%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM336+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 : n017.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 2.31s 0.82s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 17 unt; 0 def)
% Number of atoms : 84 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 36 ~; 33 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 78 ( 77 !; 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(f293,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X1,X2)
& sum(X0,X1,X3) )
=> X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',unique_sum) ).
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(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,
! [X0] :
( difference(X0,n2,n3)
=> X0 = n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_only_n5_n2_n3) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( difference(X0,n2,n3)
=> X0 = n5 ),
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(f435,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3) ),
inference(ennf_transformation,[],[f293]) ).
fof(f436,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3) ),
inference(flattening,[],[f435]) ).
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] :
( n5 != X0
& difference(X0,n2,n3) ),
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(f745,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
inference(cnf_transformation,[],[f436]) ).
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_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
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,
difference(sK0,n2,n3),
inference(cnf_transformation,[],[f450]) ).
fof(f856,plain,
n5 != sK0,
inference(cnf_transformation,[],[f450]) ).
fof(f858,plain,
sum(n2,n3,sK0),
inference(resolution,[],[f748,f855]) ).
fof(f865,plain,
! [X0] :
( ~ sum(n2,n3,X0)
| sK0 = X0 ),
inference(resolution,[],[f745,f858]) ).
fof(f5281,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)) ),
inference(resolution,[],[f750,f805]) ).
fof(f6351,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[],[f5281,f778]) ).
fof(f7351,plain,
! [X2,X0,X1] :
( ~ rdn_translate(X2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n5)))
| sum(X2,X1,X0) ),
inference(resolution,[],[f6351,f739]) ).
fof(f10143,plain,
! [X0,X1] :
( ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| sum(n2,X0,X1) ),
inference(resolution,[],[f7351,f453]) ).
fof(f16275,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n3)))
| sum(n2,X0,n5) ),
inference(resolution,[],[f10143,f456]) ).
fof(f16276,plain,
sum(n2,n3,n5),
inference(resolution,[],[f16275,f454]) ).
fof(f16280,plain,
n5 = sK0,
inference(resolution,[],[f16276,f865]) ).
fof(f16286,plain,
$false,
inference(forward_subsumption_resolution,[],[f16280,f856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM336+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 19:30:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 Running first-order model finding
% 0.14/0.40 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
% 2.31/0.82 % (2891116)Will run a generic schedule for satisfiability detection.
% 2.31/0.82 % (2891121)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=398480257_2999 on theBenchmark for (2999ds/0Mi)
% 2.31/0.82 % (2891122)% WARNING: option uhcvi not known.
% 2.31/0.82 % (2891122)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2197853787:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.31/0.82 % (2891123)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1417770016:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.31/0.82 % (2891124)dis+10_1_sil=32000:sp=arity:random_seed=1899543783:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.31/0.82 % (2891125)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2382003480:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.31/0.82 % (2891127)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3649417418:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.31/0.82 % (2891126)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=232900542:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.31/0.82 % TRYING [1]
% 2.31/0.82 % TRYING [2]
% 2.31/0.82 % TRYING [3]
% 2.31/0.82 % (2891124)Instruction limit reached!
% 2.31/0.82 % (2891124)------------------------------
% 2.31/0.82 % (2891124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891124)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891124)Termination reason: Instruction limit
% 2.31/0.82 % (2891124)Termination phase: Saturation
% 2.31/0.82 % (2891124)Time elapsed: 0.049 s
% 2.31/0.82 % (2891124)Peak memory usage: 13 MB
% 2.31/0.82 % (2891124)Instructions burned: 105 (million)
% 2.31/0.82 % TRYING [4]
% 2.31/0.82 % (2891125)Instruction limit reached!
% 2.31/0.82 % (2891125)------------------------------
% 2.31/0.82 % (2891125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891125)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891125)Termination reason: Instruction limit
% 2.31/0.82 % (2891125)Termination phase: Saturation
% 2.31/0.82 % (2891125)Time elapsed: 0.062 s
% 2.31/0.82 % (2891125)Peak memory usage: 13 MB
% 2.31/0.82 % (2891125)Instructions burned: 117 (million)
% 2.31/0.82 % (2891126)Instruction limit reached!
