TSTP Solution File: NUM316+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM316+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 08:18:44 EDT 2024
% Result : Theorem 11.31s 1.99s
% Output : Refutation 11.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 27 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 50 ~; 41 |; 11 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 92 ( 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f170058,plain,
$false,
inference(subsumption_resolution,[],[f170057,f95570]) ).
fof(f95570,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(unit_resulting_resolution,[],[f769,f755,f871]) ).
fof(f871,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(cnf_transformation,[],[f456]) ).
fof(f456,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(flattening,[],[f455]) ).
fof(f455,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0)) ),
inference(ennf_transformation,[],[f417]) ).
fof(f417,plain,
! [X0,X1,X2,X3,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(rectify,[],[f297]) ).
fof(f297,axiom,
! [X20,X21,X22,X23,X24] :
( ( rdn_digit_add(rdnn(X24),rdnn(X20),rdnn(X23),rdnn(n0))
& rdn_digit_add(rdnn(X21),rdnn(X22),rdnn(X24),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X20),rdnn(X21),rdnn(X22),rdnn(X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f755,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n5_n0_n5_n0) ).
fof(f769,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n2_n3_n5_n0) ).
fof(f170057,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(unit_resulting_resolution,[],[f131438,f510,f129828,f899]) ).
fof(f899,plain,
! [X3,X0,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X0,rdn_pos(X3))
| sP9(X4,X0,X5) ),
inference(cnf_transformation,[],[f899_D]) ).
fof(f899_D,plain,
! [X5,X0,X4] :
( ! [X3] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X0,rdn_pos(X3)) )
<=> ~ sP9(X4,X0,X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f129828,plain,
~ sP9(rdnn(n5),n2,rdnn(n3)),
inference(unit_resulting_resolution,[],[f501,f89924,f900]) ).
fof(f900,plain,
! [X0,X1,X4,X5] :
( ~ sP9(X4,X0,X5)
| ~ sP8(X0,X5,X1)
| ~ rdn_translate(X1,rdn_neg(X4)) ),
inference(general_splitting,[],[f898,f899_D]) ).
fof(f898,plain,
! [X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ sP8(X0,X5,X1) ),
inference(general_splitting,[],[f874,f897_D]) ).
fof(f897,plain,
! [X2,X0,X1,X5] :
( ~ rdn_translate(X2,rdn_neg(X5))
| sum(X0,X1,X2)
| sP8(X0,X5,X1) ),
inference(cnf_transformation,[],[f897_D]) ).
fof(f897_D,plain,
! [X1,X5,X0] :
( ! [X2] :
( ~ rdn_translate(X2,rdn_neg(X5))
| sum(X0,X1,X2) )
<=> ~ sP8(X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP8])]) ).
fof(f874,plain,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f461]) ).
fof(f461,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(flattening,[],[f460]) ).
fof(f460,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_add_with_carry(rdnn(n0),X3,X5,X4)
| ~ rdn_positive_less(X3,X4)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f420]) ).
fof(f420,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_neg(X5))
& rdn_add_with_carry(rdnn(n0),X3,X5,X4)
& rdn_positive_less(X3,X4)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
inference(rectify,[],[f289]) ).
fof(f289,axiom,
! [X0,X1,X2,X9,X10,X11] :
( ( rdn_translate(X2,rdn_neg(X11))
& rdn_add_with_carry(rdnn(n0),X9,X11,X10)
& rdn_positive_less(X9,X10)
& rdn_translate(X1,rdn_neg(X10))
& rdn_translate(X0,rdn_pos(X9)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_neg_1) ).
fof(f89924,plain,
sP8(n2,rdnn(n3),nn5),
inference(unit_resulting_resolution,[],[f475,f502,f897]) ).
fof(f502,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[],[f131]) ).
fof(f131,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn3) ).
fof(f475,plain,
~ sum(n2,nn5,nn3),
inference(cnf_transformation,[],[f404]) ).
fof(f404,plain,
~ sum(n2,nn5,nn3),
inference(flattening,[],[f403]) ).
fof(f403,negated_conjecture,
~ sum(n2,nn5,nn3),
inference(negated_conjecture,[],[f402]) ).
fof(f402,conjecture,
sum(n2,nn5,nn3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_nn5_nn3) ).
fof(f501,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn5) ).
fof(f510,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn2) ).
fof(f131438,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(unit_resulting_resolution,[],[f490,f91848,f860]) ).
fof(f860,plain,
! [X2,X0,X1] :
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[],[f439]) ).
fof(f439,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(flattening,[],[f438]) ).
fof(f438,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(ennf_transformation,[],[f275]) ).
fof(f275,axiom,
! [X0,X1,X2] :
( ( rdn_positive_less(rdnn(X1),rdnn(X2))
& rdn_positive_less(rdnn(X0),rdnn(X1)) )
=> rdn_positive_less(rdnn(X0),rdnn(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).
fof(f91848,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(unit_resulting_resolution,[],[f491,f487,f860]) ).
fof(f487,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[],[f269]) ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less34) ).
fof(f491,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[],[f268]) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less23) ).
fof(f490,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[],[f270]) ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less45) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM316+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 15:03:07 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (3259)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38 % (3263)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (3264)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.38 % (3266)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.38 % (3265)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.39 % (3261)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39 % (3262)WARNING: value z3 for option sas not known
% 0.20/0.39 % (3260)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39 % (3262)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.42 TRYING [1]
% 0.20/0.42 TRYING [2]
% 0.20/0.46 TRYING [1]
% 0.20/0.47 TRYING [3]
% 0.20/0.48 TRYING [2]
% 0.20/0.54 TRYING [3]
% 2.11/0.68 TRYING [4]
% 2.11/0.72 TRYING [4]
% 7.01/1.39 TRYING [5]
% 7.84/1.52 TRYING [1]
% 7.84/1.52 TRYING [2]
% 8.31/1.57 TRYING [3]
% 9.21/1.68 TRYING [5]
% 9.80/1.77 TRYING [4]
% 11.31/1.99 % (3266)First to succeed.
% 11.31/1.99 % (3266)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3259"
% 11.31/1.99 % (3266)Refutation found. Thanks to Tanya!
% 11.31/1.99 % SZS status Theorem for theBenchmark
% 11.31/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 11.31/1.99 % (3266)------------------------------
% 11.31/1.99 % (3266)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.31/1.99 % (3266)Termination reason: Refutation
% 11.31/1.99
% 11.31/1.99 % (3266)Memory used [KB]: 39911
% 11.31/1.99 % (3266)Time elapsed: 1.604 s
% 11.31/1.99 % (3266)Instructions burned: 5005 (million)
% 11.31/1.99 % (3259)Success in time 1.632 s
%------------------------------------------------------------------------------