%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM325+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 : n007.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 12:18:20 PM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 26 unt; 2 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 175 ( 90 ~; 74 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 94 ( 0 sgn 92 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(f290,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X0,rdn_pos(X3))
& rdn_translate(X1,rdn_neg(X4))
& rdn_positive_less(X4,X3)
& rdn_add_with_carry(rdnn(n0),X4,X5,X3)
& rdn_translate(X2,rdn_pos(X5)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_2) ).
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(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,nn2,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn2_n3) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,nn2,n3),
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(f429,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(X4,X3)
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(ennf_transformation,[],[f290]) ).
fof(f430,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(X4,X3)
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(flattening,[],[f429]) ).
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(X0,nn2,n3),
inference(ennf_transformation,[],[f403]) ).
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(f580,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
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(f742,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_positive_less(X4,X3)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f430]) ).
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(X0,nn2,n3),
inference(cnf_transformation,[],[f450]) ).
fof(f1140,plain,
! [X0] :
( rdn_positive_less(rdnn(X0),rdnn(n4))
| ~ rdn_positive_less(rdnn(X0),rdnn(n3)) ),
inference(resolution,[],[f725,f719]) ).
fof(f1141,plain,
! [X0] :
( rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_positive_less(rdnn(X0),rdnn(n4)) ),
inference(resolution,[],[f725,f720]) ).
fof(f1166,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(X1)))
| ~ rdn_positive_less(rdnn(X0),rdnn(X3))
| ~ rdn_translate(X5,rdn_neg(rdnn(X0)))
| ~ rdn_translate(X6,rdn_pos(rdnn(X3)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[],[f750,f742]) ).
fof(f1414,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_positive_less(rdnn(X3),rdnn(X1))
| ~ rdn_translate(n3,rdn_pos(rdnn(X2)))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X3)))
| ~ rdn_translate(X4,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X3),rdnn(X2),rdnn(X0),rdnn(n0)) ),
inference(resolution,[],[f1166,f855]) ).
fof(f1436,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(n3,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X2)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
| ~ rdn_digit_add(rdnn(X2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_positive_less(rdnn(X2),rdnn(n4)) ),
inference(resolution,[],[f1414,f1141]) ).
fof(f1496,definition,
( spl0_13
<=> ! [X2] : ~ rdn_translate(X2,rdn_pos(rdnn(n5))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f1497,plain,
( ! [X2] : ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1561,definition,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ rdn_translate(n3,rdn_pos(rdnn(X0)))
| ~ rdn_positive_less(rdnn(X2),rdnn(n4))
| ~ rdn_digit_add(rdnn(X2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X2)))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f1562,plain,
( ! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X2),rdnn(n4))
| ~ rdn_translate(n3,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X2)))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0)) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f1563,plain,
( spl0_13
| spl0_30 ),
inference(avatar_split_clause,[],[f1436,f1561,f1496]) ).
fof(f1675,plain,
( $false
| ~ spl0_13 ),
inference(resolution,[],[f1497,f456]) ).
fof(f1676,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f1675]) ).
fof(f1771,plain,
( ! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(n3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X0),rdnn(X2),rdnn(n0))
| ~ rdn_translate(nn2,rdn_neg(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X0))) )
| ~ spl0_30 ),
inference(resolution,[],[f1562,f1140]) ).
fof(f1817,plain,
( ! [X0,X1] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_translate(nn2,rdn_neg(rdnn(n2)))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X0))) )
| ~ spl0_30 ),
inference(resolution,[],[f1771,f718]) ).
fof(f1818,plain,
( ! [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(n3,rdn_pos(rdnn(X0))) )
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1817,f580]) ).
fof(f1819,plain,
( ! [X0] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X0),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X0))) )
| ~ spl0_30 ),
inference(resolution,[],[f1818,f805]) ).
fof(f1820,plain,
( ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ spl0_30 ),
inference(resolution,[],[f1819,f778]) ).
fof(f1821,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1820,f454]) ).
fof(f1822,plain,
~ spl0_30,
inference(avatar_contradiction_clause,[],[f1821]) ).
cnf(s14,plain,
( spl0_13
| spl0_30 ),
inference(sat_conversion,[],[f1563]) ).
cnf(s22,plain,
~ spl0_13,
inference(sat_conversion,[],[f1676]) ).
cnf(s26,plain,
~ spl0_30,
inference(sat_conversion,[],[f1822]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s14,s26,s22]) ).
fof(f1823,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM325+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n007.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 19:31:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.19/0.50 % (1731333)Will run a generic schedule for satisfiability detection.
% 0.19/0.50 % (1731342)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2331718939:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.50 % (1731339)% WARNING: option uhcvi not known.
% 0.19/0.50 % (1731338)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=51900535_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.50 % (1731339)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3513432108:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.50 % (1731341)dis+10_1_sil=32000:sp=arity:random_seed=2479312426:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.50 % (1731340)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1939648481:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.50 % (1731343)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3451418969:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.50 % (1731344)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3873800061:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.50 % (1731342) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1731333-1731342"...
% 0.19/0.50 % (1731342)...printing done.
% 0.19/0.50 % (1731342)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (1731342)------------------------------
% 0.19/0.50 % (1731342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.50 % (1731342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.50 % (1731342)CaDiCaL version: 2.1.3
% 0.19/0.50 % (1731342)Termination reason: Refutation
% 0.19/0.50 % (1731342)Time elapsed: 0.030 s
% 0.19/0.50 % (1731342)Peak memory usage: 14 MB
% 0.19/0.50 % (1731342)Instructions burned: 105 (million)
% 0.19/0.50 % (1731333)Success in time 0.077 s
% 0.19/0.50 % Vampire exiting
%------------------------------------------------------------------------------