%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:18:18 PM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 23 unt; 1 def)
% Number of atoms : 136 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 78 ~; 66 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 109 ( 0 sgn 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(f7,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn6) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f281,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_pos(X2))
& rdn_translate(X1,rdn_pos(X3))
& rdn_positive_less(X2,X3) )
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(f284,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( ~ less(X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_property) ).
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/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(f294,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X2,X3)
& sum(X1,X2,X3) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',unique_LHS) ).
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/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f335,axiom,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n3_n3_n6_n0) ).
fof(f362,axiom,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n6_n0_n6_n0) ).
fof(f402,conjecture,
~ sum(n2,n3,n6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_n3_not_n6) ).
fof(f403,negated_conjecture,
~ ~ sum(n2,n3,n6),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
sum(n2,n3,n6),
inference(flattening,[],[f403]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(ennf_transformation,[],[f281]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_positive_less(X2,X3) ),
inference(flattening,[],[f414]) ).
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(f438,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ sum(X0,X2,X3)
| ~ sum(X1,X2,X3) ),
inference(ennf_transformation,[],[f294]) ).
fof(f439,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ sum(X0,X2,X3)
| ~ sum(X1,X2,X3) ),
inference(flattening,[],[f438]) ).
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(f457,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(cnf_transformation,[],[f7]) ).
fof(f718,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f731,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_positive_less(X2,X3) ),
inference(cnf_transformation,[],[f415]) ).
fof(f734,plain,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f284]) ).
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(f746,plain,
! [X2,X3,X0,X1] :
( ~ sum(X1,X2,X3)
| ~ sum(X0,X2,X3)
| X0 = X1 ),
inference(cnf_transformation,[],[f439]) ).
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(f788,plain,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
inference(cnf_transformation,[],[f335]) ).
fof(f815,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(cnf_transformation,[],[f362]) ).
fof(f855,plain,
sum(n2,n3,n6),
inference(cnf_transformation,[],[f404]) ).
fof(f856,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f734]) ).
fof(f1128,plain,
! [X0] :
( ~ sum(X0,n3,n6)
| n2 = X0 ),
inference(resolution,[],[f746,f855]) ).
fof(f1140,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(X2,X1)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f731,f856]) ).
fof(f1189,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(f1467,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X2)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X4)))
| ~ rdn_translate(n6,rdn_pos(rdnn(X1)))
| n2 = X3 ),
inference(resolution,[],[f1189,f1128]) ).
fof(f1477,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n6),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n6,rdn_pos(rdnn(n6)))
| n2 = X2 ),
inference(resolution,[],[f1467,f815]) ).
fof(f1551,definition,
( spl0_22
<=> ! [X1] :
( ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| n2 = X1 ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f1552,plain,
( ! [X1] :
( ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| n2 = X1 )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1551]) ).
fof(f1603,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n6),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| n2 = X2 ),
inference(forward_subsumption_resolution,[],[f1477,f457]) ).
fof(f1817,plain,
! [X0] :
( ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| n2 = X0 ),
inference(resolution,[],[f1603,f788]) ).
fof(f1821,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| n2 = X0 ),
inference(forward_subsumption_resolution,[],[f1817,f454]) ).
fof(f1837,plain,
spl0_22,
inference(avatar_split_clause,[],[f1821,f1551]) ).
fof(f1858,plain,
( n2 = n3
| ~ spl0_22 ),
inference(resolution,[],[f1552,f454]) ).
fof(f1910,plain,
( rdn_positive_less(rdnn(n2),rdnn(n2))
| ~ spl0_22 ),
inference(superposition,[],[f718,f1858]) ).
fof(f2130,plain,
( ! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) )
| ~ spl0_22 ),
inference(resolution,[],[f1910,f1140]) ).
fof(f2131,plain,
( ! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f2130]) ).
fof(f2137,plain,
( $false
| ~ spl0_22 ),
inference(resolution,[],[f2131,f453]) ).
fof(f2138,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f2137]) ).
cnf(s29,plain,
spl0_22,
inference(sat_conversion,[],[f1837]) ).
cnf(s48,plain,
~ spl0_22,
inference(sat_conversion,[],[f2138]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s29,s48]) ).
fof(f2139,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 19:30:34 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.52 % (3356583)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (3356594)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2530557059:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % (3356589)% WARNING: option uhcvi not known.
% 0.16/0.52 % (3356589)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=84435706:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (3356592)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3761908862:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (3356588)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2295113082_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (3356590)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1350456328:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (3356591)dis+10_1_sil=32000:sp=arity:random_seed=3370983256:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (3356593)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2650773107:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % (3356594)Instruction limit reached!
% 0.16/0.52 % (3356594)------------------------------
% 0.16/0.52 % (3356594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3356594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3356594)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3356594)Termination reason: Instruction limit
% 0.16/0.52 % (3356594)Termination phase: Saturation
% 0.16/0.52 % (3356594)Time elapsed: 0.044 s
% 0.16/0.52 % (3356594)Peak memory usage: 15 MB
% 0.16/0.52 % (3356594)Instructions burned: 159 (million)
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % (3356602)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3215057908:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.52 % (3356591)Instruction limit reached!
% 0.16/0.52 % (3356591)------------------------------
% 0.16/0.52 % (3356591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3356591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3356591)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3356591)Termination reason: Instruction limit
% 0.16/0.52 % (3356591)Termination phase: Saturation
% 0.16/0.52 % (3356591)Time elapsed: 0.050 s
% 0.16/0.52 % (3356591)Peak memory usage: 13 MB
% 0.16/0.52 % (3356591)Instructions burned: 104 (million)
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % (3356592) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3356583-3356592"...
% 0.16/0.52 % (3356592)...printing done.
% 0.16/0.52 % (3356592)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (3356592)------------------------------
% 0.16/0.52 % (3356592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3356592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3356592)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3356592)Termination reason: Refutation
% 0.16/0.52 % (3356592)Time elapsed: 0.059 s
% 0.16/0.52 % (3356592)Peak memory usage: 14 MB
% 0.16/0.52 % (3356592)Instructions burned: 110 (million)
% 0.16/0.52 % (3356583)Success in time 0.102 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------