TSTP Solution File: FLD026-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD026-3 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.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 : Mon May 20 19:56:24 EDT 2024
% Result : Unsatisfiable 14.58s 2.44s
% Output : Refutation 14.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 81 ( 13 unt; 0 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 241 ( 113 ~; 124 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70671,plain,
$false,
inference(avatar_sat_refutation,[],[f7591,f9826,f10192,f70600,f70662]) ).
fof(f70662,plain,
( spl0_30
| ~ spl0_6710 ),
inference(avatar_contradiction_clause,[],[f70661]) ).
fof(f70661,plain,
( $false
| spl0_30
| ~ spl0_6710 ),
inference(subsumption_resolution,[],[f70626,f392]) ).
fof(f392,plain,
( ~ sum(additive_identity,multiplicative_identity,additive_identity)
| spl0_30 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f391,plain,
( spl0_30
<=> sum(additive_identity,multiplicative_identity,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f70626,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ spl0_6710 ),
inference(resolution,[],[f70578,f1327]) ).
fof(f1327,plain,
! [X0] :
( ~ sum(multiplicative_identity,X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f415,f17]) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f415,plain,
! [X0,X1] :
( ~ defined(X0)
| sum(additive_identity,X1,additive_identity)
| ~ sum(X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f409,plain,
! [X0,X1] :
( ~ sum(X0,X1,X0)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[],[f130,f4]) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( ~ sum(additive_inverse(X0),X2,X3)
| ~ sum(X0,X1,X2)
| sum(additive_identity,X1,X3)
| ~ defined(X0) ),
inference(resolution,[],[f2,f4]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X1,X2)
| sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f70578,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ spl0_6710 ),
inference(avatar_component_clause,[],[f70576]) ).
fof(f70576,plain,
( spl0_6710
<=> sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6710])]) ).
fof(f70600,plain,
( spl0_6710
| ~ spl0_927 ),
inference(avatar_split_clause,[],[f70599,f9800,f70576]) ).
fof(f9800,plain,
( spl0_927
<=> sum(additive_identity,additive_identity,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f70599,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ spl0_927 ),
inference(subsumption_resolution,[],[f70598,f16872]) ).
fof(f16872,plain,
( sum(b,a,a)
| ~ spl0_927 ),
inference(resolution,[],[f16829,f5]) ).
fof(f5,axiom,
! [X3,X0,X5] :
( ~ sum(X0,X3,X5)
| sum(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f16829,plain,
( sum(a,b,a)
| ~ spl0_927 ),
inference(subsumption_resolution,[],[f16825,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f16825,plain,
( sum(a,b,a)
| ~ defined(a)
| ~ spl0_927 ),
inference(duplicate_literal_removal,[],[f16817]) ).
fof(f16817,plain,
( sum(a,b,a)
| ~ defined(a)
| ~ defined(a)
| ~ spl0_927 ),
inference(resolution,[],[f13746,f347]) ).
fof(f347,plain,
! [X2,X0,X1] :
( ~ sum(additive_inverse(X0),X1,X2)
| sum(X0,X2,X1)
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[],[f113,f33]) ).
fof(f33,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f5,f4]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( ~ sum(X3,X0,additive_identity)
| ~ sum(X0,X1,X2)
| sum(X3,X2,X1)
| ~ defined(X1) ),
inference(resolution,[],[f1,f3]) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f13746,plain,
( sum(additive_inverse(a),a,b)
| ~ spl0_927 ),
inference(resolution,[],[f10477,f5]) ).
fof(f10477,plain,
( sum(a,additive_inverse(a),b)
| ~ spl0_927 ),
inference(resolution,[],[f9802,f1551]) ).
fof(f1551,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(a,additive_inverse(a),X0) ),
inference(subsumption_resolution,[],[f1548,f27]) ).
fof(f1548,plain,
! [X0] :
( sum(a,additive_inverse(a),X0)
| ~ sum(additive_identity,additive_identity,X0)
| ~ defined(a) ),
inference(resolution,[],[f365,f33]) ).
