%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM313+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 : 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 12:12:09 PM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 16 unt; 1 def)
% Number of atoms : 95 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 54 ~; 42 |; 7 &)
% ( 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 : 88 ( 87 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',unique_RHS) ).
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(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n2_n3_n5_n0) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
! [X0] :
( sum(n2,X0,n5)
=> X0 = n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sumn2_only_n3_n5) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( sum(n2,X0,n5)
=> X0 = n3 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
? [X0] :
( n3 != X0
& sum(n2,X0,n5) ),
inference(ennf_transformation,[],[f403]) ).
fof(f407,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X1,X3)
| ~ sum(X0,X2,X3) ),
inference(ennf_transformation,[],[f295]) ).
fof(f408,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ sum(X0,X1,X3)
| ~ sum(X0,X2,X3) ),
inference(flattening,[],[f407]) ).
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(ennf_transformation,[],[f287]) ).
fof(f426,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,[],[f425]) ).
fof(f448,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(f449,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,[],[f448]) ).
fof(f451,plain,
( n3 != sK0
& sum(n2,sK0,n5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f406]) ).
fof(f454,plain,
sum(n2,sK0,n5),
inference(cnf_transformation,[],[f451]) ).
fof(f455,plain,
n3 != sK0,
inference(cnf_transformation,[],[f451]) ).
fof(f456,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| ~ sum(X0,X1,X3)
| ~ sum(X0,X2,X3) ),
inference(cnf_transformation,[],[f408]) ).
fof(f483,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f490,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f514,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f520,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,[],[f426]) ).
fof(f532,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f540,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f600,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,[],[f449]) ).
fof(f603,definition,
! [X0,X1] :
( sQ1_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
fof(f604,plain,
~ sQ1_eqProxy(n3,sK0),
inference(equality_proxy_replacement,[],[f455,f603]) ).
fof(f605,plain,
! [X2,X3,X0,X1] :
( sQ1_eqProxy(X1,X2)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X2,X3) ),
inference(equality_proxy_replacement,[],[f456,f603]) ).
fof(f681,plain,
! [X0,X1] :
( ~ sum(X0,sK0,X1)
| ~ sum(X0,n3,X1) ),
inference(resolution,[],[f605,f604]) ).
fof(f683,plain,
~ sum(n2,n3,n5),
inference(resolution,[],[f681,f454]) ).
fof(f916,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X4,X5,X6)
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
| ~ rdn_translate(X5,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X6,rdn_pos(rdnn(X3))) ),
inference(resolution,[],[f600,f520]) ).
fof(f973,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(n2,rdn_pos(rdnn(X2)))
| ~ rdn_translate(n3,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n5,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[],[f916,f683]) ).
fof(f981,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n2,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n5),rdnn(n0)) ),
inference(resolution,[],[f973,f540]) ).
fof(f997,plain,
! [X0,X1] :
( ~ rdn_translate(n2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(n3),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0)) ),
inference(resolution,[],[f981,f514]) ).
fof(f1008,plain,
! [X0] :
( ~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n5),rdnn(n0)) ),
inference(resolution,[],[f997,f490]) ).
fof(f1019,plain,
~ rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(resolution,[],[f1008,f532]) ).
fof(f1021,plain,
$false,
inference(resolution,[],[f1019,f483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM313+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n009.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 19:31:30 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.17/1.50 % (2349259)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (2349264)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=2827577608:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (2349268)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1939152548:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (2349265)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=3799720713:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (2349270)dis-21_1_sil=8000:lcm=predicate:random_seed=3828718081: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)
% 0.17/1.50 % (2349267)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2031304403:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (2349266)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=1754144354:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (2349269)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3156508667:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (2349267)Refutation not found, incomplete strategy
% 0.17/1.50 % (2349267)------------------------------
% 0.17/1.50 % (2349267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2349267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2349267)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2349267)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2349267)Time elapsed: 0.003 s
% 0.17/1.50 % (2349267)Peak memory usage: 88 MB
% 0.17/1.50 % (2349267)Instructions burned: 2 (million)
% 0.17/1.50 % (2349270)First to succeed.
% 0.17/1.50 % (2349270)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2349259"
% 0.17/1.50 % (2349268)Instruction limit reached!
% 0.17/1.50 % (2349268)------------------------------
% 0.17/1.50 % (2349268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2349268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2349268)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2349268)Termination reason: Instruction limit
% 0.17/1.50 % (2349268)Termination phase: Saturation
% 0.17/1.50 % (2349268)Time elapsed: 0.067 s
% 0.17/1.50 % (2349268)Peak memory usage: 88 MB
% 0.17/1.50 % (2349268)Instructions burned: 119 (million)
% 0.17/1.50 % (2349269)Instruction limit reached!
% 0.17/1.50 % (2349269)------------------------------
% 0.17/1.50 % (2349269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2349269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2349269)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2349269)Termination reason: Instruction limit
% 0.17/1.50 % (2349269)Termination phase: Saturation
% 0.17/1.50 % (2349269)Time elapsed: 0.082 s
% 0.17/1.50 % (2349269)Peak memory usage: 89 MB
% 0.17/1.50 % (2349269)Instructions burned: 140 (million)
% 0.17/1.50 % (2349278)lrs+10_1_sil=8000:sp=occurrence:random_seed=500271956:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.17/1.50 % (2349278)Refutation not found, incomplete strategy
% 0.17/1.50 % (2349278)------------------------------
% 0.17/1.50 % (2349278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2349278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2349278)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2349278)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2349278)Time elapsed: 0.009 s
% 0.17/1.50 % (2349278)Peak memory usage: 89 MB
% 0.17/1.50 % (2349278)Instructions burned: 11 (million)
% 0.17/1.50 % (2349267)------------------------------
% 0.17/1.50 % (2349267)------------------------------
% 0.17/1.50 % (2349279)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1470741888:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.17/1.50 % (2349279)Refutation not found, incomplete strategy
% 0.17/1.50 % (2349279)------------------------------
% 0.17/1.50 % (2349279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2349279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2349279)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2349279)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (2349279)Time elapsed: 0.004 s
% 0.17/1.50 % (2349279)Peak memory usage: 89 MB
% 0.17/1.50 % (2349279)Instructions burned: 6 (million)
% 0.17/1.50 % (2349270)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2349270)------------------------------
% 0.17/1.50 % (2349270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2349270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2349270)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2349270)Termination reason: Refutation
% 0.17/1.50 % (2349270)Time elapsed: 0.014 s
% 0.17/1.50 % (2349270)Peak memory usage: 89 MB
% 0.17/1.50 % (2349270)Instructions burned: 21 (million)
% 0.17/1.50 % (2349270)------------------------------
% 0.17/1.50 % (2349270)------------------------------
% 0.17/1.50 % (2349259)Success in time 0.447 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------