TSTP Solution File: FLD026-3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : FLD026-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n002.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 : Wed Aug 30 22:37:37 EDT 2023
% Result : Unsatisfiable 43.69s 6.67s
% Output : Refutation 43.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 82 ( 20 unt; 0 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 200 ( 108 ~; 87 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 156 (; 156 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f457351,plain,
$false,
inference(resolution,[],[f457350,f28]) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',b_is_defined) ).
fof(f457350,plain,
~ defined(b),
inference(duplicate_literal_removal,[],[f457335]) ).
fof(f457335,plain,
( ~ defined(b)
| ~ defined(b) ),
inference(resolution,[],[f457314,f437641]) ).
fof(f437641,plain,
( ~ product(multiplicative_inverse(b),a,multiplicative_identity)
| ~ defined(b) ),
inference(resolution,[],[f437402,f9020]) ).
fof(f9020,plain,
( product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b))
| ~ defined(b) ),
inference(resolution,[],[f8991,f8]) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',existence_of_identity_multiplication) ).
fof(f8991,plain,
( defined(multiplicative_inverse(b))
| ~ defined(b) ),
inference(resolution,[],[f8943,f18]) ).
fof(f18,axiom,
! [X0] :
( ~ defined(X0)
| defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',well_definedness_of_multiplicative_inverse) ).
fof(f8943,plain,
~ sum(additive_identity,b,additive_identity),
inference(resolution,[],[f8940,f4001]) ).
fof(f4001,plain,
! [X0] :
( ~ sum(b,X0,a)
| ~ sum(X0,b,additive_identity) ),
inference(resolution,[],[f3989,f5]) ).
fof(f5,axiom,
! [X3,X0,X5] :
( ~ sum(X0,X3,X5)
| sum(X3,X0,X5) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',commutativity_addition) ).
fof(f3989,plain,
! [X0] :
( ~ sum(X0,b,a)
| ~ sum(X0,b,additive_identity) ),
inference(resolution,[],[f3983,f5]) ).
fof(f3983,plain,
! [X0] :
( ~ sum(b,X0,additive_identity)
| ~ sum(X0,b,a) ),
inference(resolution,[],[f3981,f5]) ).
fof(f3981,plain,
! [X0] :
( ~ sum(b,X0,a)
| ~ sum(b,X0,additive_identity) ),
inference(resolution,[],[f180,f118]) ).
fof(f118,plain,
! [X0,X1] :
( sP3(X0,additive_identity,X1,a)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[],[f29,f38]) ).
fof(f38,plain,
! [X2,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| sum(X0,X1,X2)
| sP3(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f38_D]) ).
fof(f38_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ sum(X4,X5,X2)
| sum(X0,X1,X2) )
<=> ~ sP3(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP3])]) ).
fof(f29,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',not_sum_3) ).
fof(f180,plain,
! [X4,X5] :
( ~ sP3(b,additive_identity,X4,X5)
| ~ sum(b,X4,X5) ),
inference(resolution,[],[f66,f39]) ).
fof(f39,plain,
! [X3,X0,X1,X4,X5] :
( ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| ~ sP3(X4,X0,X5,X1) ),
inference(general_splitting,[],[f1,f38_D]) ).
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/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',associativity_addition_1) ).
fof(f66,plain,
sum(additive_identity,b,b),
inference(resolution,[],[f28,f3]) ).
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',existence_of_identity_addition) ).
fof(f8940,plain,
sum(b,additive_identity,a),
inference(resolution,[],[f8934,f14]) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',well_definedness_of_additive_identity) ).
fof(f8934,plain,
( ~ defined(additive_identity)
| sum(b,additive_identity,a) ),
inference(resolution,[],[f8884,f8]) ).
fof(f8884,plain,
! [X0] :
( ~ product(multiplicative_identity,additive_identity,X0)
| sum(b,X0,a) ),
inference(resolution,[],[f8878,f10]) ).
fof(f10,axiom,
! [X3,X0,X5] :
( ~ product(X0,X3,X5)
| product(X3,X0,X5) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',commutativity_multiplication) ).
