TSTP Solution File: NUM325+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM325+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 : n013.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 : Tue Apr 30 14:14:15 EDT 2024
% Result : Theorem 11.39s 1.99s
% Output : Refutation 11.39s
% 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 : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 98 ( 96 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f170063,plain,
$false,
inference(subsumption_resolution,[],[f170058,f95824]) ).
fof(f95824,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(unit_resulting_resolution,[],[f769,f747,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,[],[f416]) ).
fof(f416,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/sandbox2/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f747,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n2_n3_n5_n0) ).
fof(f170058,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(unit_resulting_resolution,[],[f508,f131690,f130084,f899]) ).
fof(f899,plain,
! [X3,X0,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ 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),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ rdn_translate(X0,rdn_pos(X3)) )
<=> ~ sP9(X4,X0,X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f130084,plain,
! [X0] : ~ sP9(rdnn(n2),X0,rdnn(n3)),
inference(unit_resulting_resolution,[],[f502,f90178,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),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ 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_pos(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_pos(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_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ 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_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ 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_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X4,X5,X3)
| ~ rdn_positive_less(X4,X3)
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f419]) ).
fof(f419,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X2,rdn_pos(X5))
& rdn_add_with_carry(rdnn(n0),X4,X5,X3)
& rdn_positive_less(X4,X3)
& rdn_translate(X1,rdn_neg(X4))
& rdn_translate(X0,rdn_pos(X3)) )
=> sum(X0,X1,X2) ),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X0,X1,X2,X9,X10,X11] :
( ( rdn_translate(X2,rdn_pos(X11))
& rdn_add_with_carry(rdnn(n0),X10,X11,X9)
& rdn_positive_less(X10,X9)
& rdn_translate(X1,rdn_neg(X10))
& rdn_translate(X0,rdn_pos(X9)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_entry_point_pos_neg_2) ).
fof(f90178,plain,
! [X0] : sP8(X0,rdnn(n3),nn2),
inference(unit_resulting_resolution,[],[f475,f509,f897]) ).
fof(f509,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn3) ).
fof(f475,plain,
! [X0] : ~ sum(X0,nn2,n3),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
! [X0] : ~ sum(X0,nn2,n3),
inference(ennf_transformation,[],[f403]) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,nn2,n3),
inference(negated_conjecture,[],[f402]) ).
fof(f402,conjecture,
? [X0] : sum(X0,nn2,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_what_nn2_n3) ).
fof(f502,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn2) ).
fof(f131690,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(unit_resulting_resolution,[],[f489,f92102,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/sandbox2/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).
fof(f92102,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(unit_resulting_resolution,[],[f491,f490,f860]) ).
fof(f490,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rdn_positive_less23) ).
fof(f489,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/sandbox2/benchmark/theBenchmark.p',rdn_positive_less45) ).
fof(f508,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM325+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:38:19 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (13814)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (13824)WARNING: value z3 for option sas not known
% 0.15/0.40 % (13825)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40 % (13823)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.40 % (13826)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)
% 0.15/0.40 % (13822)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.40 % (13827)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)
% 0.15/0.40 % (13824)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)
% 0.15/0.40 % (13828)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)
% 0.22/0.43 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.48 TRYING [1]
% 0.22/0.49 TRYING [2]
% 0.22/0.49 TRYING [3]
% 0.22/0.57 TRYING [3]
% 1.96/0.65 TRYING [4]
% 2.38/0.75 TRYING [4]
% 7.18/1.41 TRYING [5]
% 7.84/1.51 TRYING [1]
% 8.09/1.51 TRYING [2]
% 8.23/1.54 TRYING [3]
% 8.83/1.67 TRYING [4]
% 9.41/1.72 TRYING [5]
% 11.39/1.99 % (13828)First to succeed.
% 11.39/1.99 % (13828)Refutation found. Thanks to Tanya!
% 11.39/1.99 % SZS status Theorem for theBenchmark
% 11.39/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 11.39/1.99 % (13828)------------------------------
% 11.39/1.99 % (13828)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 11.39/1.99 % (13828)Termination reason: Refutation
% 11.39/1.99
% 11.39/1.99 % (13828)Memory used [KB]: 39911
% 11.39/1.99 % (13828)Time elapsed: 1.591 s
% 11.39/1.99 % (13828)Instructions burned: 4998 (million)
% 11.39/1.99 % (13828)------------------------------
% 11.39/1.99 % (13828)------------------------------
% 11.39/1.99 % (13814)Success in time 1.615 s
%------------------------------------------------------------------------------