% 2.31/0.82 % (2891126)------------------------------
% 2.31/0.82 % (2891126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891126)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891126)Termination reason: Instruction limit
% 2.31/0.82 % (2891126)Termination phase: Saturation
% 2.31/0.82 % (2891126)Time elapsed: 0.063 s
% 2.31/0.82 % (2891126)Peak memory usage: 14 MB
% 2.31/0.82 % (2891126)Instructions burned: 132 (million)
% 2.31/0.82 % (2891135)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1963958094:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.31/0.82 % (2891127)Instruction limit reached!
% 2.31/0.82 % (2891127)------------------------------
% 2.31/0.82 % (2891127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891127)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891127)Termination reason: Instruction limit
% 2.31/0.82 % (2891127)Termination phase: Saturation
% 2.31/0.82 % (2891127)Time elapsed: 0.074 s
% 2.31/0.82 % (2891127)Peak memory usage: 14 MB
% 2.31/0.82 % (2891127)Instructions burned: 161 (million)
% 2.31/0.82 % (2891136)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=247862354:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.31/0.82 % (2891137)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3076262870:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.31/0.82 % (2891139)ott-21_1_sil=16000:fs=off:random_seed=4202715960:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.31/0.82 % TRYING [1]
% 2.31/0.82 % TRYING [2]
% 2.31/0.82 % TRYING [3]
% 2.31/0.82 % (2891136)Instruction limit reached!
% 2.31/0.82 % (2891136)------------------------------
% 2.31/0.82 % (2891136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891136)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891136)Termination reason: Instruction limit
% 2.31/0.82 % (2891136)Termination phase: Saturation
% 2.31/0.82 % (2891136)Time elapsed: 0.066 s
% 2.31/0.82 % (2891136)Peak memory usage: 14 MB
% 2.31/0.82 % (2891136)Instructions burned: 131 (million)
% 2.31/0.82 % (2891143)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4014784487:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.31/0.82 % (2891139)Instruction limit reached!
% 2.31/0.82 % (2891139)------------------------------
% 2.31/0.82 % (2891139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891139)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891139)Termination reason: Instruction limit
% 2.31/0.82 % (2891139)Termination phase: Saturation
% 2.31/0.82 % (2891139)Time elapsed: 0.082 s
% 2.31/0.82 % (2891139)Peak memory usage: 13 MB
% 2.31/0.82 % (2891139)Instructions burned: 182 (million)
% 2.31/0.82 % (2891145)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2693160033:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.31/0.82 % TRYING [4]
% 2.31/0.82 % TRYING [1]
% 2.31/0.82 % TRYING [2]
% 2.31/0.82 % TRYING [5]
% 2.31/0.82 % TRYING [3]
% 2.31/0.82 % (2891135)Instruction limit reached!
% 2.31/0.82 % (2891135)------------------------------
% 2.31/0.82 % (2891135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891135)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891135)Termination reason: Instruction limit
% 2.31/0.82 % (2891135)Termination phase: Finite model building constraint generation
% 2.31/0.82 % (2891135)Time elapsed: 0.267 s
% 2.31/0.82 % (2891135)Peak memory usage: 38 MB
% 2.31/0.82 % (2891135)Instructions burned: 714 (million)
% 2.31/0.82 % (2891137) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2891116-2891137"...
% 2.31/0.82 % (2891137)...printing done.
% 2.31/0.82 % (2891137)Refutation found. Thanks to Tanya!
% 2.31/0.82 % SZS status Theorem for theBenchmark
% 2.31/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.82 % (2891137)------------------------------
% 2.31/0.82 % (2891137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.82 % (2891137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.82 % (2891137)CaDiCaL version: 2.1.3
% 2.31/0.82 % (2891137)Termination reason: Refutation
% 2.31/0.82 % (2891137)Time elapsed: 0.265 s
% 2.31/0.82 % (2891137)Peak memory usage: 19 MB
% 2.31/0.82 % (2891137)Instructions burned: 479 (million)
% 2.31/0.82 % (2891116)Success in time 0.409 s
% 2.31/0.82 % Vampire exiting
%------------------------------------------------------------------------------