 % (3827561)Instructions burned: 100 (million)
% 0.18/0.49 % (3827552)Success in time 0.068 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------