fof(f8878,plain,
! [X0] :
( ~ product(additive_identity,multiplicative_identity,X0)
| sum(b,X0,a) ),
inference(resolution,[],[f8784,f242]) ).
fof(f242,plain,
! [X14,X15] :
( sP5(a,a,X14,X15)
| ~ product(additive_identity,X14,X15) ),
inference(resolution,[],[f151,f42]) ).
fof(f42,plain,
! [X3,X0,X9,X7,X5] :
( ~ product(X3,X5,X7)
| ~ sum(X0,X3,X9)
| sP5(X9,X0,X5,X7) ),
inference(cnf_transformation,[],[f42_D]) ).
fof(f42_D,plain,
! [X7,X5,X0,X9] :
( ! [X3] :
( ~ product(X3,X5,X7)
| ~ sum(X0,X3,X9) )
<=> ~ sP5(X9,X0,X5,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f151,plain,
sum(a,additive_identity,a),
inference(resolution,[],[f50,f5]) ).
fof(f50,plain,
sum(additive_identity,a,a),
inference(resolution,[],[f27,f3]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',a_is_defined) ).
fof(f8784,plain,
! [X0] :
( ~ sP5(a,a,multiplicative_identity,X0)
| sum(b,X0,a) ),
inference(resolution,[],[f147,f255]) ).
fof(f255,plain,
! [X16,X17] :
( ~ sP6(multiplicative_identity,a,X16,X17)
| sum(X16,X17,a) ),
inference(resolution,[],[f163,f45]) ).
fof(f45,plain,
! [X8,X6,X9,X7,X5] :
( ~ product(X9,X5,X8)
| sum(X6,X7,X8)
| ~ sP6(X5,X9,X6,X7) ),
inference(general_splitting,[],[f43,f44_D]) ).
fof(f44,plain,
! [X0,X6,X9,X7,X5] :
( ~ product(X0,X5,X6)
| ~ sP5(X9,X0,X5,X7)
| sP6(X5,X9,X6,X7) ),
inference(cnf_transformation,[],[f44_D]) ).
fof(f44_D,plain,
! [X7,X6,X9,X5] :
( ! [X0] :
( ~ product(X0,X5,X6)
| ~ sP5(X9,X0,X5,X7) )
<=> ~ sP6(X5,X9,X6,X7) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).
fof(f43,plain,
! [X0,X8,X6,X9,X7,X5] :
( ~ product(X0,X5,X6)
| ~ product(X9,X5,X8)
| sum(X6,X7,X8)
| ~ sP5(X9,X0,X5,X7) ),
inference(general_splitting,[],[f11,f42_D]) ).
fof(f11,axiom,
! [X3,X0,X8,X6,X9,X7,X5] :
( ~ product(X3,X5,X7)
| ~ product(X0,X5,X6)
| ~ product(X9,X5,X8)
| ~ sum(X0,X3,X9)
| sum(X6,X7,X8) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',distributivity_1) ).
fof(f163,plain,
product(a,multiplicative_identity,a),
inference(resolution,[],[f52,f10]) ).
fof(f52,plain,
product(multiplicative_identity,a,a),
inference(resolution,[],[f27,f8]) ).
fof(f147,plain,
! [X14,X15] :
( sP6(multiplicative_identity,X14,b,X15)
| ~ sP5(X14,a,multiplicative_identity,X15) ),
inference(resolution,[],[f121,f44]) ).
fof(f121,plain,
product(a,multiplicative_identity,b),
inference(resolution,[],[f30,f10]) ).
fof(f30,axiom,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',product_4) ).
fof(f437402,plain,
! [X0] :
( ~ product(multiplicative_identity,X0,multiplicative_inverse(b))
| ~ product(X0,a,multiplicative_identity) ),
inference(resolution,[],[f437230,f10]) ).
fof(f437230,plain,
! [X7] :
( ~ product(a,X7,multiplicative_identity)
| ~ product(multiplicative_identity,X7,multiplicative_inverse(b)) ),
inference(resolution,[],[f437222,f388]) ).