fof(f365,plain,
! [X2,X0,X1] :
( ~ sum(a,X2,X0)
| sum(a,X2,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[],[f128,f27]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ defined(X0)
| ~ sum(additive_identity,X2,X3)
| sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[],[f2,f3]) ).
fof(f9802,plain,
( sum(additive_identity,additive_identity,b)
| ~ spl0_927 ),
inference(avatar_component_clause,[],[f9800]) ).
fof(f70598,plain,
( ~ sum(b,a,a)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(subsumption_resolution,[],[f70597,f27]) ).
fof(f70597,plain,
( ~ defined(a)
| ~ sum(b,a,a)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(subsumption_resolution,[],[f70561,f29]) ).
fof(f29,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f70561,plain,
( sum(additive_identity,a,additive_identity)
| ~ defined(a)
| ~ sum(b,a,a)
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(resolution,[],[f6829,f964]) ).
fof(f964,plain,
product(b,multiplicative_inverse(a),multiplicative_identity),
inference(subsumption_resolution,[],[f958,f17]) ).
fof(f958,plain,
( product(b,multiplicative_inverse(a),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[],[f325,f8]) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f325,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| product(b,multiplicative_inverse(a),X0) ),
inference(subsumption_resolution,[],[f324,f29]) ).
fof(f324,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| product(b,multiplicative_inverse(a),X0)
| sum(additive_identity,a,additive_identity) ),
inference(subsumption_resolution,[],[f320,f27]) ).
fof(f320,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| product(b,multiplicative_inverse(a),X0)
| ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[],[f151,f54]) ).
fof(f54,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f9,f10]) ).
fof(f10,axiom,
! [X3,X0,X5] :
( ~ product(X0,X3,X5)
| product(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ product(a,X0,X1)
| ~ product(multiplicative_identity,X1,X2)
| product(b,X0,X2) ),
inference(resolution,[],[f7,f30]) ).
fof(f30,axiom,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X0,X1,X2)
| product(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
fof(f6829,plain,
! [X2,X0,X1] :
( ~ product(X1,multiplicative_inverse(X0),X2)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| ~ sum(X1,X0,X0)
| sum(X2,multiplicative_identity,multiplicative_identity) ),
inference(duplicate_literal_removal,[],[f6822]) ).
fof(f6822,plain,
! [X2,X0,X1] :
( sum(additive_identity,X0,additive_identity)
| ~ product(X1,multiplicative_inverse(X0),X2)
| ~ defined(X0)
| ~ sum(X1,X0,X0)
| sum(X2,multiplicative_identity,multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f296,f54]) ).
fof(f296,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X3,multiplicative_inverse(X0),X4)
| sum(additive_identity,X0,additive_identity)
| ~ product(X1,multiplicative_inverse(X0),X2)
| ~ defined(X0)
| ~ sum(X1,X3,X0)
| sum(X2,X4,multiplicative_identity) ),
inference(resolution,[],[f54,f11]) ).
fof(f11,axiom,
! [X3,X0,X8,X6,X9,X7,X5] :
( ~ product(X9,X5,X8)
| ~ product(X0,X5,X6)
| ~ product(X3,X5,X7)
| ~ sum(X0,X3,X9)
| sum(X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
fof(f10192,plain,
( spl0_927
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f10182,f250,f9800]) ).
fof(f250,plain,
( spl0_23
<=> sum(additive_identity,b,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f10182,plain,
( sum(additive_identity,additive_identity,b)
| ~ spl0_23 ),
inference(resolution,[],[f252,f1286]) ).
fof(f1286,plain,
! [X0] :
( ~ sum(additive_identity,b,X0)
| sum(additive_identity,X0,b) ),
inference(resolution,[],[f348,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f348,plain,
! [X0,X1] :
( ~ defined(X0)
| sum(additive_identity,X1,X0)
| ~ sum(additive_identity,X0,X1) ),
inference(subsumption_resolution,[],[f343,f14]) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f343,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ defined(additive_identity) ),
inference(resolution,[],[f113,f3]) ).
