%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM338+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 : n009.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 12:18:21 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 97 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 49 ~; 46 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 90 ( 89 !; 1 ?)
% 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(f295,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X1,X3)
& sum(X0,X2,X3) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',unique_RHS) ).
fof(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',minus_entry_point) ).
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(f334,axiom,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n3_n2_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] :
( difference(n5,n3,X0)
=> X0 = n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_n5_n3_only_n2) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( difference(n5,n3,X0)
=> X0 = n2 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
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(f439,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X1,X3)
| ~ sum(X0,X2,X3) ),
inference(ennf_transformation,[],[f295]) ).
fof(f440,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X1,X3)
| ~ sum(X0,X2,X3) ),
inference(flattening,[],[f439]) ).
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] :
( n2 != X0
& difference(n5,n3,X0) ),
inference(ennf_transformation,[],[f403]) ).
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,[],[f424]) ).
fof(f747,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X3)
| X1 = X2 ),
inference(cnf_transformation,[],[f440]) ).
fof(f748,plain,
! [X2,X0,X1] :
( ~ difference(X0,X1,X2)
| sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f296]) ).
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(f787,plain,
rdn_digit_add(rdnn(n3),rdnn(n2),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f334]) ).
fof(f805,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f855,plain,
difference(n5,n3,sK0),
inference(cnf_transformation,[],[f450]) ).
fof(f856,plain,
n2 != sK0,
inference(cnf_transformation,[],[f450]) ).
fof(f858,plain,
sum(n3,sK0,n5),
inference(resolution,[],[f748,f855]) ).
fof(f877,plain,
! [X0] :
( ~ sum(n3,X0,n5)
| sK0 = X0 ),
inference(resolution,[],[f747,f858]) ).
fof(f1198,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(f1487,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X3),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X2,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n3,rdn_pos(rdnn(X4)))
| ~ rdn_translate(n5,rdn_pos(rdnn(X1)))
| sK0 = X2 ),
inference(resolution,[],[f1198,f877]) ).
fof(f1493,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X2,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n3,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sK0 = X2 ),
inference(resolution,[],[f1487,f805]) ).
fof(f1623,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X2,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n3,rdn_pos(rdnn(X0)))
| sK0 = X2 ),
inference(forward_subsumption_resolution,[],[f1493,f456]) ).
fof(f1903,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| sK0 = X0 ),
inference(resolution,[],[f1623,f787]) ).
fof(f1906,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| sK0 = X0 ),
inference(forward_subsumption_resolution,[],[f1903,f454]) ).
fof(f1907,plain,
n2 = sK0,
inference(resolution,[],[f1906,f453]) ).
fof(f1908,plain,
$false,
inference(forward_subsumption_resolution,[],[f1907,f856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM338+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 19:35:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.16/0.48 % (2351387)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2351396)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=267141756:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2351393)% WARNING: option uhcvi not known.
% 0.16/0.48 % (2351392)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2981856089_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (2351393)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2748935775:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2351394)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=514272153:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2351395)dis+10_1_sil=32000:sp=arity:random_seed=4166055599:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2351398)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2040158303:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (2351397)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2662541455:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (2351396) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2351387-2351396"...
% 0.16/0.48 % (2351396)...printing done.
% 0.16/0.48 % (2351396)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (2351396)------------------------------
% 0.16/0.48 % (2351396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2351396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2351396)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2351396)Termination reason: Refutation
% 0.16/0.48 % (2351396)Time elapsed: 0.031 s
% 0.16/0.48 % (2351396)Peak memory usage: 13 MB
% 0.16/0.48 % (2351396)Instructions burned: 102 (million)
% 0.16/0.48 % (2351387)Success in time 0.07 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------