fof(f388,plain,
! [X0,X1] :
( sP1(X0,multiplicative_inverse(a),X1,multiplicative_identity)
| ~ product(X0,X1,multiplicative_inverse(b)) ),
inference(resolution,[],[f379,f34]) ).
fof(f34,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| product(X0,X1,X2)
| sP1(X4,X0,X5,X1) ),
inference(cnf_transformation,[],[f34_D]) ).
fof(f34_D,plain,
! [X1,X5,X0,X4] :
( ! [X2] :
( ~ product(X4,X5,X2)
| product(X0,X1,X2) )
<=> ~ sP1(X4,X0,X5,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f379,plain,
~ product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b)),
inference(resolution,[],[f31,f10]) ).
fof(f31,axiom,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',not_product_5) ).
fof(f437222,plain,
! [X0,X1] :
( ~ sP1(multiplicative_identity,multiplicative_inverse(a),X0,X1)
| ~ product(a,X0,X1) ),
inference(resolution,[],[f670,f27]) ).
fof(f670,plain,
! [X2,X3] :
( ~ defined(a)
| ~ product(a,X2,X3)
| ~ sP1(multiplicative_identity,multiplicative_inverse(a),X2,X3) ),
inference(resolution,[],[f114,f35]) ).
fof(f35,plain,
! [X3,X0,X1,X4,X5] :
( ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ sP1(X4,X0,X5,X1) ),
inference(general_splitting,[],[f6,f34_D]) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',associativity_multiplication_1) ).
fof(f114,plain,
( product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ defined(a) ),
inference(resolution,[],[f29,f9]) ).
fof(f9,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',existence_of_inverse_multiplication) ).
fof(f457314,plain,
( product(multiplicative_inverse(b),a,multiplicative_identity)
| ~ defined(b) ),
inference(resolution,[],[f457188,f8990]) ).
fof(f8990,plain,
( product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(b) ),
inference(resolution,[],[f8943,f9]) ).
fof(f457188,plain,
! [X3] :
( ~ product(X3,b,multiplicative_identity)
| product(X3,a,multiplicative_identity) ),
inference(resolution,[],[f456980,f3710]) ).
fof(f3710,plain,
! [X4,X5] :
( ~ sP1(X5,X4,multiplicative_identity,a)
| ~ product(X4,b,X5) ),
inference(resolution,[],[f3693,f35]) ).
fof(f3693,plain,
product(b,multiplicative_identity,a),
inference(resolution,[],[f3685,f10]) ).
fof(f3685,plain,
product(multiplicative_identity,b,a),
inference(resolution,[],[f3671,f163]) ).
fof(f3671,plain,
! [X0] :
( ~ product(a,X0,a)
| product(X0,b,a) ),
inference(resolution,[],[f3670,f10]) ).
fof(f3670,plain,
! [X3] :
( product(b,X3,a)
| ~ product(a,X3,a) ),
inference(resolution,[],[f168,f127]) ).
fof(f127,plain,
! [X8,X9] :
( ~ sP2(X8,b,multiplicative_identity,X9)
| ~ product(a,X8,X9) ),
inference(resolution,[],[f30,f37]) ).
fof(f37,plain,
! [X3,X0,X1,X4,X5] :
( ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ sP2(X5,X4,X0,X1) ),
inference(general_splitting,[],[f7,f36_D]) ).
fof(f36,plain,
! [X2,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| product(X4,X5,X2)
| sP2(X5,X4,X0,X1) ),
inference(cnf_transformation,[],[f36_D]) ).
fof(f36_D,plain,
! [X1,X0,X4,X5] :
( ! [X2] :
( ~ product(X0,X1,X2)
| product(X4,X5,X2) )
<=> ~ sP2(X5,X4,X0,X1) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X4,X5,X2) ),
file('/export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374',associativity_multiplication_2) ).
fof(f168,plain,
! [X6,X7] :
( sP2(X7,X6,multiplicative_identity,a)
| product(X6,X7,a) ),
inference(resolution,[],[f52,f36]) ).
fof(f456980,plain,
! [X0,X1] :
( sP1(multiplicative_identity,X0,multiplicative_identity,X1)
| product(X0,X1,multiplicative_identity) ),
inference(resolution,[],[f456879,f34]) ).