fof(f252,plain,
( sum(additive_identity,b,additive_identity)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f9826,plain,
spl0_23,
inference(avatar_split_clause,[],[f9825,f250]) ).
fof(f9825,plain,
sum(additive_identity,b,additive_identity),
inference(subsumption_resolution,[],[f9824,f28]) ).
fof(f9824,plain,
( sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(subsumption_resolution,[],[f3636,f31]) ).
fof(f31,axiom,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_5) ).
fof(f3636,plain,
( product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(resolution,[],[f864,f964]) ).
fof(f864,plain,
! [X0,X1] :
( ~ product(X0,X1,multiplicative_identity)
| product(multiplicative_identity,X1,multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f859,f18]) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| defined(multiplicative_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f859,plain,
! [X0,X1] :
( ~ product(X0,X1,multiplicative_identity)
| product(multiplicative_identity,X1,multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| ~ defined(multiplicative_inverse(X0)) ),
inference(resolution,[],[f153,f36]) ).
fof(f36,plain,
! [X0] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f10,f8]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ product(multiplicative_inverse(X0),X2,X3)
| ~ product(X0,X1,X2)
| product(multiplicative_identity,X1,X3)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f7,f9]) ).
fof(f7591,plain,
~ spl0_30,
inference(avatar_contradiction_clause,[],[f7590]) ).
fof(f7590,plain,
( $false
| ~ spl0_30 ),
inference(subsumption_resolution,[],[f7583,f26]) ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
fof(f7583,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ spl0_30 ),
inference(resolution,[],[f1281,f393]) ).
fof(f393,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f1281,plain,
! [X0] :
( ~ sum(additive_identity,multiplicative_identity,X0)
| sum(additive_identity,X0,multiplicative_identity) ),
inference(resolution,[],[f348,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : FLD026-3 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat May 18 21:49:53 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % (29288)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (29290)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 % (29293)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.34 % (29289)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.34 % (29294)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.34 % (29292)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 % (29295)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.34 TRYING [2]
% 0.11/0.34 % (29291)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [1]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [4]
% 0.11/0.35 TRYING [4]
% 0.11/0.36 TRYING [4]
% 0.11/0.36 TRYING [4]
% 0.11/0.37 TRYING [5]
% 0.11/0.38 TRYING [5]
% 0.11/0.38 TRYING [5]
% 0.16/0.39 TRYING [5]
% 0.16/0.43 TRYING [6]
% 0.16/0.43 TRYING [6]
% 0.16/0.45 TRYING [6]
% 0.16/0.50 TRYING [6]
% 1.52/0.61 TRYING [7]
% 1.52/0.63 TRYING [7]
% 2.19/0.64 TRYING [7]
% 3.37/0.83 TRYING [7]
% 4.74/1.00 TRYING [8]
% 4.74/1.02 TRYING [8]
% 4.74/1.04 TRYING [8]
% 8.52/1.57 TRYING [8]
% 10.05/1.81 TRYING [9]
% 10.52/1.85 TRYING [9]
% 10.84/1.89 TRYING [9]
% 14.58/2.43 % (29294)First to succeed.
% 14.58/2.44 % (29294)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29288"
% 14.58/2.44 % (29294)Refutation found. Thanks to Tanya!
% 14.58/2.44 % SZS status Unsatisfiable for theBenchmark
% 14.58/2.44 % SZS output start Proof for theBenchmark
% See solution above
% 14.58/2.44 % (29294)------------------------------
% 14.58/2.44 % (29294)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 14.58/2.44 % (29294)Termination reason: Refutation
% 14.58/2.44
% 14.58/2.44 % (29294)Memory used [KB]: 22599
% 14.58/2.44 % (29294)Time elapsed: 2.099 s
% 14.58/2.44 % (29294)Instructions burned: 4191 (million)
% 14.58/2.44 % (29288)Success in time 2.11 s
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