%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM305+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 : 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 12:18:17 PM UTC 2026
% Result : Theorem 0.16s 0.75s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 41 ~; 33 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
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/sandbox2/benchmark/Axioms/NUM005+2.ax',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/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,
sum(n2,n3,n5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n2_n3_n5) ).
fof(f403,negated_conjecture,
~ sum(n2,n3,n5),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ sum(n2,n3,n5),
inference(flattening,[],[f403]) ).
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(ennf_transformation,[],[f287]) ).
fof(f425,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,[],[f424]) ).
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(ennf_transformation,[],[f297]) ).
fof(f443,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,[],[f442]) ).
fof(f453,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f454,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f456,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f739,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f425]) ).
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,[],[f443]) ).
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,
~ sum(n2,n3,n5),
inference(cnf_transformation,[],[f404]) ).
fof(f1169,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_pos(rdnn(X3)))
| ~ rdn_translate(X5,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X6,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[],[f750,f739]) ).
fof(f1424,plain,
! [X2,X3,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n5,rdn_pos(rdnn(X1))) ),
inference(resolution,[],[f1169,f855]) ).
fof(f1446,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5))) ),
inference(resolution,[],[f1424,f805]) ).
fof(f1578,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X0))) ),
inference(forward_subsumption_resolution,[],[f1446,f456]) ).
fof(f1763,plain,
( ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(resolution,[],[f1578,f778]) ).
fof(f1772,plain,
~ rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(forward_subsumption_resolution,[],[f1763,f454]) ).
fof(f1783,plain,
$false,
inference(forward_subsumption_resolution,[],[f1772,f453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM305+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.61 % Computer : n015.cluster.edu
% 0.13/0.61 % Model : x86_64 x86_64
% 0.13/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.61 % Memory : 8046.5625MB
% 0.13/0.61 % OS : Linux 6.8.0-71-generic
% 0.13/0.61 % CPULimit : 300
% 0.13/0.61 % WCLimit : 300
% 0.13/0.61 % DateTime : Sun Sep 27 19:33:19 UTC 2026
% 0.13/0.61 % CPUTime :
% 0.13/0.61 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.64 Running first-order model finding
% 0.16/0.64 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
% 0.16/0.75 % (1965989)Will run a generic schedule for satisfiability detection.
% 0.16/0.75 % (1965999)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2130536957:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.75 % (1965995)% WARNING: option uhcvi not known.
% 0.16/0.75 % (1965994)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1047798973_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.75 % (1965995)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=878975419:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.75 % (1965996)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1644126760:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.75 % (1965997)dis+10_1_sil=32000:sp=arity:random_seed=4102465147:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.75 % (1965998)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=117223574:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.75 % (1966000)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4136641838:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.75 % (1965999)Instruction limit reached!
% 0.16/0.75 % (1965999)------------------------------
% 0.16/0.75 % (1965999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.75 % (1965999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.75 % (1965999)CaDiCaL version: 2.1.3
% 0.16/0.75 % (1965999)Termination reason: Instruction limit
% 0.16/0.75 % (1965999)Termination phase: Saturation
% 0.16/0.75 % (1965999)Time elapsed: 0.034 s
% 0.16/0.75 % (1965999)Peak memory usage: 14 MB
% 0.16/0.75 % (1965999)Instructions burned: 134 (million)
% 0.16/0.75 % TRYING [1]
% 0.16/0.75 % TRYING [2]
% 0.16/0.75 % (1966008)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=649960962:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.75 % (1965998) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1965989-1965998"...
% 0.16/0.75 % (1965997)Instruction limit reached!
% 0.16/0.75 % (1965997)------------------------------
% 0.16/0.75 % (1965997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.75 % (1965997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.75 % (1965997)CaDiCaL version: 2.1.3
% 0.16/0.75 % (1965997)Termination reason: Instruction limit
% 0.16/0.75 % (1965997)Termination phase: Saturation
% 0.16/0.75 % (1965997)Time elapsed: 0.048 s
% 0.16/0.75 % (1965997)Peak memory usage: 13 MB
% 0.16/0.75 % (1965997)Instructions burned: 104 (million)
% 0.16/0.75 % (1965998)...printing done.
% 0.16/0.75 % (1965998)Refutation found. Thanks to Tanya!
% 0.16/0.75 % SZS status Theorem for theBenchmark
% 0.16/0.75 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.75 % (1965998)------------------------------
% 0.16/0.75 % (1965998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.75 % (1965998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.75 % (1965998)CaDiCaL version: 2.1.3
% 0.16/0.75 % (1965998)Termination reason: Refutation
% 0.16/0.75 % (1965998)Time elapsed: 0.047 s
% 0.16/0.75 % (1965998)Peak memory usage: 13 MB
% 0.16/0.75 % (1965998)Instructions burned: 90 (million)
% 0.16/0.75 % (1965989)Success in time 0.096 s
% 0.16/0.75 % Vampire exiting
%------------------------------------------------------------------------------