%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM315+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:12:09 PM UTC 2026
% Result : Theorem 2.32s 0.93s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 41 ~; 33 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn2) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn5) ).
fof(f135,axiom,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn7) ).
fof(f288,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X0,rdn_neg(X3))
& rdn_translate(X1,rdn_neg(X4))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X2,rdn_neg(X5)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_entry_point_neg_neg) ).
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/theBenchmark.p',add_digit_digit_digit) ).
fof(f327,axiom,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n2_n5_n7_n0) ).
fof(f372,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n7_n0_n7_n0) ).
fof(f402,conjecture,
sum(nn2,nn5,nn7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_nn2_nn5_nn7) ).
fof(f403,negated_conjecture,
~ sum(nn2,nn5,nn7),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
~ sum(nn2,nn5,nn7),
inference(flattening,[],[f403]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(ennf_transformation,[],[f288]) ).
fof(f422,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(flattening,[],[f421]) ).
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,
~ sum(nn2,nn5,nn7),
inference(cnf_transformation,[],[f404]) ).
fof(f461,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(cnf_transformation,[],[f422]) ).
fof(f463,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f464,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f465,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(cnf_transformation,[],[f135]) ).
fof(f488,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f372]) ).
fof(f518,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f327]) ).
fof(f563,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(f648,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_neg(rdnn(X0)))
| ~ rdn_translate(X5,rdn_neg(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X6,rdn_neg(rdnn(X3))) ),
inference(resolution,[],[f563,f461]) ).
fof(f696,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(nn2,rdn_neg(rdnn(X2)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(X3)))
| ~ rdn_translate(nn7,rdn_neg(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,[],[f648,f453]) ).
fof(f697,plain,
! [X2,X0,X1] :
( ~ rdn_translate(nn2,rdn_neg(rdnn(X0)))
| ~ rdn_translate(nn5,rdn_neg(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,[],[f696,f465]) ).
fof(f699,plain,
! [X0,X1] :
( ~ rdn_translate(nn2,rdn_neg(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(n5),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n7),rdnn(n0)) ),
inference(resolution,[],[f697,f464]) ).
fof(f701,plain,
! [X0] :
( ~ rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n7),rdnn(n0)) ),
inference(resolution,[],[f699,f463]) ).
fof(f703,plain,
~ rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(resolution,[],[f701,f488]) ).
fof(f705,plain,
$false,
inference(resolution,[],[f703,f518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM315+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 19:31:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.32/0.93 % (2686207)Detected formulas, will run a generic FOF schedule.
% 2.32/0.93 % (2686214)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=815224558:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.32/0.93 % (2686218)dis-21_1_sil=8000:lcm=predicate:random_seed=3209653563: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)
% 2.32/0.93 % (2686216)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1379527500:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.32/0.93 % (2686212)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=3900705083:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.32/0.93 % (2686217)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1597999372:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.32/0.93 % (2686215)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2854003763:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.32/0.93 % (2686213)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=3874617809:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.32/0.93 % (2686215)Refutation not found, incomplete strategy
% 2.32/0.93 % (2686215)------------------------------
% 2.32/0.93 % (2686215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2686215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2686215)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2686215)Termination reason: Refutation not found, incomplete strategy
% 2.32/0.93 % (2686215)Time elapsed: 0.001 s
% 2.32/0.93 % (2686215)Peak memory usage: 87 MB
% 2.32/0.93 % (2686215)Instructions burned: 1 (million)
% 2.32/0.93 % (2686216)Refutation not found, incomplete strategy
% 2.32/0.93 % (2686216)------------------------------
% 2.32/0.93 % (2686216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2686216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2686216)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2686216)Termination reason: Refutation not found, incomplete strategy
% 2.32/0.93 % (2686216)Time elapsed: 0.001 s
% 2.32/0.93 % (2686216)Peak memory usage: 87 MB
% 2.32/0.93 % (2686216)Instructions burned: 2 (million)
% 2.32/0.93 % (2686218)First to succeed.
% 2.32/0.93 % (2686218)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2686207"
% 2.32/0.93 % (2686217)Instruction limit reached!
% 2.32/0.93 % (2686217)------------------------------
% 2.32/0.93 % (2686217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2686217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2686217)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2686217)Termination reason: Instruction limit
% 2.32/0.93 % (2686217)Termination phase: Saturation
% 2.32/0.93 % (2686217)Time elapsed: 0.048 s
% 2.32/0.93 % (2686217)Peak memory usage: 90 MB
% 2.32/0.93 % (2686217)Instructions burned: 139 (million)
% 2.32/0.93 % (2686215)------------------------------
% 2.32/0.93 % (2686215)------------------------------
% 2.32/0.93 % (2686216)------------------------------
% 2.32/0.93 % (2686216)------------------------------
% 2.32/0.93 % (2686218)Refutation found. Thanks to Tanya!
% 2.32/0.93 % SZS status Theorem for theBenchmark
% 2.32/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/0.93 % (2686218)------------------------------
% 2.32/0.93 % (2686218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2686218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2686218)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2686218)Termination reason: Refutation
% 2.32/0.93 % (2686218)Time elapsed: 0.005 s
% 2.32/0.93 % (2686218)Peak memory usage: 88 MB
% 2.32/0.93 % (2686218)Instructions burned: 16 (million)
% 2.32/0.93 % (2686218)------------------------------
% 2.32/0.93 % (2686218)------------------------------
% 2.32/0.93 % (2686207)Success in time 0.301 s
% 2.32/0.93 % Vampire exiting
%------------------------------------------------------------------------------