fof(f456879,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(resolution,[],[f456860,f163]) ).
fof(f456860,plain,
! [X0] :
( ~ product(a,X0,a)
| product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[],[f454931,f445635]) ).
fof(f445635,plain,
! [X0,X1] :
( sP2(X1,X0,multiplicative_inverse(a),a)
| product(X0,X1,multiplicative_identity) ),
inference(resolution,[],[f672,f27]) ).
fof(f672,plain,
! [X6,X7] :
( ~ defined(a)
| product(X6,X7,multiplicative_identity)
| sP2(X7,X6,multiplicative_inverse(a),a) ),
inference(resolution,[],[f114,f36]) ).
fof(f454931,plain,
! [X0,X1] :
( ~ sP2(X0,multiplicative_identity,multiplicative_inverse(a),X1)
| ~ product(a,X0,X1) ),
inference(resolution,[],[f673,f27]) ).
fof(f673,plain,
! [X8,X9] :
( ~ defined(a)
| ~ product(a,X8,X9)
| ~ sP2(X8,multiplicative_identity,multiplicative_inverse(a),X9) ),
inference(resolution,[],[f114,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : FLD026-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.12 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 01:03:34 EDT 2023
% 0.18/0.33 % CPUTime :
% 0.18/0.33 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.18/0.34 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.zoFKzuVf7z/Vampire---4.8_17374
% 0.18/0.34 % (17484)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.39 % (17487)lrs+11_4:3_aac=none:add=off:amm=off:anc=none:bd=preordered:bs=on:bce=on:flr=on:fsd=off:fsr=off:fde=none:nwc=2.5:sims=off:sp=reverse_arity:tgt=full:stl=188_1106 on Vampire---4 for (1106ds/0Mi)
% 0.18/0.39 % (17488)dis-1_128_add=large:amm=sco:anc=all_dependent:bs=on:bsr=on:bce=on:cond=fast:fsr=off:gsp=on:gs=on:gsem=off:lcm=predicate:lma=on:nm=32:nwc=4.0:nicw=on:sac=on:sp=weighted_frequency_692 on Vampire---4 for (692ds/0Mi)
% 0.18/0.39 % (17485)lrs-1_7_acc=on:amm=off:anc=all:bs=on:bsr=on:cond=fast:flr=on:fsr=off:gsp=on:lcm=reverse:lma=on:msp=off:nm=0:nwc=1.2:sp=frequency:stl=188_1354 on Vampire---4 for (1354ds/0Mi)
% 0.18/0.39 % (17491)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.18/0.39 % (17489)ott-1010_5_add=off:amm=off:anc=none:bce=on:cond=fast:flr=on:lma=on:nm=2:nwc=1.1:sp=occurrence:tgt=ground_470 on Vampire---4 for (470ds/0Mi)
% 0.18/0.39 % (17490)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_415 on Vampire---4 for (415ds/0Mi)
% 0.18/0.39 % (17486)dis-1002_1_av=off:bsr=on:cond=on:flr=on:fsr=off:gsp=on:nwc=2.0:sims=off_1218 on Vampire---4 for (1218ds/0Mi)
% 43.69/6.66 % (17491)First to succeed.
% 43.69/6.67 % (17491)Refutation found. Thanks to Tanya!
% 43.69/6.67 % SZS status Unsatisfiable for Vampire---4
% 43.69/6.67 % SZS output start Proof for Vampire---4
% See solution above
% 43.69/6.67 % (17491)------------------------------
% 43.69/6.67 % (17491)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 43.69/6.67 % (17491)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 43.69/6.67 % (17491)Termination reason: Refutation
% 43.69/6.67
% 43.69/6.67 % (17491)Memory used [KB]: 52707
% 43.69/6.67 % (17491)Time elapsed: 6.267 s
% 43.69/6.67 % (17491)------------------------------
% 43.69/6.67 % (17491)------------------------------
% 43.69/6.67 % (17484)Success in time 6.314 s
% 43.69/6.67 % Vampire---4.8 exiting
%------------------------------------------------------------------------------