%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM327+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 : 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 12:12:11 PM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 41 ~; 33 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 66 ( 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn0) ).
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(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(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n0_n0_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,n0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_zero_identity) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,n0,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
! [X0] : ~ sum(X0,n0,X0),
inference(ennf_transformation,[],[f403]) ).
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(f444,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(f445,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,[],[f444]) ).
fof(f453,plain,
! [X0] : ~ sum(X0,n0,X0),
inference(cnf_transformation,[],[f406]) ).
fof(f517,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f518,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f527,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,[],[f424]) ).
fof(f596,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,[],[f445]) ).
fof(f662,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,[],[f596,f527]) ).
fof(f700,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_translate(X2,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n0,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X3),rdnn(X4),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[],[f662,f453]) ).
fof(f702,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n0,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n0,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(n0),rdnn(X0),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[],[f700,f518]) ).
fof(f728,plain,
! [X0,X1] :
( ~ rdn_translate(n0,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(resolution,[],[f702,f518]) ).
fof(f818,plain,
! [X0] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
inference(resolution,[],[f728,f518]) ).
fof(f913,plain,
~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(factoring,[],[f818]) ).
fof(f994,plain,
$false,
inference(resolution,[],[f913,f517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM327+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 19:31:40 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.82/1.31 % (1731902)Detected formulas, will run a generic FOF schedule.
% 2.82/1.31 % (1731908)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=2207280722:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.82/1.31 % (1731909)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=621490672:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.82/1.31 % (1731907)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=1487166314:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.82/1.31 % (1731913)dis-21_1_sil=8000:lcm=predicate:random_seed=1833845327: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)
% 2.82/1.31 % (1731911)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=776754103:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.82/1.31 % (1731910)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3996619917:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.82/1.31 % (1731912)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4253688440:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.82/1.31 % (1731910)Refutation not found, incomplete strategy
% 2.82/1.31 % (1731910)------------------------------
% 2.82/1.31 % (1731910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.31 % (1731910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.31 % (1731910)CaDiCaL version: 2.1.3
% 2.82/1.31 % (1731910)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.31 % (1731910)Time elapsed: 0.002 s
% 2.82/1.31 % (1731910)Peak memory usage: 87 MB
% 2.82/1.31 % (1731910)Instructions burned: 1 (million)
% 2.82/1.31 % (1731911)Refutation not found, incomplete strategy
% 2.82/1.31 % (1731911)------------------------------
% 2.82/1.31 % (1731911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.31 % (1731911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.31 % (1731911)CaDiCaL version: 2.1.3
% 2.82/1.31 % (1731911)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.31 % (1731911)Time elapsed: 0.002 s
% 2.82/1.31 % (1731911)Peak memory usage: 87 MB
% 2.82/1.31 % (1731911)Instructions burned: 2 (million)
% 2.82/1.31 % (1731913)First to succeed.
% 2.82/1.31 % (1731913)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1731902"
% 2.82/1.31 % (1731912)Instruction limit reached!
% 2.82/1.31 % (1731912)------------------------------
% 2.82/1.31 % (1731912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.31 % (1731912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.31 % (1731912)CaDiCaL version: 2.1.3
% 2.82/1.31 % (1731912)Termination reason: Instruction limit
% 2.82/1.31 % (1731912)Termination phase: Saturation
% 2.82/1.31 % (1731912)Time elapsed: 0.083 s
% 2.82/1.31 % (1731912)Peak memory usage: 90 MB
% 2.82/1.31 % (1731912)Instructions burned: 139 (million)
% 2.82/1.31 [W927 19:31:41.171769983 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.82/1.31 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.82/1.31 [W927 19:31:41.171807583 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.82/1.31 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.82/1.31 [W927 19:31:41.171828868 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 2.82/1.31 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.82/1.31 [W927 19:31:41.171835368 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171848699 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171854145 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171866983 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171872386 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171903236 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171908541 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171921375 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 [W927 19:31:41.171936406 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.17/1.50 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.17/1.50 % (1731921)lrs+10_1_sil=8000:sp=occurrence:random_seed=2627639347:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.17/1.50 % (1731921)Refutation not found, incomplete strategy
% 0.17/1.50 % (1731921)------------------------------
% 0.17/1.50 % (1731921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1731921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1731921)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1731921)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (1731921)Time elapsed: 0.002 s
% 0.17/1.50 % (1731921)Peak memory usage: 87 MB
% 0.17/1.50 % (1731921)Instructions burned: 1 (million)
% 0.17/1.50 % (1731910)------------------------------
% 0.17/1.50 % (1731910)------------------------------
% 0.17/1.50 % (1731911)------------------------------
% 0.17/1.50 % (1731911)------------------------------
% 0.17/1.50 % (1731913)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 % (1731913)------------------------------
% 0.17/1.50 % (1731913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1731913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1731913)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1731913)Termination reason: Refutation
% 0.17/1.50 % (1731913)Time elapsed: 0.020 s
% 0.17/1.50 % (1731913)Peak memory usage: 89 MB
% 0.17/1.50 % (1731913)Instructions burned: 35 (million)
% 0.17/1.50 % (1731913)------------------------------
% 0.17/1.50 % (1731913)------------------------------
% 0.17/1.50 % (1731902)Success in time 0.445 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------