%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM334+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 : n015.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 3.45s 1.38s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 45 ~; 36 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).
fof(f8,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn7) ).
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(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f354,axiom,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n2_n7_n0) ).
fof(f372,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n7_n0_n7_n0) ).
fof(f402,conjecture,
difference(n7,n5,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_n7_n5_n2) ).
fof(f403,negated_conjecture,
~ difference(n7,n5,n2),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ difference(n7,n5,n2),
inference(flattening,[],[f403]) ).
fof(f433,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(f434,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,[],[f433]) ).
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(f451,plain,
! [X0,X1,X2] :
( ( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) )
& ( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f454,plain,
~ difference(n7,n5,n2),
inference(cnf_transformation,[],[f404]) ).
fof(f464,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f354]) ).
fof(f482,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f506,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f507,plain,
! [X2,X0,X1] :
( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f451]) ).
fof(f518,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f372]) ).
fof(f530,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(cnf_transformation,[],[f8]) ).
fof(f590,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,[],[f434]) ).
fof(f595,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(f613,plain,
~ sum(n5,n2,n7),
inference(resolution,[],[f507,f454]) ).
fof(f657,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,[],[f595,f590]) ).
fof(f695,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(n5,rdn_pos(rdnn(X2)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n7,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,[],[f657,f613]) ).
fof(f696,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n5,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n7),rdnn(n0)) ),
inference(resolution,[],[f695,f530]) ).
fof(f698,plain,
! [X0,X1] :
( ~ rdn_translate(n2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n5),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n7),rdnn(n0)) ),
inference(resolution,[],[f696,f506]) ).
fof(f700,plain,
! [X0] :
( ~ rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n7),rdnn(n0)) ),
inference(resolution,[],[f698,f482]) ).
fof(f702,plain,
~ rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(resolution,[],[f700,f518]) ).
fof(f704,plain,
$false,
inference(resolution,[],[f702,f464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM334+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 19:38:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 2.77/1.29 % (1968672)Detected formulas, will run a generic FOF schedule.
% 2.77/1.29 % (1968679)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=3090206881:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.29 % (1968682)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3387161015:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.29 % (1968677)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=2357283212:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.29 % (1968681)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1059360947:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.29 % (1968680)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3026653350:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.29 % (1968678)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=293664454:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.29 % (1968683)dis-21_1_sil=8000:lcm=predicate:random_seed=3588770731: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)
% 2.77/1.29 % (1968680)Refutation not found, incomplete strategy
% 2.77/1.29 % (1968680)------------------------------
% 2.77/1.29 % (1968680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.29 % (1968680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.29 % (1968680)CaDiCaL version: 2.1.3
% 2.77/1.29 % (1968680)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.29 % (1968680)Time elapsed: 0.001 s
% 2.77/1.29 % (1968680)Peak memory usage: 87 MB
% 2.77/1.29 % (1968680)Instructions burned: 1 (million)
% 2.77/1.29 % (1968681)Refutation not found, incomplete strategy
% 2.77/1.29 % (1968681)------------------------------
% 2.77/1.29 % (1968681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.29 % (1968681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.29 % (1968681)CaDiCaL version: 2.1.3
% 2.77/1.29 % (1968681)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.29 % (1968681)Time elapsed: 0.002 s
% 2.77/1.29 % (1968681)Peak memory usage: 87 MB
% 2.77/1.29 % (1968681)Instructions burned: 2 (million)
% 2.77/1.29 % (1968683)First to succeed.
% 2.77/1.29 % (1968683)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1968672"
% 2.77/1.29 % (1968682)Also succeeded, but the first one will report.
% 2.77/1.29 [W927 19:38:01.982389488 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.
% 2.77/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.77/1.29 [W927 19:38:01.982409949 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.
% 2.77/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.77/1.29 [W927 19:38:01.982432953 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.
% 2.77/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.77/1.29 [W927 19:38:01.982440593 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.
% 2.77/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 2.77/1.29 [W927 19:38:01.982454363 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.
% 2.77/1.29 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982460816 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982485993 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982491186 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982503420 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982515296 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982529907 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 [W927 19:38:01.982535347 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.
% 3.45/1.38 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.45/1.38 % (1968681)------------------------------
% 3.45/1.38 % (1968681)------------------------------
% 3.45/1.38 % (1968680)------------------------------
% 3.45/1.38 % (1968680)------------------------------
% 3.45/1.38 % (1968683)Refutation found. Thanks to Tanya!
% 3.45/1.38 % SZS status Theorem for theBenchmark
% 3.45/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.38 % (1968683)------------------------------
% 3.45/1.38 % (1968683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.38 % (1968683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.38 % (1968683)CaDiCaL version: 2.1.3
% 3.45/1.38 % (1968683)Termination reason: Refutation
% 3.45/1.38 % (1968683)Time elapsed: 0.010 s
% 3.45/1.38 % (1968683)Peak memory usage: 88 MB
% 3.45/1.38 % (1968683)Instructions burned: 16 (million)
% 3.45/1.38 % (1968683)------------------------------
% 3.45/1.38 % (1968683)------------------------------
% 3.45/1.38 % (1968672)Success in time 0.431 s
% 3.45/1.38 % Vampire exiting
%------------------------------------------------------------------------------